-/* Start: bn_fast_mp_invmod.c */
+/* Start: bn_error.c */
+#include <tommath.h>
+#ifdef BN_ERROR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
+
+static const struct {
+ int code;
+ char *msg;
+} msgs[] = {
+ { MP_OKAY, "Successful" },
+ { MP_MEM, "Out of heap" },
+ { MP_VAL, "Value out of range" }
+};
+
+/* return a char * string for a given code */
+char *mp_error_to_string(int code)
+{
+ int x;
+
+ /* scan the lookup table for the given message */
+ for (x = 0; x < (int)(sizeof(msgs) / sizeof(msgs[0])); x++) {
+ if (msgs[x].code == code) {
+ return msgs[x].msg;
+ }
+ }
+
+ /* generic reply for invalid code */
+ return "Invalid error code";
+}
+
+#endif
+
+/* End: bn_error.c */
+
+/* Start: bn_fast_mp_invmod.c */
#include <tommath.h>
+#ifdef BN_FAST_MP_INVMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
/* computes the modular inverse via binary extended euclidean algorithm,
* that is c = 1/a mod b
*
- * Based on mp_invmod except this is optimized for the case where b is
+ * Based on slow invmod except this is optimized for the case where b is
* odd as per HAC Note 14.64 on pp. 610
*/
-int
-fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
+int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
mp_int x, y, u, v, B, D;
int res, neg;
+ /* 2. [modified] b must be odd */
+ if (mp_iseven (b) == 1) {
+ return MP_VAL;
+ }
+
/* init all our temps */
if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
return res;
/* x == modulus, y == value to invert */
if ((res = mp_copy (b, &x)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
/* we need y = |a| */
- if ((res = mp_abs (a, &y)) != MP_OKAY) {
- goto __ERR;
- }
-
- /* 2. [modified] if x,y are both even then return an error!
- *
- * That is if gcd(x,y) = 2 * k then obviously there is no inverse.
- */
- if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
- res = MP_VAL;
- goto __ERR;
+ if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
+ goto LBL_ERR;
}
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
if ((res = mp_copy (&x, &u)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
if ((res = mp_copy (&y, &v)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
mp_set (&D, 1);
while (mp_iseven (&u) == 1) {
/* 4.1 u = u/2 */
if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
- /* 4.2 if A or B is odd then */
- if (mp_iseven (&B) == 0) {
+ /* 4.2 if B is odd then */
+ if (mp_isodd (&B) == 1) {
if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
}
/* B = B/2 */
if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
}
while (mp_iseven (&v) == 1) {
/* 5.1 v = v/2 */
if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
- /* 5.2 if C,D are even then */
- if (mp_iseven (&D) == 0) {
+ /* 5.2 if D is odd then */
+ if (mp_isodd (&D) == 1) {
/* D = (D-x)/2 */
if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
}
/* D = D/2 */
if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
}
if (mp_cmp (&u, &v) != MP_LT) {
/* u = u - v, B = B - D */
if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
} else {
/* v - v - u, D = D - B */
if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
}
/* if v != 1 then there is no inverse */
if (mp_cmp_d (&v, 1) != MP_EQ) {
res = MP_VAL;
- goto __ERR;
+ goto LBL_ERR;
}
/* b is now the inverse */
neg = a->sign;
while (D.sign == MP_NEG) {
if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
}
mp_exch (&D, c);
c->sign = neg;
res = MP_OKAY;
-__ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
+LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
return res;
}
+#endif
/* End: bn_fast_mp_invmod.c */
/* Start: bn_fast_mp_montgomery_reduce.c */
+#include <tommath.h>
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* computes xR**-1 == x (mod N) via Montgomery Reduction
- *
- * This is an optimized implementation of mp_montgomery_reduce
+/* computes xR**-1 == x (mod N) via Montgomery Reduction
+ *
+ * This is an optimized implementation of montgomery_reduce
* which uses the comba method to quickly calculate the columns of the
- * reduction.
+ * reduction.
*
* Based on Algorithm 14.32 on pp.601 of HAC.
*/
-int
-fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
+int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
{
int ix, res, olduse;
mp_word W[MP_WARRAY];
}
}
+ /* first we have to get the digits of the input into
+ * an array of double precision words W[...]
+ */
{
register mp_word *_W;
register mp_digit *tmpx;
- _W = W;
+ /* alias for the W[] array */
+ _W = W;
+
+ /* alias for the digits of x*/
tmpx = x->dp;
/* copy the digits of a into W[0..a->used-1] */
}
}
+ /* now we proceed to zero successive digits
+ * from the least significant upwards
+ */
for (ix = 0; ix < n->used; ix++) {
/* mu = ai * m' mod b
*
* We avoid a double precision multiplication (which isn't required)
- * by casting the value down to a mp_digit. Note this requires
+ * by casting the value down to a mp_digit. Note this requires
* that W[ix-1] have the carry cleared (see after the inner loop)
*/
register mp_digit mu;
- mu = (((mp_digit) (W[ix] & MP_MASK)) * rho) & MP_MASK;
+ mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
/* a = a + mu * m * b**i
*
* by b**i is handled by offseting which columns the results
* are added to.
*
- * Note the comba method normally doesn't handle carries in the
- * inner loop In this case we fix the carry from the previous
- * column since the Montgomery reduction requires digits of the
+ * Note the comba method normally doesn't handle carries in the
+ * inner loop In this case we fix the carry from the previous
+ * column since the Montgomery reduction requires digits of the
* result (so far) [see above] to work. This is
- * handled by fixing up one carry after the inner loop. The
- * carry fixups are done in order so after these loops the
+ * handled by fixing up one carry after the inner loop. The
+ * carry fixups are done in order so after these loops the
* first m->used words of W[] have the carries fixed
*/
{
/* inner loop */
for (iy = 0; iy < n->used; iy++) {
- *_W++ += ((mp_word) mu) * ((mp_word) * tmpn++);
+ *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
}
}
W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
}
-
+ /* now we have to propagate the carries and
+ * shift the words downward [all those least
+ * significant digits we zeroed].
+ */
{
register mp_digit *tmpx;
register mp_word *_W, *_W1;
/* nox fix rest of carries */
+
+ /* alias for current word */
_W1 = W + ix;
+
+ /* alias for next word, where the carry goes */
_W = W + ++ix;
for (; ix <= n->used * 2 + 1; ix++) {
/* copy out, A = A/b**n
*
- * The result is A/b**n but instead of converting from an
- * array of mp_word to mp_digit than calling mp_rshd
+ * The result is A/b**n but instead of converting from an
+ * array of mp_word to mp_digit than calling mp_rshd
* we just copy them in the right order
*/
+
+ /* alias for destination word */
tmpx = x->dp;
+
+ /* alias for shifted double precision result */
_W = W + n->used;
for (ix = 0; ix < n->used + 1; ix++) {
}
/* zero oldused digits, if the input a was larger than
- * m->used+1 we'll have to clear the digits */
+ * m->used+1 we'll have to clear the digits
+ */
for (; ix < olduse; ix++) {
*tmpx++ = 0;
}
}
return MP_OKAY;
}
+#endif
/* End: bn_fast_mp_montgomery_reduce.c */
/* Start: bn_fast_s_mp_mul_digs.c */
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Fast (comba) multiplier
*
* Based on Algorithm 14.12 on pp.595 of HAC.
*
*/
-int
-fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
- int olduse, res, pa, ix;
- mp_word W[MP_WARRAY];
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY];
+ register mp_word _W;
/* grow the destination as required */
if (c->alloc < digs) {
}
}
- /* clear temp buf (the columns) */
- memset (W, 0, sizeof (mp_word) * digs);
-
- /* calculate the columns */
- pa = a->used;
- for (ix = 0; ix < pa; ix++) {
- /* this multiplier has been modified to allow you to
- * control how many digits of output are produced.
- * So at most we want to make upto "digs" digits of output.
- *
- * this adds products to distinct columns (at ix+iy) of W
- * note that each step through the loop is not dependent on
- * the previous which means the compiler can easily unroll
- * the loop without scheduling problems
- */
- {
- register mp_digit tmpx, *tmpy;
- register mp_word *_W;
- register int iy, pb;
+ /* number of output digits to produce */
+ pa = MIN(digs, a->used + b->used);
- /* alias for the the word on the left e.g. A[ix] * A[iy] */
- tmpx = a->dp[ix];
+ /* clear the carry */
+ _W = 0;
+ for (ix = 0; ix < pa; ix++) {
+ int tx, ty;
+ int iy;
+ mp_digit *tmpx, *tmpy;
- /* alias for the right side */
- tmpy = b->dp;
+ /* get offsets into the two bignums */
+ ty = MIN(b->used-1, ix);
+ tx = ix - ty;
- /* alias for the columns, each step through the loop adds a new
- term to each column
- */
- _W = W + ix;
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = b->dp + ty;
- /* the number of digits is limited by their placement. E.g.
- we avoid multiplying digits that will end up above the # of
- digits of precision requested
+ /* this is the number of times the loop will iterrate, essentially
+ while (tx++ < a->used && ty-- >= 0) { ... }
*/
- pb = MIN (b->used, digs - ix);
+ iy = MIN(a->used-tx, ty+1);
- for (iy = 0; iy < pb; iy++) {
- *_W++ += ((mp_word) tmpx) * ((mp_word) * tmpy++);
+ /* execute loop */
+ for (iz = 0; iz < iy; ++iz) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
}
- }
+ /* store term */
+ W[ix] = ((mp_digit)_W) & MP_MASK;
+
+ /* make next carry */
+ _W = _W >> ((mp_word)DIGIT_BIT);
}
+ /* store final carry */
+ W[ix] = (mp_digit)(_W & MP_MASK);
+
/* setup dest */
- olduse = c->used;
- c->used = digs;
+ olduse = c->used;
+ c->used = pa;
{
register mp_digit *tmpc;
-
- /* At this point W[] contains the sums of each column. To get the
- * correct result we must take the extra bits from each column and
- * carry them down
- *
- * Note that while this adds extra code to the multiplier it
- * saves time since the carry propagation is removed from the
- * above nested loop.This has the effect of reducing the work
- * from N*(N+N*c)==N**2 + c*N**2 to N**2 + N*c where c is the
- * cost of the shifting. On very small numbers this is slower
- * but on most cryptographic size numbers it is faster.
- */
tmpc = c->dp;
- for (ix = 1; ix < digs; ix++) {
- W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
- *tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
+ for (ix = 0; ix < pa+1; ix++) {
+ /* now extract the previous digit [below the carry] */
+ *tmpc++ = W[ix];
}
- *tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK));
- /* clear unused */
+ /* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
*tmpc++ = 0;
}
}
-
mp_clamp (c);
return MP_OKAY;
}
+#endif
/* End: bn_fast_s_mp_mul_digs.c */
/* Start: bn_fast_s_mp_mul_high_digs.c */
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* this is a modified version of fast_s_mp_mul_digs that only produces
- * output digits *above* digs. See the comments for fast_s_mp_mul_digs
+/* this is a modified version of fast_s_mul_digs that only produces
+ * output digits *above* digs. See the comments for fast_s_mul_digs
* to see how it works.
*
* This is used in the Barrett reduction since for one of the multiplications
*
* Based on Algorithm 14.12 on pp.595 of HAC.
*/
-int
-fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
- int oldused, newused, res, pa, pb, ix;
- mp_word W[MP_WARRAY];
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY];
+ mp_word _W;
- /* calculate size of product and allocate more space if required */
- newused = a->used + b->used + 1;
- if (c->alloc < newused) {
- if ((res = mp_grow (c, newused)) != MP_OKAY) {
+ /* grow the destination as required */
+ pa = a->used + b->used;
+ if (c->alloc < pa) {
+ if ((res = mp_grow (c, pa)) != MP_OKAY) {
return res;
}
}
- /* like the other comba method we compute the columns first */
- pa = a->used;
- pb = b->used;
- memset (W + digs, 0, (pa + pb + 1 - digs) * sizeof (mp_word));
- for (ix = 0; ix < pa; ix++) {
- {
- register mp_digit tmpx, *tmpy;
- register int iy;
- register mp_word *_W;
+ /* number of output digits to produce */
+ pa = a->used + b->used;
+ _W = 0;
+ for (ix = digs; ix < pa; ix++) {
+ int tx, ty, iy;
+ mp_digit *tmpx, *tmpy;
- /* work todo, that is we only calculate digits that are at "digs" or above */
- iy = digs - ix;
+ /* get offsets into the two bignums */
+ ty = MIN(b->used-1, ix);
+ tx = ix - ty;
- /* copy of word on the left of A[ix] * B[iy] */
- tmpx = a->dp[ix];
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = b->dp + ty;
- /* alias for right side */
- tmpy = b->dp + iy;
-
- /* alias for the columns of output. Offset to be equal to or above the
- * smallest digit place requested
+ /* this is the number of times the loop will iterrate, essentially its
+ while (tx++ < a->used && ty-- >= 0) { ... }
*/
- _W = W + digs;
-
- /* skip cases below zero where ix > digs */
- if (iy < 0) {
- iy = abs(iy);
- tmpy += iy;
- _W += iy;
- iy = 0;
- }
+ iy = MIN(a->used-tx, ty+1);
- /* compute column products for digits above the minimum */
- for (; iy < pb; iy++) {
- *_W++ += ((mp_word) tmpx) * ((mp_word) * tmpy++);
+ /* execute loop */
+ for (iz = 0; iz < iy; iz++) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
}
- }
+
+ /* store term */
+ W[ix] = ((mp_digit)_W) & MP_MASK;
+
+ /* make next carry */
+ _W = _W >> ((mp_word)DIGIT_BIT);
}
+
+ /* store final carry */
+ W[ix] = (mp_digit)(_W & MP_MASK);
/* setup dest */
- oldused = c->used;
- c->used = newused;
+ olduse = c->used;
+ c->used = pa;
- /* now convert the array W downto what we need */
- for (ix = digs + 1; ix < newused; ix++) {
- W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
- c->dp[ix - 1] = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
- }
- c->dp[(pa + pb + 1) - 1] = (mp_digit) (W[(pa + pb + 1) - 1] & ((mp_word) MP_MASK));
+ {
+ register mp_digit *tmpc;
+
+ tmpc = c->dp + digs;
+ for (ix = digs; ix <= pa; ix++) {
+ /* now extract the previous digit [below the carry] */
+ *tmpc++ = W[ix];
+ }
- for (; ix < oldused; ix++) {
- c->dp[ix] = 0;
+ /* clear unused digits [that existed in the old copy of c] */
+ for (; ix < olduse; ix++) {
+ *tmpc++ = 0;
+ }
}
mp_clamp (c);
return MP_OKAY;
}
+#endif
/* End: bn_fast_s_mp_mul_high_digs.c */
/* Start: bn_fast_s_mp_sqr.c */
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* fast squaring
- *
- * This is the comba method where the columns of the product
- * are computed first then the carries are computed. This
- * has the effect of making a very simple inner loop that
- * is executed the most
- *
- * W2 represents the outer products and W the inner.
- *
- * A further optimizations is made because the inner
- * products are of the form "A * B * 2". The *2 part does
- * not need to be computed until the end which is good
- * because 64-bit shifts are slow!
- *
- * Based on Algorithm 14.16 on pp.597 of HAC.
- *
- */
-int
-fast_s_mp_sqr (mp_int * a, mp_int * b)
+/* the jist of squaring...
+ * you do like mult except the offset of the tmpx [one that
+ * starts closer to zero] can't equal the offset of tmpy.
+ * So basically you set up iy like before then you min it with
+ * (ty-tx) so that it never happens. You double all those
+ * you add in the inner loop
+
+After that loop you do the squares and add them in.
+*/
+
+int fast_s_mp_sqr (mp_int * a, mp_int * b)
{
- int olduse, newused, res, ix, pa;
- mp_word W2[MP_WARRAY], W[MP_WARRAY];
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY], *tmpx;
+ mp_word W1;
- /* calculate size of product and allocate as required */
- pa = a->used;
- newused = pa + pa + 1;
- if (b->alloc < newused) {
- if ((res = mp_grow (b, newused)) != MP_OKAY) {
+ /* grow the destination as required */
+ pa = a->used + a->used;
+ if (b->alloc < pa) {
+ if ((res = mp_grow (b, pa)) != MP_OKAY) {
return res;
}
}
- /* zero temp buffer (columns)
- * Note that there are two buffers. Since squaring requires
- * a outter and inner product and the inner product requires
- * computing a product and doubling it (a relatively expensive
- * op to perform n**2 times if you don't have to) the inner and
- * outer products are computed in different buffers. This way
- * the inner product can be doubled using n doublings instead of
- * n**2
- */
- memset (W, 0, newused * sizeof (mp_word));
- memset (W2, 0, newused * sizeof (mp_word));
+ /* number of output digits to produce */
+ W1 = 0;
+ for (ix = 0; ix < pa; ix++) {
+ int tx, ty, iy;
+ mp_word _W;
+ mp_digit *tmpy;
- /* This computes the inner product. To simplify the inner N**2 loop
- * the multiplication by two is done afterwards in the N loop.
- */
- for (ix = 0; ix < pa; ix++) {
- /* compute the outer product
- *
- * Note that every outer product is computed
- * for a particular column only once which means that
- * there is no need todo a double precision addition
- */
- W2[ix + ix] = ((mp_word) a->dp[ix]) * ((mp_word) a->dp[ix]);
+ /* clear counter */
+ _W = 0;
- {
- register mp_digit tmpx, *tmpy;
- register mp_word *_W;
- register int iy;
+ /* get offsets into the two bignums */
+ ty = MIN(a->used-1, ix);
+ tx = ix - ty;
+
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = a->dp + ty;
- /* copy of left side */
- tmpx = a->dp[ix];
+ /* this is the number of times the loop will iterrate, essentially
+ while (tx++ < a->used && ty-- >= 0) { ... }
+ */
+ iy = MIN(a->used-tx, ty+1);
+
+ /* now for squaring tx can never equal ty
+ * we halve the distance since they approach at a rate of 2x
+ * and we have to round because odd cases need to be executed
+ */
+ iy = MIN(iy, (ty-tx+1)>>1);
- /* alias for right side */
- tmpy = a->dp + (ix + 1);
+ /* execute loop */
+ for (iz = 0; iz < iy; iz++) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
+ }
- /* the column to store the result in */
- _W = W + (ix + ix + 1);
+ /* double the inner product and add carry */
+ _W = _W + _W + W1;
- /* inner products */
- for (iy = ix + 1; iy < pa; iy++) {
- *_W++ += ((mp_word) tmpx) * ((mp_word) * tmpy++);
+ /* even columns have the square term in them */
+ if ((ix&1) == 0) {
+ _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
}
- }
+
+ /* store it */
+ W[ix] = (mp_digit)(_W & MP_MASK);
+
+ /* make next carry */
+ W1 = _W >> ((mp_word)DIGIT_BIT);
}
/* setup dest */
olduse = b->used;
- b->used = newused;
+ b->used = a->used+a->used;
- /* now compute digits */
{
- register mp_digit *tmpb;
-
- /* double first value, since the inner products are
- * half of what they should be
- */
- W[0] += W[0] + W2[0];
-
+ mp_digit *tmpb;
tmpb = b->dp;
- for (ix = 1; ix < newused; ix++) {
- /* double/add next digit */
- W[ix] += W[ix] + W2[ix];
-
- W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT));
- *tmpb++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
+ for (ix = 0; ix < pa; ix++) {
+ *tmpb++ = W[ix] & MP_MASK;
}
- /* set the last value. Note even if the carry is zero
- * this is required since the next step will not zero
- * it if b originally had a value at b->dp[2*a.used]
- */
- *tmpb++ = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK));
- /* clear high digits */
+ /* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
*tmpb++ = 0;
}
}
-
mp_clamp (b);
return MP_OKAY;
}
+#endif
/* End: bn_fast_s_mp_sqr.c */
/* Start: bn_mp_2expt.c */
+#include <tommath.h>
+#ifdef BN_MP_2EXPT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes a = 2**b
*
{
int res;
+ /* zero a as per default */
mp_zero (a);
+
+ /* grow a to accomodate the single bit */
if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
return res;
}
+
+ /* set the used count of where the bit will go */
a->used = b / DIGIT_BIT + 1;
- a->dp[b / DIGIT_BIT] = 1 << (b % DIGIT_BIT);
+
+ /* put the single bit in its place */
+ a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
return MP_OKAY;
}
+#endif
/* End: bn_mp_2expt.c */
/* Start: bn_mp_abs.c */
+#include <tommath.h>
+#ifdef BN_MP_ABS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = |a|
*
mp_abs (mp_int * a, mp_int * b)
{
int res;
- if ((res = mp_copy (a, b)) != MP_OKAY) {
- return res;
+
+ /* copy a to b */
+ if (a != b) {
+ if ((res = mp_copy (a, b)) != MP_OKAY) {
+ return res;
+ }
}
+
+ /* force the sign of b to positive */
b->sign = MP_ZPOS;
+
return MP_OKAY;
}
+#endif
/* End: bn_mp_abs.c */
/* Start: bn_mp_add.c */
+#include <tommath.h>
+#ifdef BN_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* high level addition (handles signs) */
-int
-mp_add (mp_int * a, mp_int * b, mp_int * c)
+int mp_add (mp_int * a, mp_int * b, mp_int * c)
{
int sa, sb, res;
return res;
}
+#endif
/* End: bn_mp_add.c */
/* Start: bn_mp_add_d.c */
+#include <tommath.h>
+#ifdef BN_MP_ADD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* single digit addition */
int
mp_add_d (mp_int * a, mp_digit b, mp_int * c)
{
- mp_int t;
- int res;
+ int res, ix, oldused;
+ mp_digit *tmpa, *tmpc, mu;
- if ((res = mp_init_size(&t, 1)) != MP_OKAY) {
- return res;
+ /* grow c as required */
+ if (c->alloc < a->used + 1) {
+ if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
+ return res;
+ }
}
- mp_set (&t, b);
- res = mp_add (a, &t, c);
- mp_clear (&t);
- return res;
+ /* if a is negative and |a| >= b, call c = |a| - b */
+ if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) {
+ /* temporarily fix sign of a */
+ a->sign = MP_ZPOS;
+
+ /* c = |a| - b */
+ res = mp_sub_d(a, b, c);
+
+ /* fix sign */
+ a->sign = c->sign = MP_NEG;
+
+ return res;
+ }
+
+ /* old number of used digits in c */
+ oldused = c->used;
+
+ /* sign always positive */
+ c->sign = MP_ZPOS;
+
+ /* source alias */
+ tmpa = a->dp;
+
+ /* destination alias */
+ tmpc = c->dp;
+
+ /* if a is positive */
+ if (a->sign == MP_ZPOS) {
+ /* add digit, after this we're propagating
+ * the carry.
+ */
+ *tmpc = *tmpa++ + b;
+ mu = *tmpc >> DIGIT_BIT;
+ *tmpc++ &= MP_MASK;
+
+ /* now handle rest of the digits */
+ for (ix = 1; ix < a->used; ix++) {
+ *tmpc = *tmpa++ + mu;
+ mu = *tmpc >> DIGIT_BIT;
+ *tmpc++ &= MP_MASK;
+ }
+ /* set final carry */
+ ix++;
+ *tmpc++ = mu;
+
+ /* setup size */
+ c->used = a->used + 1;
+ } else {
+ /* a was negative and |a| < b */
+ c->used = 1;
+
+ /* the result is a single digit */
+ if (a->used == 1) {
+ *tmpc++ = b - a->dp[0];
+ } else {
+ *tmpc++ = b;
+ }
+
+ /* setup count so the clearing of oldused
+ * can fall through correctly
+ */
+ ix = 1;
+ }
+
+ /* now zero to oldused */
+ while (ix++ < oldused) {
+ *tmpc++ = 0;
+ }
+ mp_clamp(c);
+
+ return MP_OKAY;
}
+#endif
+
/* End: bn_mp_add_d.c */
/* Start: bn_mp_addmod.c */
+#include <tommath.h>
+#ifdef BN_MP_ADDMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* d = a + b (mod c) */
int
mp_clear (&t);
return res;
}
+#endif
/* End: bn_mp_addmod.c */
/* Start: bn_mp_and.c */
+#include <tommath.h>
+#ifdef BN_MP_AND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* AND two ints together */
int
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_mp_and.c */
/* Start: bn_mp_clamp.c */
+#include <tommath.h>
+#ifdef BN_MP_CLAMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* trim unused digits
*
void
mp_clamp (mp_int * a)
{
+ /* decrease used while the most significant digit is
+ * zero.
+ */
while (a->used > 0 && a->dp[a->used - 1] == 0) {
--(a->used);
}
+
+ /* reset the sign flag if used == 0 */
if (a->used == 0) {
a->sign = MP_ZPOS;
}
}
+#endif
/* End: bn_mp_clamp.c */
/* Start: bn_mp_clear.c */
+#include <tommath.h>
+#ifdef BN_MP_CLEAR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* clear one (frees) */
void
mp_clear (mp_int * a)
{
- if (a->dp != NULL) {
+ int i;
+ /* only do anything if a hasn't been freed previously */
+ if (a->dp != NULL) {
/* first zero the digits */
- memset (a->dp, 0, sizeof (mp_digit) * a->used);
+ for (i = 0; i < a->used; i++) {
+ a->dp[i] = 0;
+ }
/* free ram */
- free (a->dp);
+ XFREE(a->dp);
/* reset members to make debugging easier */
- a->dp = NULL;
+ a->dp = NULL;
a->alloc = a->used = 0;
+ a->sign = MP_ZPOS;
}
}
+#endif
/* End: bn_mp_clear.c */
-/* Start: bn_mp_cmp.c */
+/* Start: bn_mp_clear_multi.c */
+#include <tommath.h>
+#ifdef BN_MP_CLEAR_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
+#include <stdarg.h>
+
+void mp_clear_multi(mp_int *mp, ...)
+{
+ mp_int* next_mp = mp;
+ va_list args;
+ va_start(args, mp);
+ while (next_mp != NULL) {
+ mp_clear(next_mp);
+ next_mp = va_arg(args, mp_int*);
+ }
+ va_end(args);
+}
+#endif
+
+/* End: bn_mp_clear_multi.c */
+
+/* Start: bn_mp_cmp.c */
#include <tommath.h>
+#ifdef BN_MP_CMP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
/* compare two ints (signed)*/
int
mp_cmp (mp_int * a, mp_int * b)
{
/* compare based on sign */
- if (a->sign == MP_NEG && b->sign == MP_ZPOS) {
- return MP_LT;
- }
-
- if (a->sign == MP_ZPOS && b->sign == MP_NEG) {
- return MP_GT;
+ if (a->sign != b->sign) {
+ if (a->sign == MP_NEG) {
+ return MP_LT;
+ } else {
+ return MP_GT;
+ }
}
/* compare digits */
return mp_cmp_mag(a, b);
}
}
+#endif
/* End: bn_mp_cmp.c */
/* Start: bn_mp_cmp_d.c */
+#include <tommath.h>
+#ifdef BN_MP_CMP_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* compare a digit */
-int
-mp_cmp_d (mp_int * a, mp_digit b)
+int mp_cmp_d(mp_int * a, mp_digit b)
{
-
+ /* compare based on sign */
if (a->sign == MP_NEG) {
return MP_LT;
}
+ /* compare based on magnitude */
if (a->used > 1) {
return MP_GT;
}
+ /* compare the only digit of a to b */
if (a->dp[0] > b) {
return MP_GT;
} else if (a->dp[0] < b) {
return MP_EQ;
}
}
+#endif
/* End: bn_mp_cmp_d.c */
/* Start: bn_mp_cmp_mag.c */
+#include <tommath.h>
+#ifdef BN_MP_CMP_MAG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* compare maginitude of two ints (unsigned) */
-int
-mp_cmp_mag (mp_int * a, mp_int * b)
+int mp_cmp_mag (mp_int * a, mp_int * b)
{
int n;
+ mp_digit *tmpa, *tmpb;
/* compare based on # of non-zero digits */
if (a->used > b->used) {
return MP_GT;
- }
+ }
if (a->used < b->used) {
return MP_LT;
}
+ /* alias for a */
+ tmpa = a->dp + (a->used - 1);
+
+ /* alias for b */
+ tmpb = b->dp + (a->used - 1);
+
/* compare based on digits */
- for (n = a->used - 1; n >= 0; n--) {
- if (a->dp[n] > b->dp[n]) {
+ for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
+ if (*tmpa > *tmpb) {
return MP_GT;
- }
-
- if (a->dp[n] < b->dp[n]) {
+ }
+
+ if (*tmpa < *tmpb) {
return MP_LT;
}
}
return MP_EQ;
}
+#endif
/* End: bn_mp_cmp_mag.c */
-/* Start: bn_mp_copy.c */
+/* Start: bn_mp_cnt_lsb.c */
+#include <tommath.h>
+#ifdef BN_MP_CNT_LSB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
+
+static const int lnz[16] = {
+ 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
+};
+
+/* Counts the number of lsbs which are zero before the first zero bit */
+int mp_cnt_lsb(mp_int *a)
+{
+ int x;
+ mp_digit q, qq;
+
+ /* easy out */
+ if (mp_iszero(a) == 1) {
+ return 0;
+ }
+
+ /* scan lower digits until non-zero */
+ for (x = 0; x < a->used && a->dp[x] == 0; x++);
+ q = a->dp[x];
+ x *= DIGIT_BIT;
+
+ /* now scan this digit until a 1 is found */
+ if ((q & 1) == 0) {
+ do {
+ qq = q & 15;
+ x += lnz[qq];
+ q >>= 4;
+ } while (qq == 0);
+ }
+ return x;
+}
+
+#endif
+
+/* End: bn_mp_cnt_lsb.c */
+
+/* Start: bn_mp_copy.c */
#include <tommath.h>
+#ifdef BN_MP_COPY_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
/* copy, b = a */
int
}
/* grow dest */
- if ((res = mp_grow (b, a->used)) != MP_OKAY) {
- return res;
+ if (b->alloc < a->used) {
+ if ((res = mp_grow (b, a->used)) != MP_OKAY) {
+ return res;
+ }
}
/* zero b and copy the parameters over */
register mp_digit *tmpa, *tmpb;
/* pointer aliases */
+
+ /* source */
tmpa = a->dp;
+
+ /* destination */
tmpb = b->dp;
/* copy all the digits */
*tmpb++ = 0;
}
}
+
+ /* copy used count and sign */
b->used = a->used;
b->sign = a->sign;
return MP_OKAY;
}
+#endif
/* End: bn_mp_copy.c */
/* Start: bn_mp_count_bits.c */
+#include <tommath.h>
+#ifdef BN_MP_COUNT_BITS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* returns the number of bits in an int */
int
}
return r;
}
+#endif
/* End: bn_mp_count_bits.c */
/* Start: bn_mp_div.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
+
+#ifdef BN_MP_DIV_SMALL
+
+/* slower bit-bang division... also smaller */
+int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ mp_int ta, tb, tq, q;
+ int res, n, n2;
+
+ /* is divisor zero ? */
+ if (mp_iszero (b) == 1) {
+ return MP_VAL;
+ }
+
+ /* if a < b then q=0, r = a */
+ if (mp_cmp_mag (a, b) == MP_LT) {
+ if (d != NULL) {
+ res = mp_copy (a, d);
+ } else {
+ res = MP_OKAY;
+ }
+ if (c != NULL) {
+ mp_zero (c);
+ }
+ return res;
+ }
+
+ /* init our temps */
+ if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
+ return res;
+ }
+
+
+ mp_set(&tq, 1);
+ n = mp_count_bits(a) - mp_count_bits(b);
+ if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
+ ((res = mp_abs(b, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
+ goto LBL_ERR;
+ }
+
+ while (n-- >= 0) {
+ if (mp_cmp(&tb, &ta) != MP_GT) {
+ if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
+ ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
+ goto LBL_ERR;
+ }
+ }
+ if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
+ ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* now q == quotient and ta == remainder */
+ n = a->sign;
+ n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
+ if (c != NULL) {
+ mp_exch(c, &q);
+ c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
+ }
+ if (d != NULL) {
+ mp_exch(d, &ta);
+ d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
+ }
+LBL_ERR:
+ mp_clear_multi(&ta, &tb, &tq, &q, NULL);
+ return res;
+}
+
+#else
/* integer signed division.
* c*b + d == a [e.g. a/b, c=quotient, d=remainder]
* The overall algorithm is as described as
* 14.20 from HAC but fixed to treat these cases.
*/
-int
-mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
mp_int q, x, y, t1, t2;
int res, n, t, i, norm, neg;
q.used = a->used + 2;
if ((res = mp_init (&t1)) != MP_OKAY) {
- goto __Q;
+ goto LBL_Q;
}
if ((res = mp_init (&t2)) != MP_OKAY) {
- goto __T1;
+ goto LBL_T1;
}
if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
- goto __T2;
+ goto LBL_T2;
}
if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
- goto __X;
+ goto LBL_X;
}
/* fix the sign */
if (norm < (int)(DIGIT_BIT-1)) {
norm = (DIGIT_BIT-1) - norm;
if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
- goto __Y;
+ goto LBL_Y;
}
if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
- goto __Y;
+ goto LBL_Y;
}
} else {
norm = 0;
/* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
- goto __Y;
+ goto LBL_Y;
}
while (mp_cmp (&x, &y) != MP_LT) {
++(q.dp[n - t]);
if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
- goto __Y;
+ goto LBL_Y;
}
}
/* step 3. for i from n down to (t + 1) */
for (i = n; i >= (t + 1); i--) {
- if (i > x.used)
+ if (i > x.used) {
continue;
+ }
/* step 3.1 if xi == yt then set q{i-t-1} to b-1,
* otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
t1.dp[1] = y.dp[t];
t1.used = 2;
if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
- goto __Y;
+ goto LBL_Y;
}
/* find right hand */
/* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
- goto __Y;
+ goto LBL_Y;
}
if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
- goto __Y;
+ goto LBL_Y;
}
if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
- goto __Y;
+ goto LBL_Y;
}
/* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
if (x.sign == MP_NEG) {
if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
- goto __Y;
+ goto LBL_Y;
}
if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
- goto __Y;
+ goto LBL_Y;
}
if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
- goto __Y;
+ goto LBL_Y;
}
q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
*/
/* get sign before writing to c */
- x.sign = a->sign;
+ x.sign = x.used == 0 ? MP_ZPOS : a->sign;
if (c != NULL) {
mp_clamp (&q);
res = MP_OKAY;
-__Y:mp_clear (&y);
-__X:mp_clear (&x);
-__T2:mp_clear (&t2);
-__T1:mp_clear (&t1);
-__Q:mp_clear (&q);
+LBL_Y:mp_clear (&y);
+LBL_X:mp_clear (&x);
+LBL_T2:mp_clear (&t2);
+LBL_T1:mp_clear (&t1);
+LBL_Q:mp_clear (&q);
return res;
}
+#endif
+
+#endif
+
/* End: bn_mp_div.c */
/* Start: bn_mp_div_2.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = a/2 */
-int
-mp_div_2 (mp_int * a, mp_int * b)
+int mp_div_2(mp_int * a, mp_int * b)
{
int x, res, oldused;
mp_clamp (b);
return MP_OKAY;
}
+#endif
/* End: bn_mp_div_2.c */
/* Start: bn_mp_div_2d.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
-int
-mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
+int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
{
mp_digit D, r, rr;
int x, res;
/* shift any bit count < DIGIT_BIT */
D = (mp_digit) (b % DIGIT_BIT);
if (D != 0) {
- register mp_digit *tmpc, mask;
+ register mp_digit *tmpc, mask, shift;
/* mask */
mask = (((mp_digit)1) << D) - 1;
+ /* shift for lsb */
+ shift = DIGIT_BIT - D;
+
/* alias */
tmpc = c->dp + (c->used - 1);
rr = *tmpc & mask;
/* shift the current word and mix in the carry bits from the previous word */
- *tmpc = (*tmpc >> D) | (r << (DIGIT_BIT - D));
+ *tmpc = (*tmpc >> D) | (r << shift);
--tmpc;
/* set the carry to the carry bits of the current word found above */
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_mp_div_2d.c */
/* Start: bn_mp_div_3.c */
-/* LibTomMath, multiple-precision integer library -- Tom St Denis\r
- *\r
- * LibTomMath is library that provides for multiple-precision\r
- * integer arithmetic as well as number theoretic functionality.\r
- *\r
- * The library is designed directly after the MPI library by\r
- * Michael Fromberger but has been written from scratch with\r
- * additional optimizations in place.\r
- *\r
- * The library is free for all purposes without any express\r
- * guarantee it works.\r
- *\r
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org\r
- */\r
-#include <tommath.h>\r
-\r
-/* divide by three (based on routine from MPI and the GMP manual) */\r
-int\r
-mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)\r
-{\r
- mp_int q;\r
- mp_word w, t;\r
- mp_digit b;\r
- int res, ix;\r
- \r
- /* b = 2**DIGIT_BIT / 3 */\r
- b = (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3);\r
-\r
- if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {\r
- return res;\r
- }\r
- \r
- q.used = a->used;\r
- q.sign = a->sign;\r
- w = 0;\r
- for (ix = a->used - 1; ix >= 0; ix--) {\r
- w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);\r
- \r
- if (w >= 3) {\r
- t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT);\r
- w -= (t << ((mp_word)1)) + t;\r
- while (w >= 3) {\r
- t += 1;\r
- w -= 3;\r
- }\r
- } else {\r
- t = 0;\r
- }\r
- q.dp[ix] = (mp_digit)t;\r
- }\r
- \r
- if (d != NULL) {\r
- *d = (mp_digit)w;\r
- }\r
- \r
- if (c != NULL) {\r
- mp_clamp(&q);\r
- mp_exch(&q, c);\r
- }\r
- mp_clear(&q);\r
- \r
- return res;\r
-}\r
-\r
+#include <tommath.h>
+#ifdef BN_MP_DIV_3_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* divide by three (based on routine from MPI and the GMP manual) */
+int
+mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
+{
+ mp_int q;
+ mp_word w, t;
+ mp_digit b;
+ int res, ix;
+
+ /* b = 2**DIGIT_BIT / 3 */
+ b = (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3);
+
+ if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
+ return res;
+ }
+
+ q.used = a->used;
+ q.sign = a->sign;
+ w = 0;
+ for (ix = a->used - 1; ix >= 0; ix--) {
+ w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
+
+ if (w >= 3) {
+ /* multiply w by [1/3] */
+ t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT);
+
+ /* now subtract 3 * [w/3] from w, to get the remainder */
+ w -= t+t+t;
+
+ /* fixup the remainder as required since
+ * the optimization is not exact.
+ */
+ while (w >= 3) {
+ t += 1;
+ w -= 3;
+ }
+ } else {
+ t = 0;
+ }
+ q.dp[ix] = (mp_digit)t;
+ }
+
+ /* [optional] store the remainder */
+ if (d != NULL) {
+ *d = (mp_digit)w;
+ }
+
+ /* [optional] store the quotient */
+ if (c != NULL) {
+ mp_clamp(&q);
+ mp_exch(&q, c);
+ }
+ mp_clear(&q);
+
+ return res;
+}
+
+#endif
/* End: bn_mp_div_3.c */
/* Start: bn_mp_div_d.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
+
+static int s_is_power_of_two(mp_digit b, int *p)
+{
+ int x;
+
+ for (x = 1; x < DIGIT_BIT; x++) {
+ if (b == (((mp_digit)1)<<x)) {
+ *p = x;
+ return 1;
+ }
+ }
+ return 0;
+}
/* single digit division (based on routine from MPI) */
-int
-mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
+int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
{
mp_int q;
mp_word w;
mp_digit t;
int res, ix;
-
+
+ /* cannot divide by zero */
if (b == 0) {
return MP_VAL;
}
-
+
+ /* quick outs */
+ if (b == 1 || mp_iszero(a) == 1) {
+ if (d != NULL) {
+ *d = 0;
+ }
+ if (c != NULL) {
+ return mp_copy(a, c);
+ }
+ return MP_OKAY;
+ }
+
+ /* power of two ? */
+ if (s_is_power_of_two(b, &ix) == 1) {
+ if (d != NULL) {
+ *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
+ }
+ if (c != NULL) {
+ return mp_div_2d(a, ix, c, NULL);
+ }
+ return MP_OKAY;
+ }
+
+#ifdef BN_MP_DIV_3_C
+ /* three? */
if (b == 3) {
return mp_div_3(a, c, d);
}
-
+#endif
+
+ /* no easy answer [c'est la vie]. Just division */
if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
return res;
}
if (w >= b) {
t = (mp_digit)(w / b);
- w = w % b;
+ w -= ((mp_word)t) * ((mp_word)b);
} else {
t = 0;
}
return res;
}
+#endif
/* End: bn_mp_div_d.c */
/* Start: bn_mp_dr_is_modulus.c */
-/* LibTomMath, multiple-precision integer library -- Tom St Denis\r
- *\r
- * LibTomMath is library that provides for multiple-precision\r
- * integer arithmetic as well as number theoretic functionality.\r
- *\r
- * The library is designed directly after the MPI library by\r
- * Michael Fromberger but has been written from scratch with\r
- * additional optimizations in place.\r
- *\r
- * The library is free for all purposes without any express\r
- * guarantee it works.\r
- *\r
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org\r
- */\r
-#include <tommath.h>\r
-\r
-/* determines if a number is a valid DR modulus */\r
-int mp_dr_is_modulus(mp_int *a)\r
-{\r
- int ix;\r
-\r
- /* must be at least two digits */\r
- if (a->used < 2) {\r
- return 0;\r
- }\r
-\r
- for (ix = 1; ix < a->used; ix++) {\r
- if (a->dp[ix] != MP_MASK) {\r
- return 0;\r
- }\r
- }\r
- return 1;\r
-}\r
-\r
+#include <tommath.h>
+#ifdef BN_MP_DR_IS_MODULUS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* determines if a number is a valid DR modulus */
+int mp_dr_is_modulus(mp_int *a)
+{
+ int ix;
+
+ /* must be at least two digits */
+ if (a->used < 2) {
+ return 0;
+ }
+
+ /* must be of the form b**k - a [a <= b] so all
+ * but the first digit must be equal to -1 (mod b).
+ */
+ for (ix = 1; ix < a->used; ix++) {
+ if (a->dp[ix] != MP_MASK) {
+ return 0;
+ }
+ }
+ return 1;
+}
+
+#endif
/* End: bn_mp_dr_is_modulus.c */
/* Start: bn_mp_dr_reduce.c */
+#include <tommath.h>
+#ifdef BN_MP_DR_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
*
* Based on algorithm from the paper
*
* "Generating Efficient Primes for Discrete Log Cryptosystems"
- * Chae Hoon Lim, Pil Loong Lee,
+ * Chae Hoon Lim, Pil Joong Lee,
* POSTECH Information Research Laboratories
*
* The modulus must be of a special format [see manual]
*
* Has been modified to use algorithm 7.10 from the LTM book instead
+ *
+ * Input x must be in the range 0 <= x <= (n-1)**2
*/
int
mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k)
int err, i, m;
mp_word r;
mp_digit mu, *tmpx1, *tmpx2;
-
+
/* m = digits in modulus */
m = n->used;
-
+
/* ensure that "x" has at least 2m digits */
if (x->alloc < m + m) {
if ((err = mp_grow (x, m + m)) != MP_OKAY) {
}
}
-/* top of loop, this is where the code resumes if
+/* top of loop, this is where the code resumes if
* another reduction pass is required.
*/
top:
/* aliases for digits */
/* alias for lower half of x */
tmpx1 = x->dp;
-
+
/* alias for upper half of x, or x/B**m */
tmpx2 = x->dp + m;
-
+
/* set carry to zero */
mu = 0;
-
- /* compute (x mod B**m) + mp * [x/B**m] inline and inplace */
+
+ /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
for (i = 0; i < m; i++) {
r = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
*tmpx1++ = (mp_digit)(r & MP_MASK);
mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
}
-
+
/* set final carry */
*tmpx1++ = mu;
-
+
/* zero words above m */
for (i = m + 1; i < x->used; i++) {
*tmpx1++ = 0;
/* clamp, sub and return */
mp_clamp (x);
- /* if x >= n then subtract and reduce again
+ /* if x >= n then subtract and reduce again
* Each successive "recursion" makes the input smaller and smaller.
*/
if (mp_cmp_mag (x, n) != MP_LT) {
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_dr_reduce.c */
/* Start: bn_mp_dr_setup.c */
-/* LibTomMath, multiple-precision integer library -- Tom St Denis\r
- *\r
- * LibTomMath is library that provides for multiple-precision\r
- * integer arithmetic as well as number theoretic functionality.\r
- *\r
- * The library is designed directly after the MPI library by\r
- * Michael Fromberger but has been written from scratch with\r
- * additional optimizations in place.\r
- *\r
- * The library is free for all purposes without any express\r
- * guarantee it works.\r
- *\r
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org\r
- */\r
-#include <tommath.h>\r
-\r
-/* determines the setup value */\r
-void mp_dr_setup(mp_int *a, mp_digit *d)\r
-{\r
- /* the casts are required if DIGIT_BIT is one less than\r
- * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]\r
- */\r
- *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) - \r
- ((mp_word)a->dp[0]));\r
-}\r
-\r
+#include <tommath.h>
+#ifdef BN_MP_DR_SETUP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* determines the setup value */
+void mp_dr_setup(mp_int *a, mp_digit *d)
+{
+ /* the casts are required if DIGIT_BIT is one less than
+ * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
+ */
+ *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
+ ((mp_word)a->dp[0]));
+}
+
+#endif
/* End: bn_mp_dr_setup.c */
/* Start: bn_mp_exch.c */
+#include <tommath.h>
+#ifdef BN_MP_EXCH_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* swap the elements of two integers, for cases where you can't simply swap the
- * mp_int pointers around
+ * mp_int pointers around
*/
void
mp_exch (mp_int * a, mp_int * b)
{
mp_int t;
- t = *a;
+ t = *a;
*a = *b;
*b = t;
}
+#endif
/* End: bn_mp_exch.c */
/* Start: bn_mp_expt_d.c */
+#include <tommath.h>
+#ifdef BN_MP_EXPT_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* calculate c = a**b using a square-multiply algorithm */
-int
-mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
+int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
{
int res, x;
mp_int g;
mp_clear (&g);
return MP_OKAY;
}
+#endif
/* End: bn_mp_expt_d.c */
/* Start: bn_mp_exptmod.c */
+#include <tommath.h>
+#ifdef BN_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* this is a shell function that calls either the normal or Montgomery
* embedded in the normal function but that wasted alot of stack space
* for nothing (since 99% of the time the Montgomery code would be called)
*/
-int
-mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
+int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
{
int dr;
/* if exponent X is negative we have to recurse */
if (X->sign == MP_NEG) {
+#ifdef BN_MP_INVMOD_C
mp_int tmpG, tmpX;
int err;
err = mp_exptmod(&tmpG, &tmpX, P, Y);
mp_clear_multi(&tmpG, &tmpX, NULL);
return err;
+#else
+ /* no invmod */
+ return MP_VAL;
+#endif
}
+/* modified diminished radix reduction */
+#if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C)
+ if (mp_reduce_is_2k_l(P) == MP_YES) {
+ return s_mp_exptmod(G, X, P, Y, 1);
+ }
+#endif
+
+#ifdef BN_MP_DR_IS_MODULUS_C
+ /* is it a DR modulus? */
dr = mp_dr_is_modulus(P);
+#else
+ /* default to no */
+ dr = 0;
+#endif
+
+#ifdef BN_MP_REDUCE_IS_2K_C
+ /* if not, is it a unrestricted DR modulus? */
if (dr == 0) {
dr = mp_reduce_is_2k(P) << 1;
}
+#endif
- /* if the modulus is odd or dr != 0 use the fast method */
+ /* if the modulus is odd or dr != 0 use the montgomery method */
+#ifdef BN_MP_EXPTMOD_FAST_C
if (mp_isodd (P) == 1 || dr != 0) {
return mp_exptmod_fast (G, X, P, Y, dr);
} else {
- return s_mp_exptmod (G, X, P, Y);
+#endif
+#ifdef BN_S_MP_EXPTMOD_C
+ /* otherwise use the generic Barrett reduction technique */
+ return s_mp_exptmod (G, X, P, Y, 0);
+#else
+ /* no exptmod for evens */
+ return MP_VAL;
+#endif
+#ifdef BN_MP_EXPTMOD_FAST_C
}
+#endif
}
+#endif
/* End: bn_mp_exptmod.c */
/* Start: bn_mp_exptmod_fast.c */
+#include <tommath.h>
+#ifdef BN_MP_EXPTMOD_FAST_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* computes Y == G^X mod P, HAC pp.616, Algorithm 14.85
+/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
*
* Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
* The value of k changes based on the size of the exponent.
*
* Uses Montgomery or Diminished Radix reduction [whichever appropriate]
*/
-int
-mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
+
+#ifdef MP_LOW_MEM
+ #define TAB_SIZE 32
+#else
+ #define TAB_SIZE 256
+#endif
+
+int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
{
- mp_int M[256], res;
+ mp_int M[TAB_SIZE], res;
mp_digit buf, mp;
int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
-
+
/* use a pointer to the reduction algorithm. This allows us to use
* one of many reduction algorithms without modding the guts of
- * the code with if statements everywhere.
+ * the code with if statements everywhere.
*/
int (*redux)(mp_int*,mp_int*,mp_digit);
}
#endif
+ /* init M array */
+ /* init first cell */
+ if ((err = mp_init(&M[1])) != MP_OKAY) {
+ return err;
+ }
- /* init G array */
- for (x = 0; x < (1 << winsize); x++) {
- if ((err = mp_init (&M[x])) != MP_OKAY) {
- for (y = 0; y < x; y++) {
+ /* now init the second half of the array */
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+ if ((err = mp_init(&M[x])) != MP_OKAY) {
+ for (y = 1<<(winsize-1); y < x; y++) {
mp_clear (&M[y]);
}
+ mp_clear(&M[1]);
return err;
}
}
/* determine and setup reduction code */
if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_SETUP_C
/* now setup montgomery */
if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
- goto __M;
+ goto LBL_M;
}
-
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
+
/* automatically pick the comba one if available (saves quite a few calls/ifs) */
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
if (((P->used * 2 + 1) < MP_WARRAY) &&
P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
redux = fast_mp_montgomery_reduce;
- } else {
- /* use slower baselien method */
+ } else
+#endif
+ {
+#ifdef BN_MP_MONTGOMERY_REDUCE_C
+ /* use slower baseline Montgomery method */
redux = mp_montgomery_reduce;
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
}
} else if (redmode == 1) {
- /* setup DR reduction */
+#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
+ /* setup DR reduction for moduli of the form B**k - b */
mp_dr_setup(P, &mp);
redux = mp_dr_reduce;
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
} else {
- /* setup 2k reduction */
+#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
+ /* setup DR reduction for moduli of the form 2**k - b */
if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
- goto __M;
+ goto LBL_M;
}
redux = mp_reduce_2k;
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
}
/* setup result */
if ((err = mp_init (&res)) != MP_OKAY) {
- goto __RES;
+ goto LBL_M;
}
/* create M table
*
- * The M table contains powers of the input base, e.g. M[x] = G^x mod P
+
*
* The first half of the table is not computed though accept for M[0] and M[1]
*/
if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
/* now we need R mod m */
if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
+#else
+ err = MP_VAL;
+ goto LBL_RES;
+#endif
/* now set M[1] to G * R mod m */
if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
} else {
mp_set(&res, 1);
if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
}
/* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
for (x = 0; x < (winsize - 1); x++) {
if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
}
/* create upper table */
for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
}
for (;;) {
/* grab next digit as required */
if (--bitcnt == 0) {
+ /* if digidx == -1 we are out of digits so break */
if (digidx == -1) {
break;
}
- buf = X->dp[digidx--];
- bitcnt = (int) DIGIT_BIT;
+ /* read next digit and reset bitcnt */
+ buf = X->dp[digidx--];
+ bitcnt = (int)DIGIT_BIT;
}
/* grab the next msb from the exponent */
- y = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
+ y = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
buf <<= (mp_digit)1;
/* if the bit is zero and mode == 0 then we ignore it
/* if the bit is zero and mode == 1 then we square */
if (mode == 1 && y == 0) {
if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
if ((err = redux (&res, P, mp)) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
continue;
}
/* else we add it to the window */
bitbuf |= (y << (winsize - ++bitcpy));
- mode = 2;
+ mode = 2;
if (bitcpy == winsize) {
/* ok window is filled so square as required and multiply */
/* square first */
for (x = 0; x < winsize; x++) {
if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
if ((err = redux (&res, P, mp)) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
}
/* then multiply */
if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
if ((err = redux (&res, P, mp)) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
/* empty window and reset */
bitcpy = 0;
bitbuf = 0;
- mode = 1;
+ mode = 1;
}
}
/* square then multiply if the bit is set */
for (x = 0; x < bitcpy; x++) {
if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
if ((err = redux (&res, P, mp)) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
+ /* get next bit of the window */
bitbuf <<= 1;
if ((bitbuf & (1 << winsize)) != 0) {
/* then multiply */
if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
if ((err = redux (&res, P, mp)) != MP_OKAY) {
- goto __RES;
+ goto LBL_RES;
}
}
}
}
if (redmode == 0) {
- /* fixup result if Montgomery reduction is used */
- if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) {
- goto __RES;
+ /* fixup result if Montgomery reduction is used
+ * recall that any value in a Montgomery system is
+ * actually multiplied by R mod n. So we have
+ * to reduce one more time to cancel out the factor
+ * of R.
+ */
+ if ((err = redux(&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
}
}
+ /* swap res with Y */
mp_exch (&res, Y);
err = MP_OKAY;
-__RES:mp_clear (&res);
-__M:
- for (x = 0; x < (1 << winsize); x++) {
+LBL_RES:mp_clear (&res);
+LBL_M:
+ mp_clear(&M[1]);
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
mp_clear (&M[x]);
}
return err;
}
+#endif
+
/* End: bn_mp_exptmod_fast.c */
-/* Start: bn_mp_gcd.c */
+/* Start: bn_mp_exteuclid.c */
+#include <tommath.h>
+#ifdef BN_MP_EXTEUCLID_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* Extended euclidean algorithm of (a, b) produces
+ a*u1 + b*u2 = u3
+ */
+int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
+{
+ mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp;
+ int err;
+
+ if ((err = mp_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) {
+ return err;
+ }
+
+ /* initialize, (u1,u2,u3) = (1,0,a) */
+ mp_set(&u1, 1);
+ if ((err = mp_copy(a, &u3)) != MP_OKAY) { goto _ERR; }
+
+ /* initialize, (v1,v2,v3) = (0,1,b) */
+ mp_set(&v2, 1);
+ if ((err = mp_copy(b, &v3)) != MP_OKAY) { goto _ERR; }
+
+ /* loop while v3 != 0 */
+ while (mp_iszero(&v3) == MP_NO) {
+ /* q = u3/v3 */
+ if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY) { goto _ERR; }
+
+ /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
+ if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY) { goto _ERR; }
+
+ /* (u1,u2,u3) = (v1,v2,v3) */
+ if ((err = mp_copy(&v1, &u1)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_copy(&v2, &u2)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_copy(&v3, &u3)) != MP_OKAY) { goto _ERR; }
+
+ /* (v1,v2,v3) = (t1,t2,t3) */
+ if ((err = mp_copy(&t1, &v1)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_copy(&t2, &v2)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_copy(&t3, &v3)) != MP_OKAY) { goto _ERR; }
+ }
+
+ /* make sure U3 >= 0 */
+ if (u3.sign == MP_NEG) {
+ mp_neg(&u1, &u1);
+ mp_neg(&u2, &u2);
+ mp_neg(&u3, &u3);
+ }
+
+ /* copy result out */
+ if (U1 != NULL) { mp_exch(U1, &u1); }
+ if (U2 != NULL) { mp_exch(U2, &u2); }
+ if (U3 != NULL) { mp_exch(U3, &u3); }
+
+ err = MP_OKAY;
+_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
+ return err;
+}
+#endif
+
+/* End: bn_mp_exteuclid.c */
+
+/* Start: bn_mp_fread.c */
+#include <tommath.h>
+#ifdef BN_MP_FREAD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
+
+/* read a bigint from a file stream in ASCII */
+int mp_fread(mp_int *a, int radix, FILE *stream)
+{
+ int err, ch, neg, y;
+
+ /* clear a */
+ mp_zero(a);
+
+ /* if first digit is - then set negative */
+ ch = fgetc(stream);
+ if (ch == '-') {
+ neg = MP_NEG;
+ ch = fgetc(stream);
+ } else {
+ neg = MP_ZPOS;
+ }
+
+ for (;;) {
+ /* find y in the radix map */
+ for (y = 0; y < radix; y++) {
+ if (mp_s_rmap[y] == ch) {
+ break;
+ }
+ }
+ if (y == radix) {
+ break;
+ }
+
+ /* shift up and add */
+ if ((err = mp_mul_d(a, radix, a)) != MP_OKAY) {
+ return err;
+ }
+ if ((err = mp_add_d(a, y, a)) != MP_OKAY) {
+ return err;
+ }
+
+ ch = fgetc(stream);
+ }
+ if (mp_cmp_d(a, 0) != MP_EQ) {
+ a->sign = neg;
+ }
+
+ return MP_OKAY;
+}
+
+#endif
+
+/* End: bn_mp_fread.c */
+
+/* Start: bn_mp_fwrite.c */
#include <tommath.h>
+#ifdef BN_MP_FWRITE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+int mp_fwrite(mp_int *a, int radix, FILE *stream)
+{
+ char *buf;
+ int err, len, x;
+
+ if ((err = mp_radix_size(a, radix, &len)) != MP_OKAY) {
+ return err;
+ }
+
+ buf = OPT_CAST(char) XMALLOC (len);
+ if (buf == NULL) {
+ return MP_MEM;
+ }
+
+ if ((err = mp_toradix(a, buf, radix)) != MP_OKAY) {
+ XFREE (buf);
+ return err;
+ }
+
+ for (x = 0; x < len; x++) {
+ if (fputc(buf[x], stream) == EOF) {
+ XFREE (buf);
+ return MP_VAL;
+ }
+ }
+
+ XFREE (buf);
+ return MP_OKAY;
+}
-/* Greatest Common Divisor using the binary method [Algorithm B, page 338, vol2 of TAOCP]
+#endif
+
+/* End: bn_mp_fwrite.c */
+
+/* Start: bn_mp_gcd.c */
+#include <tommath.h>
+#ifdef BN_MP_GCD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-int
-mp_gcd (mp_int * a, mp_int * b, mp_int * c)
+
+/* Greatest Common Divisor using the binary method */
+int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
{
- mp_int u, v, t;
- int k, res, neg;
+ mp_int u, v;
+ int k, u_lsb, v_lsb, res;
/* either zero than gcd is the largest */
if (mp_iszero (a) == 1 && mp_iszero (b) == 0) {
- return mp_copy (b, c);
+ return mp_abs (b, c);
}
if (mp_iszero (a) == 0 && mp_iszero (b) == 1) {
- return mp_copy (a, c);
+ return mp_abs (a, c);
}
- if (mp_iszero (a) == 1 && mp_iszero (b) == 1) {
- mp_set (c, 1);
+
+ /* optimized. At this point if a == 0 then
+ * b must equal zero too
+ */
+ if (mp_iszero (a) == 1) {
+ mp_zero(c);
return MP_OKAY;
}
- /* if both are negative they share (-1) as a common divisor */
- neg = (a->sign == b->sign) ? a->sign : MP_ZPOS;
-
+ /* get copies of a and b we can modify */
if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
return res;
}
if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
- goto __U;
+ goto LBL_U;
}
/* must be positive for the remainder of the algorithm */
u.sign = v.sign = MP_ZPOS;
- if ((res = mp_init (&t)) != MP_OKAY) {
- goto __V;
- }
+ /* B1. Find the common power of two for u and v */
+ u_lsb = mp_cnt_lsb(&u);
+ v_lsb = mp_cnt_lsb(&v);
+ k = MIN(u_lsb, v_lsb);
- /* B1. Find power of two */
- k = 0;
- while (mp_iseven(&u) == 1 && mp_iseven(&v) == 1) {
- ++k;
- if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
- goto __T;
- }
- if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
- goto __T;
- }
- }
+ if (k > 0) {
+ /* divide the power of two out */
+ if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
- /* B2. Initialize */
- if (mp_isodd(&u) == 1) {
- /* t = -v */
- if ((res = mp_copy (&v, &t)) != MP_OKAY) {
- goto __T;
- }
- t.sign = MP_NEG;
- } else {
- /* t = u */
- if ((res = mp_copy (&u, &t)) != MP_OKAY) {
- goto __T;
- }
+ if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
}
- do {
- /* B3 (and B4). Halve t, if even */
- while (t.used != 0 && mp_iseven(&t) == 1) {
- if ((res = mp_div_2 (&t, &t)) != MP_OKAY) {
- goto __T;
- }
- }
+ /* divide any remaining factors of two out */
+ if (u_lsb != k) {
+ if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
- /* B5. if t>0 then u=t otherwise v=-t */
- if (t.used != 0 && t.sign != MP_NEG) {
- if ((res = mp_copy (&t, &u)) != MP_OKAY) {
- goto __T;
- }
- } else {
- if ((res = mp_copy (&t, &v)) != MP_OKAY) {
- goto __T;
- }
- v.sign = (v.sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
- }
+ if (v_lsb != k) {
+ if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
- /* B6. t = u - v, if t != 0 loop otherwise terminate */
- if ((res = mp_sub (&u, &v, &t)) != MP_OKAY) {
- goto __T;
- }
- } while (mp_iszero(&t) == 0);
+ while (mp_iszero(&v) == 0) {
+ /* make sure v is the largest */
+ if (mp_cmp_mag(&u, &v) == MP_GT) {
+ /* swap u and v to make sure v is >= u */
+ mp_exch(&u, &v);
+ }
+
+ /* subtract smallest from largest */
+ if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
+ goto LBL_V;
+ }
+
+ /* Divide out all factors of two */
+ if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
- /* multiply by 2^k which we divided out at the beginning */
- if ((res = mp_mul_2d (&u, k, &u)) != MP_OKAY) {
- goto __T;
+ /* multiply by 2**k which we divided out at the beginning */
+ if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
+ goto LBL_V;
}
-
- mp_exch (&u, c);
- c->sign = neg;
+ c->sign = MP_ZPOS;
res = MP_OKAY;
-__T:mp_clear (&t);
-__V:mp_clear (&u);
-__U:mp_clear (&v);
+LBL_V:mp_clear (&u);
+LBL_U:mp_clear (&v);
return res;
}
+#endif
/* End: bn_mp_gcd.c */
-/* Start: bn_mp_grow.c */
+/* Start: bn_mp_get_int.c */
+#include <tommath.h>
+#ifdef BN_MP_GET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
+
+/* get the lower 32-bits of an mp_int */
+unsigned long mp_get_int(mp_int * a)
+{
+ int i;
+ unsigned long res;
+
+ if (a->used == 0) {
+ return 0;
+ }
+
+ /* get number of digits of the lsb we have to read */
+ i = MIN(a->used,(int)((sizeof(unsigned long)*CHAR_BIT+DIGIT_BIT-1)/DIGIT_BIT))-1;
+
+ /* get most significant digit of result */
+ res = DIGIT(a,i);
+
+ while (--i >= 0) {
+ res = (res << DIGIT_BIT) | DIGIT(a,i);
+ }
+
+ /* force result to 32-bits always so it is consistent on non 32-bit platforms */
+ return res & 0xFFFFFFFFUL;
+}
+#endif
+
+/* End: bn_mp_get_int.c */
+
+/* Start: bn_mp_grow.c */
#include <tommath.h>
+#ifdef BN_MP_GROW_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
/* grow as required */
-int
-mp_grow (mp_int * a, int size)
+int mp_grow (mp_int * a, int size)
{
int i;
+ mp_digit *tmp;
/* if the alloc size is smaller alloc more ram */
if (a->alloc < size) {
/* ensure there are always at least MP_PREC digits extra on top */
- size += (MP_PREC * 2) - (size & (MP_PREC - 1));
+ size += (MP_PREC * 2) - (size % MP_PREC);
- a->dp = OPT_CAST realloc (a->dp, sizeof (mp_digit) * size);
- if (a->dp == NULL) {
+ /* reallocate the array a->dp
+ *
+ * We store the return in a temporary variable
+ * in case the operation failed we don't want
+ * to overwrite the dp member of a.
+ */
+ tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
+ if (tmp == NULL) {
+ /* reallocation failed but "a" is still valid [can be freed] */
return MP_MEM;
}
+ /* reallocation succeeded so set a->dp */
+ a->dp = tmp;
+
/* zero excess digits */
i = a->alloc;
a->alloc = size;
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_grow.c */
/* Start: bn_mp_init.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* init a new bigint */
-int
-mp_init (mp_int * a)
+/* init a new mp_int */
+int mp_init (mp_int * a)
{
- /* allocate ram required and clear it */
- a->dp = OPT_CAST calloc (sizeof (mp_digit), MP_PREC);
+ int i;
+
+ /* allocate memory required and clear it */
+ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
if (a->dp == NULL) {
return MP_MEM;
}
+ /* set the digits to zero */
+ for (i = 0; i < MP_PREC; i++) {
+ a->dp[i] = 0;
+ }
+
/* set the used to zero, allocated digits to the default precision
* and sign to positive */
a->used = 0;
return MP_OKAY;
}
+#endif
/* End: bn_mp_init.c */
/* Start: bn_mp_init_copy.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* creates "a" then copies b into it */
-int
-mp_init_copy (mp_int * a, mp_int * b)
+int mp_init_copy (mp_int * a, mp_int * b)
{
int res;
}
return mp_copy (b, a);
}
+#endif
/* End: bn_mp_init_copy.c */
-/* Start: bn_mp_init_size.c */
+/* Start: bn_mp_init_multi.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
+#include <stdarg.h>
+
+int mp_init_multi(mp_int *mp, ...)
+{
+ mp_err res = MP_OKAY; /* Assume ok until proven otherwise */
+ int n = 0; /* Number of ok inits */
+ mp_int* cur_arg = mp;
+ va_list args;
+
+ va_start(args, mp); /* init args to next argument from caller */
+ while (cur_arg != NULL) {
+ if (mp_init(cur_arg) != MP_OKAY) {
+ /* Oops - error! Back-track and mp_clear what we already
+ succeeded in init-ing, then return error.
+ */
+ va_list clean_args;
+
+ /* end the current list */
+ va_end(args);
+
+ /* now start cleaning up */
+ cur_arg = mp;
+ va_start(clean_args, mp);
+ while (n--) {
+ mp_clear(cur_arg);
+ cur_arg = va_arg(clean_args, mp_int*);
+ }
+ va_end(clean_args);
+ res = MP_MEM;
+ break;
+ }
+ n++;
+ cur_arg = va_arg(args, mp_int*);
+ }
+ va_end(args);
+ return res; /* Assumed ok, if error flagged above. */
+}
+
+#endif
+
+/* End: bn_mp_init_multi.c */
+
+/* Start: bn_mp_init_set.c */
#include <tommath.h>
+#ifdef BN_MP_INIT_SET_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
-/* init a mp_init and grow it to a given size */
-int
-mp_init_size (mp_int * a, int size)
+/* initialize and set a digit */
+int mp_init_set (mp_int * a, mp_digit b)
+{
+ int err;
+ if ((err = mp_init(a)) != MP_OKAY) {
+ return err;
+ }
+ mp_set(a, b);
+ return err;
+}
+#endif
+
+/* End: bn_mp_init_set.c */
+
+/* Start: bn_mp_init_set_int.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_SET_INT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* initialize and set a digit */
+int mp_init_set_int (mp_int * a, unsigned long b)
+{
+ int err;
+ if ((err = mp_init(a)) != MP_OKAY) {
+ return err;
+ }
+ return mp_set_int(a, b);
+}
+#endif
+
+/* End: bn_mp_init_set_int.c */
+
+/* Start: bn_mp_init_size.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_SIZE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* init an mp_init for a given size */
+int mp_init_size (mp_int * a, int size)
{
+ int x;
/* pad size so there are always extra digits */
- size += (MP_PREC * 2) - (size & (MP_PREC - 1));
+ size += (MP_PREC * 2) - (size % MP_PREC);
/* alloc mem */
- a->dp = OPT_CAST calloc (sizeof (mp_digit), size);
+ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
if (a->dp == NULL) {
return MP_MEM;
}
- a->used = 0;
+
+ /* set the members */
+ a->used = 0;
a->alloc = size;
- a->sign = MP_ZPOS;
+ a->sign = MP_ZPOS;
+
+ /* zero the digits */
+ for (x = 0; x < size; x++) {
+ a->dp[x] = 0;
+ }
return MP_OKAY;
}
+#endif
/* End: bn_mp_init_size.c */
/* Start: bn_mp_invmod.c */
+#include <tommath.h>
+#ifdef BN_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
+
+/* hac 14.61, pp608 */
+int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
+{
+ /* b cannot be negative */
+ if (b->sign == MP_NEG || mp_iszero(b) == 1) {
+ return MP_VAL;
+ }
+
+#ifdef BN_FAST_MP_INVMOD_C
+ /* if the modulus is odd we can use a faster routine instead */
+ if (mp_isodd (b) == 1) {
+ return fast_mp_invmod (a, b, c);
+ }
+#endif
+
+#ifdef BN_MP_INVMOD_SLOW_C
+ return mp_invmod_slow(a, b, c);
+#endif
+
+ return MP_VAL;
+}
+#endif
+
+/* End: bn_mp_invmod.c */
+
+/* Start: bn_mp_invmod_slow.c */
#include <tommath.h>
+#ifdef BN_MP_INVMOD_SLOW_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
-int
-mp_invmod (mp_int * a, mp_int * b, mp_int * c)
+/* hac 14.61, pp608 */
+int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
{
mp_int x, y, u, v, A, B, C, D;
int res;
/* b cannot be negative */
- if (b->sign == MP_NEG) {
+ if (b->sign == MP_NEG || mp_iszero(b) == 1) {
return MP_VAL;
}
- /* if the modulus is odd we can use a faster routine instead */
- if (mp_iseven (b) == 0) {
- return fast_mp_invmod (a, b, c);
- }
-
/* init temps */
- if ((res = mp_init_multi(&x, &y, &u, &v, &A, &B, &C, &D, NULL)) != MP_OKAY) {
+ if ((res = mp_init_multi(&x, &y, &u, &v,
+ &A, &B, &C, &D, NULL)) != MP_OKAY) {
return res;
}
/* x = a, y = b */
- if ((res = mp_copy (a, &x)) != MP_OKAY) {
- goto __ERR;
+ if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
+ goto LBL_ERR;
}
if ((res = mp_copy (b, &y)) != MP_OKAY) {
- goto __ERR;
- }
-
- if ((res = mp_abs (&x, &x)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
/* 2. [modified] if x,y are both even then return an error! */
if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
res = MP_VAL;
- goto __ERR;
+ goto LBL_ERR;
}
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
if ((res = mp_copy (&x, &u)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
if ((res = mp_copy (&y, &v)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
mp_set (&A, 1);
mp_set (&D, 1);
-
top:
/* 4. while u is even do */
while (mp_iseven (&u) == 1) {
/* 4.1 u = u/2 */
if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
/* 4.2 if A or B is odd then */
- if (mp_iseven (&A) == 0 || mp_iseven (&B) == 0) {
+ if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
/* A = (A+y)/2, B = (B-x)/2 */
if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
}
/* A = A/2, B = B/2 */
if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
}
-
/* 5. while v is even do */
while (mp_iseven (&v) == 1) {
/* 5.1 v = v/2 */
if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
- /* 5.2 if C,D are even then */
- if (mp_iseven (&C) == 0 || mp_iseven (&D) == 0) {
+ /* 5.2 if C or D is odd then */
+ if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
/* C = (C+y)/2, D = (D-x)/2 */
if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
}
/* C = C/2, D = D/2 */
if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
}
if (mp_cmp (&u, &v) != MP_LT) {
/* u = u - v, A = A - C, B = B - D */
if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
} else {
/* v - v - u, C = C - A, D = D - B */
if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
- goto __ERR;
+ goto LBL_ERR;
}
}
/* if v != 1 then there is no inverse */
if (mp_cmp_d (&v, 1) != MP_EQ) {
res = MP_VAL;
- goto __ERR;
+ goto LBL_ERR;
}
- /* a is now the inverse */
+ /* if its too low */
+ while (mp_cmp_d(&C, 0) == MP_LT) {
+ if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* too big */
+ while (mp_cmp_mag(&C, b) != MP_LT) {
+ if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* C is now the inverse */
mp_exch (&C, c);
res = MP_OKAY;
+LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
+ return res;
+}
+#endif
+
+/* End: bn_mp_invmod_slow.c */
+
+/* Start: bn_mp_is_square.c */
+#include <tommath.h>
+#ifdef BN_MP_IS_SQUARE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* Check if remainders are possible squares - fast exclude non-squares */
+static const char rem_128[128] = {
+ 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1
+};
+
+static const char rem_105[105] = {
+ 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
+ 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1,
+ 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
+ 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
+ 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1,
+ 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1
+};
+
+/* Store non-zero to ret if arg is square, and zero if not */
+int mp_is_square(mp_int *arg,int *ret)
+{
+ int res;
+ mp_digit c;
+ mp_int t;
+ unsigned long r;
+
+ /* Default to Non-square :) */
+ *ret = MP_NO;
+
+ if (arg->sign == MP_NEG) {
+ return MP_VAL;
+ }
+
+ /* digits used? (TSD) */
+ if (arg->used == 0) {
+ return MP_OKAY;
+ }
+
+ /* First check mod 128 (suppose that DIGIT_BIT is at least 7) */
+ if (rem_128[127 & DIGIT(arg,0)] == 1) {
+ return MP_OKAY;
+ }
+
+ /* Next check mod 105 (3*5*7) */
+ if ((res = mp_mod_d(arg,105,&c)) != MP_OKAY) {
+ return res;
+ }
+ if (rem_105[c] == 1) {
+ return MP_OKAY;
+ }
+
+
+ if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) {
+ return res;
+ }
+ if ((res = mp_mod(arg,&t,&t)) != MP_OKAY) {
+ goto ERR;
+ }
+ r = mp_get_int(&t);
+ /* Check for other prime modules, note it's not an ERROR but we must
+ * free "t" so the easiest way is to goto ERR. We know that res
+ * is already equal to MP_OKAY from the mp_mod call
+ */
+ if ( (1L<<(r%11)) & 0x5C4L ) goto ERR;
+ if ( (1L<<(r%13)) & 0x9E4L ) goto ERR;
+ if ( (1L<<(r%17)) & 0x5CE8L ) goto ERR;
+ if ( (1L<<(r%19)) & 0x4F50CL ) goto ERR;
+ if ( (1L<<(r%23)) & 0x7ACCA0L ) goto ERR;
+ if ( (1L<<(r%29)) & 0xC2EDD0CL ) goto ERR;
+ if ( (1L<<(r%31)) & 0x6DE2B848L ) goto ERR;
+
+ /* Final check - is sqr(sqrt(arg)) == arg ? */
+ if ((res = mp_sqrt(arg,&t)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sqr(&t,&t)) != MP_OKAY) {
+ goto ERR;
+ }
-__ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
+ *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO;
+ERR:mp_clear(&t);
return res;
}
+#endif
-/* End: bn_mp_invmod.c */
+/* End: bn_mp_is_square.c */
/* Start: bn_mp_jacobi.c */
+#include <tommath.h>
+#ifdef BN_MP_JACOBI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes the jacobi c = (a | n) (or Legendre if n is prime)
* HAC pp. 73 Algorithm 2.149
*/
-int
-mp_jacobi (mp_int * a, mp_int * n, int *c)
+int mp_jacobi (mp_int * a, mp_int * p, int *c)
{
- mp_int a1, n1, e;
- int s, r, res;
+ mp_int a1, p1;
+ int k, s, r, res;
mp_digit residue;
+ /* if p <= 0 return MP_VAL */
+ if (mp_cmp_d(p, 0) != MP_GT) {
+ return MP_VAL;
+ }
+
/* step 1. if a == 0, return 0 */
if (mp_iszero (a) == 1) {
*c = 0;
/* default */
s = 0;
- /* step 3. write a = a1 * 2^e */
+ /* step 3. write a = a1 * 2**k */
if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
return res;
}
- if ((res = mp_init (&n1)) != MP_OKAY) {
- goto __A1;
- }
-
- if ((res = mp_init (&e)) != MP_OKAY) {
- goto __N1;
+ if ((res = mp_init (&p1)) != MP_OKAY) {
+ goto LBL_A1;
}
- while (mp_iseven (&a1) == 1) {
- if ((res = mp_add_d (&e, 1, &e)) != MP_OKAY) {
- goto __E;
- }
-
- if ((res = mp_div_2 (&a1, &a1)) != MP_OKAY) {
- goto __E;
- }
+ /* divide out larger power of two */
+ k = mp_cnt_lsb(&a1);
+ if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
+ goto LBL_P1;
}
/* step 4. if e is even set s=1 */
- if (mp_iseven (&e) == 1) {
+ if ((k & 1) == 0) {
s = 1;
} else {
- /* else set s=1 if n = 1/7 (mod 8) or s=-1 if n = 3/5 (mod 8) */
- if ((res = mp_mod_d (n, 8, &residue)) != MP_OKAY) {
- goto __E;
- }
+ /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
+ residue = p->dp[0] & 7;
if (residue == 1 || residue == 7) {
s = 1;
}
}
- /* step 5. if n == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
- if ((res = mp_mod_d (n, 4, &residue)) != MP_OKAY) {
- goto __E;
- }
- if (residue == 3) {
- if ((res = mp_mod_d (&a1, 4, &residue)) != MP_OKAY) {
- goto __E;
- }
- if (residue == 3) {
- s = -s;
- }
+ /* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
+ if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
+ s = -s;
}
/* if a1 == 1 we're done */
*c = s;
} else {
/* n1 = n mod a1 */
- if ((res = mp_mod (n, &a1, &n1)) != MP_OKAY) {
- goto __E;
+ if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) {
+ goto LBL_P1;
}
- if ((res = mp_jacobi (&n1, &a1, &r)) != MP_OKAY) {
- goto __E;
+ if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
+ goto LBL_P1;
}
*c = s * r;
}
/* done */
res = MP_OKAY;
-__E:mp_clear (&e);
-__N1:mp_clear (&n1);
-__A1:mp_clear (&a1);
+LBL_P1:mp_clear (&p1);
+LBL_A1:mp_clear (&a1);
return res;
}
+#endif
/* End: bn_mp_jacobi.c */
/* Start: bn_mp_karatsuba_mul.c */
+#include <tommath.h>
+#ifdef BN_MP_KARATSUBA_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* c = |a| * |b| using Karatsuba Multiplication using
* three half size multiplications
* Generally though the overhead of this method doesn't pay off
* until a certain size (N ~ 80) is reached.
*/
-int
-mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
+int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
{
mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
int B, err;
B = MIN (a->used, b->used);
/* now divide in two */
- B = B / 2;
+ B = B >> 1;
/* init copy all the temps */
if (mp_init_size (&x0, B) != MP_OKAY)
goto X0Y0;
/* now shift the digits */
- x0.sign = x1.sign = a->sign;
- y0.sign = y1.sign = b->sign;
-
x0.used = y0.used = B;
x1.used = a->used - B;
y1.used = b->used - B;
ERR:
return err;
}
+#endif
/* End: bn_mp_karatsuba_mul.c */
/* Start: bn_mp_karatsuba_sqr.c */
+#include <tommath.h>
+#ifdef BN_MP_KARATSUBA_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Karatsuba squaring, computes b = a*a using three
* half size squarings
*
- * See comments of mp_karatsuba_mul for details. It
+ * See comments of karatsuba_mul for details. It
* is essentially the same algorithm but merely
* tuned to perform recursive squarings.
*/
-int
-mp_karatsuba_sqr (mp_int * a, mp_int * b)
+int mp_karatsuba_sqr (mp_int * a, mp_int * b)
{
mp_int x0, x1, t1, t2, x0x0, x1x1;
int B, err;
B = a->used;
/* now divide in two */
- B = B / 2;
+ B = B >> 1;
/* init copy all the temps */
if (mp_init_size (&x0, B) != MP_OKAY)
ERR:
return err;
}
+#endif
/* End: bn_mp_karatsuba_sqr.c */
/* Start: bn_mp_lcm.c */
+#include <tommath.h>
+#ifdef BN_MP_LCM_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* computes least common multiple as a*b/(a, b) */
-int
-mp_lcm (mp_int * a, mp_int * b, mp_int * c)
+/* computes least common multiple as |a*b|/(a, b) */
+int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
{
int res;
- mp_int t;
+ mp_int t1, t2;
- if ((res = mp_init (&t)) != MP_OKAY) {
+ if ((res = mp_init_multi (&t1, &t2, NULL)) != MP_OKAY) {
return res;
}
- if ((res = mp_mul (a, b, &t)) != MP_OKAY) {
- mp_clear (&t);
- return res;
+ /* t1 = get the GCD of the two inputs */
+ if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) {
+ goto LBL_T;
}
- if ((res = mp_gcd (a, b, c)) != MP_OKAY) {
- mp_clear (&t);
- return res;
+ /* divide the smallest by the GCD */
+ if (mp_cmp_mag(a, b) == MP_LT) {
+ /* store quotient in t2 such that t2 * b is the LCM */
+ if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
+ goto LBL_T;
+ }
+ res = mp_mul(b, &t2, c);
+ } else {
+ /* store quotient in t2 such that t2 * a is the LCM */
+ if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
+ goto LBL_T;
+ }
+ res = mp_mul(a, &t2, c);
}
- res = mp_div (&t, c, c, NULL);
- mp_clear (&t);
+ /* fix the sign to positive */
+ c->sign = MP_ZPOS;
+
+LBL_T:
+ mp_clear_multi (&t1, &t2, NULL);
return res;
}
+#endif
/* End: bn_mp_lcm.c */
/* Start: bn_mp_lshd.c */
+#include <tommath.h>
+#ifdef BN_MP_LSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift left a certain amount of digits */
-int
-mp_lshd (mp_int * a, int b)
+int mp_lshd (mp_int * a, int b)
{
int x, res;
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_lshd.c */
/* Start: bn_mp_mod.c */
+#include <tommath.h>
+#ifdef BN_MP_MOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* c = a mod b, 0 <= c < b */
int
mp_int t;
int res;
-
if ((res = mp_init (&t)) != MP_OKAY) {
return res;
}
return res;
}
- if (t.sign == MP_NEG) {
+ if (t.sign != b->sign) {
res = mp_add (b, &t, c);
} else {
res = MP_OKAY;
mp_clear (&t);
return res;
}
+#endif
/* End: bn_mp_mod.c */
/* Start: bn_mp_mod_2d.c */
+#include <tommath.h>
+#ifdef BN_MP_MOD_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* calc a value mod 2^b */
+/* calc a value mod 2**b */
int
mp_mod_2d (mp_int * a, int b, mp_int * c)
{
int x, res;
-
/* if b is <= 0 then zero the int */
if (b <= 0) {
mp_zero (c);
}
/* if the modulus is larger than the value than return */
- if (b > (int) (a->used * DIGIT_BIT)) {
+ if (b >= (int) (a->used * DIGIT_BIT)) {
res = mp_copy (a, c);
return res;
}
mp_clamp (c);
return MP_OKAY;
}
+#endif
/* End: bn_mp_mod_2d.c */
/* Start: bn_mp_mod_d.c */
+#include <tommath.h>
+#ifdef BN_MP_MOD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
int
mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
{
return mp_div_d(a, b, NULL, c);
}
+#endif
/* End: bn_mp_mod_d.c */
/* Start: bn_mp_montgomery_calc_normalization.c */
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* calculates a = B^n mod b for Montgomery reduction
- * Where B is the base [e.g. 2^DIGIT_BIT].
- * B^n mod b is computed by first computing
- * A = B^(n-1) which doesn't require a reduction but a simple OR.
- * then C = A * B = B^n is computed by performing upto DIGIT_BIT
+/*
* shifts with subtractions when the result is greater than b.
*
* The method is slightly modified to shift B unconditionally upto just under
* the leading bit of b. This saves alot of multiple precision shifting.
*/
-int
-mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
+int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
{
int x, bits, res;
/* how many bits of last digit does b use */
bits = mp_count_bits (b) % DIGIT_BIT;
- /* compute A = B^(n-1) * 2^(bits-1) */
- if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
- return res;
+ if (b->used > 1) {
+ if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
+ return res;
+ }
+ } else {
+ mp_set(a, 1);
+ bits = 1;
}
+
/* now compute C = A * B mod b */
for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
return MP_OKAY;
}
+#endif
/* End: bn_mp_montgomery_calc_normalization.c */
/* Start: bn_mp_montgomery_reduce.c */
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int
/* can the fast reduction [comba] method be used?
*
- * Note that unlike in mp_mul you're safely allowed *less*
+ * Note that unlike in mul you're safely allowed *less*
* than the available columns [255 per default] since carries
* are fixed up in the inner loop.
*/
digs = n->used * 2 + 1;
- if ((digs < MP_WARRAY) &&
- n->used <
+ if ((digs < MP_WARRAY) &&
+ n->used <
(1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
return fast_mp_montgomery_reduce (x, n, rho);
}
x->used = digs;
for (ix = 0; ix < n->used; ix++) {
- /* mu = ai * m' mod b */
- mu = (x->dp[ix] * rho) & MP_MASK;
+ /* mu = ai * rho mod b
+ *
+ * The value of rho must be precalculated via
+ * montgomery_setup() such that
+ * it equals -1/n0 mod b this allows the
+ * following inner loop to reduce the
+ * input one digit at a time
+ */
+ mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
/* a = a + mu * m * b**i */
{
register mp_digit *tmpn, *tmpx, u;
register mp_word r;
- /* aliases */
+ /* alias for digits of the modulus */
tmpn = n->dp;
+
+ /* alias for the digits of x [the input] */
tmpx = x->dp + ix;
/* set the carry to zero */
u = 0;
-
+
/* Multiply and add in place */
for (iy = 0; iy < n->used; iy++) {
- r = ((mp_word) mu) * ((mp_word) * tmpn++) +
+ /* compute product and sum */
+ r = ((mp_word)mu) * ((mp_word)*tmpn++) +
((mp_word) u) + ((mp_word) * tmpx);
+
+ /* get carry */
u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+
+ /* fix digit */
*tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
}
- /* propagate carries */
+ /* At this point the ix'th digit of x should be zero */
+
+
+ /* propagate carries upwards as required*/
while (u) {
*tmpx += u;
u = *tmpx >> DIGIT_BIT;
}
}
+ /* at this point the n.used'th least
+ * significant digits of x are all zero
+ * which means we can shift x to the
+ * right by n.used digits and the
+ * residue is unchanged.
+ */
+
/* x = x/b**n.used */
mp_clamp(x);
mp_rshd (x, n->used);
- /* if A >= m then A = A - m */
+ /* if x >= n then x = x - n */
if (mp_cmp_mag (x, n) != MP_LT) {
return s_mp_sub (x, n, x);
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_montgomery_reduce.c */
/* Start: bn_mp_montgomery_setup.c */
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* setups the montgomery reduction stuff */
int
#endif
/* rho = -1/m mod b */
- *rho = (((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - x) & MP_MASK;
+ *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
return MP_OKAY;
}
+#endif
/* End: bn_mp_montgomery_setup.c */
/* Start: bn_mp_mul.c */
+#include <tommath.h>
+#ifdef BN_MP_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* high level multiplication (handles sign) */
-int
-mp_mul (mp_int * a, mp_int * b, mp_int * c)
+int mp_mul (mp_int * a, mp_int * b, mp_int * c)
{
int res, neg;
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
-
+
+ /* use Toom-Cook? */
+#ifdef BN_MP_TOOM_MUL_C
if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
res = mp_toom_mul(a, b, c);
- } else if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_MUL_C
+ /* use Karatsuba? */
+ if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
res = mp_karatsuba_mul (a, b, c);
- } else {
-
+ } else
+#endif
+ {
/* can we use the fast multiplier?
*
* The fast multiplier can be used if the output will
*/
int digs = a->used + b->used + 1;
+#ifdef BN_FAST_S_MP_MUL_DIGS_C
if ((digs < MP_WARRAY) &&
MIN(a->used, b->used) <=
(1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
res = fast_s_mp_mul_digs (a, b, c, digs);
- } else {
- res = s_mp_mul (a, b, c);
- }
+ } else
+#endif
+#ifdef BN_S_MP_MUL_DIGS_C
+ res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
+#else
+ res = MP_VAL;
+#endif
}
- c->sign = neg;
+ c->sign = (c->used > 0) ? neg : MP_ZPOS;
return res;
}
+#endif
/* End: bn_mp_mul.c */
/* Start: bn_mp_mul_2.c */
+#include <tommath.h>
+#ifdef BN_MP_MUL_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = a*2 */
-int
-mp_mul_2 (mp_int * a, mp_int * b)
+int mp_mul_2(mp_int * a, mp_int * b)
{
int x, res, oldused;
if (r != 0) {
/* add a MSB which is always 1 at this point */
*tmpb = 1;
- ++b->used;
+ ++(b->used);
}
/* now zero any excess digits on the destination
b->sign = a->sign;
return MP_OKAY;
}
+#endif
/* End: bn_mp_mul_2.c */
/* Start: bn_mp_mul_2d.c */
+#include <tommath.h>
+#ifdef BN_MP_MUL_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-
-/* NOTE: This routine requires updating. For instance the c->used = c->alloc bit
- is wrong. We should just shift c->used digits then set the carry as c->dp[c->used] = carry
-
- To be fixed for LTM 0.18
- */
/* shift left by a certain bit count */
-int
-mp_mul_2d (mp_int * a, int b, mp_int * c)
+int mp_mul_2d (mp_int * a, int b, mp_int * c)
{
mp_digit d;
int res;
}
}
- if (c->alloc < (int)(c->used + b/DIGIT_BIT + 2)) {
- if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 2)) != MP_OKAY) {
+ if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
+ if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
return res;
}
}
return res;
}
}
- c->used = c->alloc;
/* shift any bit count < DIGIT_BIT */
d = (mp_digit) (b % DIGIT_BIT);
if (d != 0) {
- register mp_digit *tmpc, mask, r, rr;
+ register mp_digit *tmpc, shift, mask, r, rr;
register int x;
/* bitmask for carries */
mask = (((mp_digit)1) << d) - 1;
+ /* shift for msbs */
+ shift = DIGIT_BIT - d;
+
/* alias */
tmpc = c->dp;
r = 0;
for (x = 0; x < c->used; x++) {
/* get the higher bits of the current word */
- rr = (*tmpc >> (DIGIT_BIT - d)) & mask;
+ rr = (*tmpc >> shift) & mask;
/* shift the current word and OR in the carry */
*tmpc = ((*tmpc << d) | r) & MP_MASK;
/* set the carry to the carry bits of the current word */
r = rr;
}
+
+ /* set final carry */
+ if (r != 0) {
+ c->dp[(c->used)++] = r;
+ }
}
mp_clamp (c);
return MP_OKAY;
}
+#endif
/* End: bn_mp_mul_2d.c */
/* Start: bn_mp_mul_d.c */
+#include <tommath.h>
+#ifdef BN_MP_MUL_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* multiply by a digit */
int
mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
{
- int res, pa, olduse;
+ mp_digit u, *tmpa, *tmpc;
+ mp_word r;
+ int ix, res, olduse;
/* make sure c is big enough to hold a*b */
- pa = a->used;
- if (c->alloc < pa + 1) {
- if ((res = mp_grow (c, pa + 1)) != MP_OKAY) {
+ if (c->alloc < a->used + 1) {
+ if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
return res;
}
}
/* get the original destinations used count */
olduse = c->used;
- /* set the new temporary used count */
- c->used = pa + 1;
+ /* set the sign */
c->sign = a->sign;
- {
- register mp_digit u, *tmpa, *tmpc;
- register mp_word r;
- register int ix;
+ /* alias for a->dp [source] */
+ tmpa = a->dp;
- /* alias for a->dp [source] */
- tmpa = a->dp;
+ /* alias for c->dp [dest] */
+ tmpc = c->dp;
- /* alias for c->dp [dest] */
- tmpc = c->dp;
+ /* zero carry */
+ u = 0;
- /* zero carry */
- u = 0;
- for (ix = 0; ix < pa; ix++) {
- /* compute product and carry sum for this term */
- r = ((mp_word) u) + ((mp_word) * tmpa++) * ((mp_word) b);
+ /* compute columns */
+ for (ix = 0; ix < a->used; ix++) {
+ /* compute product and carry sum for this term */
+ r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
- /* mask off higher bits to get a single digit */
- *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
+ /* mask off higher bits to get a single digit */
+ *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
- /* send carry into next iteration */
- u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
- }
- /* store final carry [if any] */
- *tmpc++ = u;
+ /* send carry into next iteration */
+ u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
+ }
- /* now zero digits above the top */
- for (; pa < olduse; pa++) {
- *tmpc++ = 0;
- }
+ /* store final carry [if any] and increment ix offset */
+ *tmpc++ = u;
+ ++ix;
+
+ /* now zero digits above the top */
+ while (ix++ < olduse) {
+ *tmpc++ = 0;
}
- mp_clamp (c);
+ /* set used count */
+ c->used = a->used + 1;
+ mp_clamp(c);
+
return MP_OKAY;
}
+#endif
/* End: bn_mp_mul_d.c */
/* Start: bn_mp_mulmod.c */
+#include <tommath.h>
+#ifdef BN_MP_MULMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* d = a * b (mod c) */
int
int res;
mp_int t;
-
if ((res = mp_init (&t)) != MP_OKAY) {
return res;
}
mp_clear (&t);
return res;
}
+#endif
/* End: bn_mp_mulmod.c */
-/* Start: bn_mp_multi.c */
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is library that provides for multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library is designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-#include <tommath.h>
-#include <stdarg.h>
-
-int mp_init_multi(mp_int *mp, ...)
-{
- mp_err res = MP_OKAY; /* Assume ok until proven otherwise */
- int n = 0; /* Number of ok inits */
- mp_int* cur_arg = mp;
- va_list args;
-
- va_start(args, mp); /* init args to next argument from caller */
- while (cur_arg != NULL) {
- if (mp_init(cur_arg) != MP_OKAY) {
- /* Oops - error! Back-track and mp_clear what we already
- succeeded in init-ing, then return error.
- */
- va_list clean_args;
-
- /* end the current list */
- va_end(args);
-
- /* now start cleaning up */
- cur_arg = mp;
- va_start(clean_args, mp);
- while (n--) {
- mp_clear(cur_arg);
- cur_arg = va_arg(clean_args, mp_int*);
- }
- va_end(clean_args);
- res = MP_MEM;
- break;
- }
- n++;
- cur_arg = va_arg(args, mp_int*);
- }
- va_end(args);
- return res; /* Assumed ok, if error flagged above. */
-}
-
-void mp_clear_multi(mp_int *mp, ...)
-{
- mp_int* next_mp = mp;
- va_list args;
- va_start(args, mp);
- while (next_mp != NULL) {
- mp_clear(next_mp);
- next_mp = va_arg(args, mp_int*);
- }
- va_end(args);
-}
-
-/* End: bn_mp_multi.c */
-
/* Start: bn_mp_n_root.c */
+#include <tommath.h>
+#ifdef BN_MP_N_ROOT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* find the n'th root of an integer
*
* each step involves a fair bit. This is not meant to
* find huge roots [square and cube, etc].
*/
-int
-mp_n_root (mp_int * a, mp_digit b, mp_int * c)
+int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
{
mp_int t1, t2, t3;
int res, neg;
}
if ((res = mp_init (&t2)) != MP_OKAY) {
- goto __T1;
+ goto LBL_T1;
}
if ((res = mp_init (&t3)) != MP_OKAY) {
- goto __T2;
+ goto LBL_T2;
}
/* if a is negative fudge the sign but keep track */
- neg = a->sign;
+ neg = a->sign;
a->sign = MP_ZPOS;
/* t2 = 2 */
do {
/* t1 = t2 */
if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
- goto __T3;
+ goto LBL_T3;
}
/* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
/* t3 = t1**(b-1) */
if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) {
- goto __T3;
+ goto LBL_T3;
}
/* numerator */
/* t2 = t1**b */
if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
- goto __T3;
+ goto LBL_T3;
}
/* t2 = t1**b - a */
if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
- goto __T3;
+ goto LBL_T3;
}
/* denominator */
/* t3 = t1**(b-1) * b */
if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
- goto __T3;
+ goto LBL_T3;
}
/* t3 = (t1**b - a)/(b * t1**(b-1)) */
if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
- goto __T3;
+ goto LBL_T3;
}
if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
- goto __T3;
+ goto LBL_T3;
}
} while (mp_cmp (&t1, &t2) != MP_EQ);
/* result can be off by a few so check */
for (;;) {
if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) {
- goto __T3;
+ goto LBL_T3;
}
if (mp_cmp (&t2, a) == MP_GT) {
if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
- goto __T3;
+ goto LBL_T3;
}
} else {
break;
res = MP_OKAY;
-__T3:mp_clear (&t3);
-__T2:mp_clear (&t2);
-__T1:mp_clear (&t1);
+LBL_T3:mp_clear (&t3);
+LBL_T2:mp_clear (&t2);
+LBL_T1:mp_clear (&t1);
return res;
}
+#endif
/* End: bn_mp_n_root.c */
/* Start: bn_mp_neg.c */
+#include <tommath.h>
+#ifdef BN_MP_NEG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = -a */
-int
-mp_neg (mp_int * a, mp_int * b)
+int mp_neg (mp_int * a, mp_int * b)
{
int res;
- if ((res = mp_copy (a, b)) != MP_OKAY) {
- return res;
+ if (a != b) {
+ if ((res = mp_copy (a, b)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ if (mp_iszero(b) != MP_YES) {
+ b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
+ } else {
+ b->sign = MP_ZPOS;
}
- b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
+
return MP_OKAY;
}
+#endif
/* End: bn_mp_neg.c */
/* Start: bn_mp_or.c */
+#include <tommath.h>
+#ifdef BN_MP_OR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* OR two ints together */
-int
-mp_or (mp_int * a, mp_int * b, mp_int * c)
+int mp_or (mp_int * a, mp_int * b, mp_int * c)
{
int res, ix, px;
mp_int t, *x;
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_mp_or.c */
/* Start: bn_mp_prime_fermat.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_FERMAT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* performs one Fermat test.
*
- * If "a" were prime then b^a == b (mod a) since the order of
+ * If "a" were prime then b**a == b (mod a) since the order of
* the multiplicative sub-group would be phi(a) = a-1. That means
- * it would be the same as b^(a mod (a-1)) == b^1 == b (mod a).
+ * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a).
*
* Sets result to 1 if the congruence holds, or zero otherwise.
*/
-int
-mp_prime_fermat (mp_int * a, mp_int * b, int *result)
+int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
{
mp_int t;
int err;
- /* default to fail */
- *result = 0;
+ /* default to composite */
+ *result = MP_NO;
+
+ /* ensure b > 1 */
+ if (mp_cmp_d(b, 1) != MP_GT) {
+ return MP_VAL;
+ }
/* init t */
if ((err = mp_init (&t)) != MP_OKAY) {
return err;
}
- /* compute t = b^a mod a */
+ /* compute t = b**a mod a */
if ((err = mp_exptmod (b, a, a, &t)) != MP_OKAY) {
- goto __T;
+ goto LBL_T;
}
/* is it equal to b? */
if (mp_cmp (&t, b) == MP_EQ) {
- *result = 1;
+ *result = MP_YES;
}
err = MP_OKAY;
-__T:mp_clear (&t);
+LBL_T:mp_clear (&t);
return err;
}
+#endif
/* End: bn_mp_prime_fermat.c */
/* Start: bn_mp_prime_is_divisible.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* determines if an integers is divisible by one of the first 256 primes or not
+/* determines if an integers is divisible by one
+ * of the first PRIME_SIZE primes or not
*
* sets result to 0 if not, 1 if yes
*/
-int
-mp_prime_is_divisible (mp_int * a, int *result)
+int mp_prime_is_divisible (mp_int * a, int *result)
{
int err, ix;
mp_digit res;
/* default to not */
- *result = 0;
+ *result = MP_NO;
for (ix = 0; ix < PRIME_SIZE; ix++) {
- /* is it equal to the prime? */
- if (mp_cmp_d (a, __prime_tab[ix]) == MP_EQ) {
- *result = 1;
- return MP_OKAY;
- }
-
- /* what is a mod __prime_tab[ix] */
- if ((err = mp_mod_d (a, __prime_tab[ix], &res)) != MP_OKAY) {
+ /* what is a mod LBL_prime_tab[ix] */
+ if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) {
return err;
}
/* is the residue zero? */
if (res == 0) {
- *result = 1;
+ *result = MP_YES;
return MP_OKAY;
}
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_prime_is_divisible.c */
/* Start: bn_mp_prime_is_prime.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_IS_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* performs a variable number of rounds of Miller-Rabin
*
* Probability of error after t rounds is no more than
- * (1/4)^t when 1 <= t <= 256
+
*
* Sets result to 1 if probably prime, 0 otherwise
*/
-int
-mp_prime_is_prime (mp_int * a, int t, int *result)
+int mp_prime_is_prime (mp_int * a, int t, int *result)
{
mp_int b;
int ix, err, res;
/* default to no */
- *result = 0;
+ *result = MP_NO;
/* valid value of t? */
- if (t < 1 || t > PRIME_SIZE) {
+ if (t <= 0 || t > PRIME_SIZE) {
return MP_VAL;
}
/* is the input equal to one of the primes in the table? */
for (ix = 0; ix < PRIME_SIZE; ix++) {
- if (mp_cmp_d(a, __prime_tab[ix]) == MP_EQ) {
+ if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
*result = 1;
return MP_OKAY;
}
if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
return err;
}
- if (res == 1) {
+
+ /* return if it was trivially divisible */
+ if (res == MP_YES) {
return MP_OKAY;
}
for (ix = 0; ix < t; ix++) {
/* set the prime */
- mp_set (&b, __prime_tab[ix]);
+ mp_set (&b, ltm_prime_tab[ix]);
if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
- goto __B;
+ goto LBL_B;
}
- if (res == 0) {
- goto __B;
+ if (res == MP_NO) {
+ goto LBL_B;
}
}
/* passed the test */
- *result = 1;
-__B:mp_clear (&b);
+ *result = MP_YES;
+LBL_B:mp_clear (&b);
return err;
}
+#endif
/* End: bn_mp_prime_is_prime.c */
/* Start: bn_mp_prime_miller_rabin.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_MILLER_RABIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Miller-Rabin test of "a" to the base of "b" as described in
* HAC pp. 139 Algorithm 4.24
* Randomly the chance of error is no more than 1/4 and often
* very much lower.
*/
-int
-mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
+int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
{
mp_int n1, y, r;
int s, j, err;
/* default */
- *result = 0;
+ *result = MP_NO;
+
+ /* ensure b > 1 */
+ if (mp_cmp_d(b, 1) != MP_GT) {
+ return MP_VAL;
+ }
/* get n1 = a - 1 */
if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
return err;
}
if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) {
- goto __N1;
+ goto LBL_N1;
}
- /* set 2^s * r = n1 */
+ /* set 2**s * r = n1 */
if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
- goto __N1;
+ goto LBL_N1;
}
- s = 0;
- while (mp_iseven (&r) == 1) {
- ++s;
- if ((err = mp_div_2 (&r, &r)) != MP_OKAY) {
- goto __R;
- }
+
+ /* count the number of least significant bits
+ * which are zero
+ */
+ s = mp_cnt_lsb(&r);
+
+ /* now divide n - 1 by 2**s */
+ if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
+ goto LBL_R;
}
- /* compute y = b^r mod a */
+ /* compute y = b**r mod a */
if ((err = mp_init (&y)) != MP_OKAY) {
- goto __R;
+ goto LBL_R;
}
if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
- goto __Y;
+ goto LBL_Y;
}
/* if y != 1 and y != n1 do */
/* while j <= s-1 and y != n1 */
while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
- goto __Y;
+ goto LBL_Y;
}
/* if y == 1 then composite */
if (mp_cmp_d (&y, 1) == MP_EQ) {
- goto __Y;
+ goto LBL_Y;
}
++j;
/* if y != n1 then composite */
if (mp_cmp (&y, &n1) != MP_EQ) {
- goto __Y;
+ goto LBL_Y;
}
}
/* probably prime now */
- *result = 1;
-__Y:mp_clear (&y);
-__R:mp_clear (&r);
-__N1:mp_clear (&n1);
+ *result = MP_YES;
+LBL_Y:mp_clear (&y);
+LBL_R:mp_clear (&r);
+LBL_N1:mp_clear (&n1);
return err;
}
+#endif
/* End: bn_mp_prime_miller_rabin.c */
/* Start: bn_mp_prime_next_prime.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_NEXT_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* finds the next prime after the number "a" using "t" trials
* of Miller-Rabin.
+ *
+ * bbs_style = 1 means the prime must be congruent to 3 mod 4
*/
-int mp_prime_next_prime(mp_int *a, int t)
+int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
{
- int err, res;
+ int err, res, x, y;
+ mp_digit res_tab[PRIME_SIZE], step, kstep;
+ mp_int b;
- if (mp_iseven(a) == 1) {
- /* force odd */
- if ((err = mp_add_d(a, 1, a)) != MP_OKAY) {
- return err;
+ /* ensure t is valid */
+ if (t <= 0 || t > PRIME_SIZE) {
+ return MP_VAL;
+ }
+
+ /* force positive */
+ a->sign = MP_ZPOS;
+
+ /* simple algo if a is less than the largest prime in the table */
+ if (mp_cmp_d(a, ltm_prime_tab[PRIME_SIZE-1]) == MP_LT) {
+ /* find which prime it is bigger than */
+ for (x = PRIME_SIZE - 2; x >= 0; x--) {
+ if (mp_cmp_d(a, ltm_prime_tab[x]) != MP_LT) {
+ if (bbs_style == 1) {
+ /* ok we found a prime smaller or
+ * equal [so the next is larger]
+ *
+ * however, the prime must be
+ * congruent to 3 mod 4
+ */
+ if ((ltm_prime_tab[x + 1] & 3) != 3) {
+ /* scan upwards for a prime congruent to 3 mod 4 */
+ for (y = x + 1; y < PRIME_SIZE; y++) {
+ if ((ltm_prime_tab[y] & 3) == 3) {
+ mp_set(a, ltm_prime_tab[y]);
+ return MP_OKAY;
+ }
+ }
+ }
+ } else {
+ mp_set(a, ltm_prime_tab[x + 1]);
+ return MP_OKAY;
+ }
+ }
+ }
+ /* at this point a maybe 1 */
+ if (mp_cmp_d(a, 1) == MP_EQ) {
+ mp_set(a, 2);
+ return MP_OKAY;
+ }
+ /* fall through to the sieve */
+ }
+
+ /* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */
+ if (bbs_style == 1) {
+ kstep = 4;
+ } else {
+ kstep = 2;
+ }
+
+ /* at this point we will use a combination of a sieve and Miller-Rabin */
+
+ if (bbs_style == 1) {
+ /* if a mod 4 != 3 subtract the correct value to make it so */
+ if ((a->dp[0] & 3) != 3) {
+ if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; };
}
} else {
- /* force to next odd number */
- if ((err = mp_add_d(a, 2, a)) != MP_OKAY) {
+ if (mp_iseven(a) == 1) {
+ /* force odd */
+ if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) {
+ return err;
+ }
+ }
+ }
+
+ /* generate the restable */
+ for (x = 1; x < PRIME_SIZE; x++) {
+ if ((err = mp_mod_d(a, ltm_prime_tab[x], res_tab + x)) != MP_OKAY) {
return err;
}
}
+ /* init temp used for Miller-Rabin Testing */
+ if ((err = mp_init(&b)) != MP_OKAY) {
+ return err;
+ }
+
for (;;) {
- /* is this prime? */
- if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) {
- return err;
+ /* skip to the next non-trivially divisible candidate */
+ step = 0;
+ do {
+ /* y == 1 if any residue was zero [e.g. cannot be prime] */
+ y = 0;
+
+ /* increase step to next candidate */
+ step += kstep;
+
+ /* compute the new residue without using division */
+ for (x = 1; x < PRIME_SIZE; x++) {
+ /* add the step to each residue */
+ res_tab[x] += kstep;
+
+ /* subtract the modulus [instead of using division] */
+ if (res_tab[x] >= ltm_prime_tab[x]) {
+ res_tab[x] -= ltm_prime_tab[x];
+ }
+
+ /* set flag if zero */
+ if (res_tab[x] == 0) {
+ y = 1;
+ }
+ }
+ } while (y == 1 && step < ((((mp_digit)1)<<DIGIT_BIT) - kstep));
+
+ /* add the step */
+ if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
+ goto LBL_ERR;
}
- if (res == 1) {
- break;
+ /* if didn't pass sieve and step == MAX then skip test */
+ if (y == 1 && step >= ((((mp_digit)1)<<DIGIT_BIT) - kstep)) {
+ continue;
}
- /* add two, next candidate */
- if ((err = mp_add_d(a, 2, a)) != MP_OKAY) {
- return err;
+ /* is this prime? */
+ for (x = 0; x < t; x++) {
+ mp_set(&b, ltm_prime_tab[t]);
+ if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if (res == MP_NO) {
+ break;
+ }
+ }
+
+ if (res == MP_YES) {
+ break;
}
}
- return MP_OKAY;
+ err = MP_OKAY;
+LBL_ERR:
+ mp_clear(&b);
+ return err;
}
+#endif
/* End: bn_mp_prime_next_prime.c */
-/* Start: bn_mp_rand.c */
+/* Start: bn_mp_prime_rabin_miller_trials.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* makes a pseudo-random int of a given size */
-int
-mp_rand (mp_int * a, int digits)
-{
- int res;
- mp_digit d;
- mp_zero (a);
- if (digits <= 0) {
- return MP_OKAY;
- }
+static const struct {
+ int k, t;
+} sizes[] = {
+{ 128, 28 },
+{ 256, 16 },
+{ 384, 10 },
+{ 512, 7 },
+{ 640, 6 },
+{ 768, 5 },
+{ 896, 4 },
+{ 1024, 4 }
+};
- /* first place a random non-zero digit */
- do {
- d = ((mp_digit) abs (rand ()));
+/* returns # of RM trials required for a given bit size */
+int mp_prime_rabin_miller_trials(int size)
+{
+ int x;
+
+ for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
+ if (sizes[x].k == size) {
+ return sizes[x].t;
+ } else if (sizes[x].k > size) {
+ return (x == 0) ? sizes[0].t : sizes[x - 1].t;
+ }
+ }
+ return sizes[x-1].t + 1;
+}
+
+
+#endif
+
+/* End: bn_mp_prime_rabin_miller_trials.c */
+
+/* Start: bn_mp_prime_random_ex.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_RANDOM_EX_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* makes a truly random prime of a given size (bits),
+ *
+ * Flags are as follows:
+ *
+ * LTM_PRIME_BBS - make prime congruent to 3 mod 4
+ * LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
+ * LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
+ * LTM_PRIME_2MSB_ON - make the 2nd highest bit one
+ *
+ * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
+ * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
+ * so it can be NULL
+ *
+ */
+
+/* This is possibly the mother of all prime generation functions, muahahahahaha! */
+int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat)
+{
+ unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb;
+ int res, err, bsize, maskOR_msb_offset;
+
+ /* sanity check the input */
+ if (size <= 1 || t <= 0) {
+ return MP_VAL;
+ }
+
+ /* LTM_PRIME_SAFE implies LTM_PRIME_BBS */
+ if (flags & LTM_PRIME_SAFE) {
+ flags |= LTM_PRIME_BBS;
+ }
+
+ /* calc the byte size */
+ bsize = (size>>3) + ((size&7)?1:0);
+
+ /* we need a buffer of bsize bytes */
+ tmp = OPT_CAST(unsigned char) XMALLOC(bsize);
+ if (tmp == NULL) {
+ return MP_MEM;
+ }
+
+ /* calc the maskAND value for the MSbyte*/
+ maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7)));
+
+ /* calc the maskOR_msb */
+ maskOR_msb = 0;
+ maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0;
+ if (flags & LTM_PRIME_2MSB_ON) {
+ maskOR_msb |= 1 << ((size - 2) & 7);
+ } else if (flags & LTM_PRIME_2MSB_OFF) {
+ maskAND &= ~(1 << ((size - 2) & 7));
+ }
+
+ /* get the maskOR_lsb */
+ maskOR_lsb = 1;
+ if (flags & LTM_PRIME_BBS) {
+ maskOR_lsb |= 3;
+ }
+
+ do {
+ /* read the bytes */
+ if (cb(tmp, bsize, dat) != bsize) {
+ err = MP_VAL;
+ goto error;
+ }
+
+ /* work over the MSbyte */
+ tmp[0] &= maskAND;
+ tmp[0] |= 1 << ((size - 1) & 7);
+
+ /* mix in the maskORs */
+ tmp[maskOR_msb_offset] |= maskOR_msb;
+ tmp[bsize-1] |= maskOR_lsb;
+
+ /* read it in */
+ if ((err = mp_read_unsigned_bin(a, tmp, bsize)) != MP_OKAY) { goto error; }
+
+ /* is it prime? */
+ if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; }
+ if (res == MP_NO) {
+ continue;
+ }
+
+ if (flags & LTM_PRIME_SAFE) {
+ /* see if (a-1)/2 is prime */
+ if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) { goto error; }
+ if ((err = mp_div_2(a, a)) != MP_OKAY) { goto error; }
+
+ /* is it prime? */
+ if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; }
+ }
+ } while (res == MP_NO);
+
+ if (flags & LTM_PRIME_SAFE) {
+ /* restore a to the original value */
+ if ((err = mp_mul_2(a, a)) != MP_OKAY) { goto error; }
+ if ((err = mp_add_d(a, 1, a)) != MP_OKAY) { goto error; }
+ }
+
+ err = MP_OKAY;
+error:
+ XFREE(tmp);
+ return err;
+}
+
+
+#endif
+
+/* End: bn_mp_prime_random_ex.c */
+
+/* Start: bn_mp_radix_size.c */
+#include <tommath.h>
+#ifdef BN_MP_RADIX_SIZE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* returns size of ASCII reprensentation */
+int mp_radix_size (mp_int * a, int radix, int *size)
+{
+ int res, digs;
+ mp_int t;
+ mp_digit d;
+
+ *size = 0;
+
+ /* special case for binary */
+ if (radix == 2) {
+ *size = mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1;
+ return MP_OKAY;
+ }
+
+ /* make sure the radix is in range */
+ if (radix < 2 || radix > 64) {
+ return MP_VAL;
+ }
+
+ if (mp_iszero(a) == MP_YES) {
+ *size = 2;
+ return MP_OKAY;
+ }
+
+ /* digs is the digit count */
+ digs = 0;
+
+ /* if it's negative add one for the sign */
+ if (a->sign == MP_NEG) {
+ ++digs;
+ }
+
+ /* init a copy of the input */
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+
+ /* force temp to positive */
+ t.sign = MP_ZPOS;
+
+ /* fetch out all of the digits */
+ while (mp_iszero (&t) == MP_NO) {
+ if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ ++digs;
+ }
+ mp_clear (&t);
+
+ /* return digs + 1, the 1 is for the NULL byte that would be required. */
+ *size = digs + 1;
+ return MP_OKAY;
+}
+
+#endif
+
+/* End: bn_mp_radix_size.c */
+
+/* Start: bn_mp_radix_smap.c */
+#include <tommath.h>
+#ifdef BN_MP_RADIX_SMAP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* chars used in radix conversions */
+const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
+#endif
+
+/* End: bn_mp_radix_smap.c */
+
+/* Start: bn_mp_rand.c */
+#include <tommath.h>
+#ifdef BN_MP_RAND_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* makes a pseudo-random int of a given size */
+int
+mp_rand (mp_int * a, int digits)
+{
+ int res;
+ mp_digit d;
+
+ mp_zero (a);
+ if (digits <= 0) {
+ return MP_OKAY;
+ }
+
+ /* first place a random non-zero digit */
+ do {
+ d = ((mp_digit) abs (rand ())) & MP_MASK;
} while (d == 0);
if ((res = mp_add_d (a, d, a)) != MP_OKAY) {
return res;
}
- while (digits-- > 0) {
+ while (--digits > 0) {
if ((res = mp_lshd (a, 1)) != MP_OKAY) {
return res;
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_rand.c */
-/* Start: bn_mp_read_signed_bin.c */
+/* Start: bn_mp_read_radix.c */
+#include <tommath.h>
+#ifdef BN_MP_READ_RADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
+
+/* read a string [ASCII] in a given radix */
+int mp_read_radix (mp_int * a, const char *str, int radix)
+{
+ int y, res, neg;
+ char ch;
+
+ /* make sure the radix is ok */
+ if (radix < 2 || radix > 64) {
+ return MP_VAL;
+ }
+
+ /* if the leading digit is a
+ * minus set the sign to negative.
+ */
+ if (*str == '-') {
+ ++str;
+ neg = MP_NEG;
+ } else {
+ neg = MP_ZPOS;
+ }
+
+ /* set the integer to the default of zero */
+ mp_zero (a);
+
+ /* process each digit of the string */
+ while (*str) {
+ /* if the radix < 36 the conversion is case insensitive
+ * this allows numbers like 1AB and 1ab to represent the same value
+ * [e.g. in hex]
+ */
+ ch = (char) ((radix < 36) ? toupper (*str) : *str);
+ for (y = 0; y < 64; y++) {
+ if (ch == mp_s_rmap[y]) {
+ break;
+ }
+ }
+
+ /* if the char was found in the map
+ * and is less than the given radix add it
+ * to the number, otherwise exit the loop.
+ */
+ if (y < radix) {
+ if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) {
+ return res;
+ }
+ if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) {
+ return res;
+ }
+ } else {
+ break;
+ }
+ ++str;
+ }
+
+ /* set the sign only if a != 0 */
+ if (mp_iszero(a) != 1) {
+ a->sign = neg;
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* End: bn_mp_read_radix.c */
+
+/* Start: bn_mp_read_signed_bin.c */
#include <tommath.h>
+#ifdef BN_MP_READ_SIGNED_BIN_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
/* read signed bin, big endian, first byte is 0==positive or 1==negative */
int
{
int res;
+ /* read magnitude */
if ((res = mp_read_unsigned_bin (a, b + 1, c - 1)) != MP_OKAY) {
return res;
}
- a->sign = ((b[0] == (unsigned char) 0) ? MP_ZPOS : MP_NEG);
+
+ /* first byte is 0 for positive, non-zero for negative */
+ if (b[0] == 0) {
+ a->sign = MP_ZPOS;
+ } else {
+ a->sign = MP_NEG;
+ }
+
return MP_OKAY;
}
+#endif
/* End: bn_mp_read_signed_bin.c */
/* Start: bn_mp_read_unsigned_bin.c */
+#include <tommath.h>
+#ifdef BN_MP_READ_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reads a unsigned char array, assumes the msb is stored first [big endian] */
int
mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c)
{
int res;
+
+ /* make sure there are at least two digits */
+ if (a->alloc < 2) {
+ if ((res = mp_grow(a, 2)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* zero the int */
mp_zero (a);
+
+ /* read the bytes in */
while (c-- > 0) {
if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
return res;
}
- if (DIGIT_BIT != 7) {
+#ifndef MP_8BIT
a->dp[0] |= *b++;
a->used += 1;
- } else {
+#else
a->dp[0] = (*b & MP_MASK);
a->dp[1] |= ((*b++ >> 7U) & 1);
a->used += 2;
- }
+#endif
}
mp_clamp (a);
return MP_OKAY;
}
+#endif
/* End: bn_mp_read_unsigned_bin.c */
/* Start: bn_mp_reduce.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reduces x mod m, assumes 0 < x < m**2, mu is
* precomputed via mp_reduce_setup.
* From HAC pp.604 Algorithm 14.42
*/
-int
-mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
+int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
{
mp_int q;
int res, um = m->used;
goto CLEANUP;
}
} else {
- if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) {
+#ifdef BN_S_MP_MUL_HIGH_DIGS_C
+ if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
goto CLEANUP;
}
- }
-
- /* q3 = q2 / b**(k+1) */
+#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
+ if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+#else
+ {
+ res = MP_VAL;
+ goto CLEANUP;
+ }
+#endif
+ }
+
+ /* q3 = q2 / b**(k+1) */
mp_rshd (&q, um + 1);
/* x = x mod b**(k+1), quick (no division) */
return res;
}
+#endif
/* End: bn_mp_reduce.c */
/* Start: bn_mp_reduce_2k.c */
-/* LibTomMath, multiple-precision integer library -- Tom St Denis\r
- *\r
- * LibTomMath is library that provides for multiple-precision\r
- * integer arithmetic as well as number theoretic functionality.\r
- *\r
- * The library is designed directly after the MPI library by\r
- * Michael Fromberger but has been written from scratch with\r
- * additional optimizations in place.\r
- *\r
- * The library is free for all purposes without any express\r
- * guarantee it works.\r
- *\r
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org\r
- */\r
-#include <tommath.h>\r
-\r
-/* reduces a modulo n where n is of the form 2**p - k */\r
-int\r
-mp_reduce_2k(mp_int *a, mp_int *n, mp_digit k)\r
-{\r
- mp_int q;\r
- int p, res;\r
- \r
- if ((res = mp_init(&q)) != MP_OKAY) {\r
- return res;\r
- }\r
- \r
- p = mp_count_bits(n); \r
-top:\r
- /* q = a/2**p, a = a mod 2**p */\r
- if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- if (k != 1) {\r
- /* q = q * k */\r
- if ((res = mp_mul_d(&q, k, &q)) != MP_OKAY) { \r
- goto ERR;\r
- }\r
- }\r
- \r
- /* a = a + q */\r
- if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- if (mp_cmp_mag(a, n) != MP_LT) {\r
- s_mp_sub(a, n, a);\r
- goto top;\r
- }\r
- \r
-ERR:\r
- mp_clear(&q);\r
- return res;\r
-}\r
-\r
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* reduces a modulo n where n is of the form 2**p - d */
+int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
+{
+ mp_int q;
+ int p, res;
+
+ if ((res = mp_init(&q)) != MP_OKAY) {
+ return res;
+ }
+
+ p = mp_count_bits(n);
+top:
+ /* q = a/2**p, a = a mod 2**p */
+ if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if (d != 1) {
+ /* q = q * d */
+ if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) {
+ goto ERR;
+ }
+ }
+
+ /* a = a + q */
+ if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if (mp_cmp_mag(a, n) != MP_LT) {
+ s_mp_sub(a, n, a);
+ goto top;
+ }
+
+ERR:
+ mp_clear(&q);
+ return res;
+}
+
+#endif
/* End: bn_mp_reduce_2k.c */
+/* Start: bn_mp_reduce_2k_l.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_L_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* reduces a modulo n where n is of the form 2**p - d
+ This differs from reduce_2k since "d" can be larger
+ than a single digit.
+*/
+int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
+{
+ mp_int q;
+ int p, res;
+
+ if ((res = mp_init(&q)) != MP_OKAY) {
+ return res;
+ }
+
+ p = mp_count_bits(n);
+top:
+ /* q = a/2**p, a = a mod 2**p */
+ if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* q = q * d */
+ if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* a = a + q */
+ if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if (mp_cmp_mag(a, n) != MP_LT) {
+ s_mp_sub(a, n, a);
+ goto top;
+ }
+
+ERR:
+ mp_clear(&q);
+ return res;
+}
+
+#endif
+
+/* End: bn_mp_reduce_2k_l.c */
+
/* Start: bn_mp_reduce_2k_setup.c */
-/* LibTomMath, multiple-precision integer library -- Tom St Denis\r
- *\r
- * LibTomMath is library that provides for multiple-precision\r
- * integer arithmetic as well as number theoretic functionality.\r
- *\r
- * The library is designed directly after the MPI library by\r
- * Michael Fromberger but has been written from scratch with\r
- * additional optimizations in place.\r
- *\r
- * The library is free for all purposes without any express\r
- * guarantee it works.\r
- *\r
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org\r
- */\r
-#include <tommath.h>\r
-\r
-/* determines the setup value */\r
-int \r
-mp_reduce_2k_setup(mp_int *a, mp_digit *d)\r
-{\r
- int res, p;\r
- mp_int tmp;\r
- \r
- if ((res = mp_init(&tmp)) != MP_OKAY) {\r
- return res;\r
- }\r
- \r
- p = mp_count_bits(a);\r
- if ((res = mp_2expt(&tmp, p)) != MP_OKAY) {\r
- mp_clear(&tmp);\r
- return res;\r
- }\r
- \r
- if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) {\r
- mp_clear(&tmp);\r
- return res;\r
- }\r
- \r
- *d = tmp.dp[0];\r
- mp_clear(&tmp);\r
- return MP_OKAY;\r
-}\r
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_SETUP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* determines the setup value */
+int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
+{
+ int res, p;
+ mp_int tmp;
+
+ if ((res = mp_init(&tmp)) != MP_OKAY) {
+ return res;
+ }
+
+ p = mp_count_bits(a);
+ if ((res = mp_2expt(&tmp, p)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+
+ if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+
+ *d = tmp.dp[0];
+ mp_clear(&tmp);
+ return MP_OKAY;
+}
+#endif
/* End: bn_mp_reduce_2k_setup.c */
+/* Start: bn_mp_reduce_2k_setup_l.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_SETUP_L_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* determines the setup value */
+int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
+{
+ int res;
+ mp_int tmp;
+
+ if ((res = mp_init(&tmp)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ERR:
+ mp_clear(&tmp);
+ return res;
+}
+#endif
+
+/* End: bn_mp_reduce_2k_setup_l.c */
+
/* Start: bn_mp_reduce_is_2k.c */
-/* LibTomMath, multiple-precision integer library -- Tom St Denis\r
- *\r
- * LibTomMath is library that provides for multiple-precision\r
- * integer arithmetic as well as number theoretic functionality.\r
- *\r
- * The library is designed directly after the MPI library by\r
- * Michael Fromberger but has been written from scratch with\r
- * additional optimizations in place.\r
- *\r
- * The library is free for all purposes without any express\r
- * guarantee it works.\r
- *\r
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org\r
- */\r
-#include <tommath.h>\r
-\r
-/* determines if mp_reduce_2k can be used */\r
-int \r
-mp_reduce_is_2k(mp_int *a)\r
-{\r
- int ix, iy;\r
- \r
- if (a->used == 0) {\r
- return 0;\r
- } else if (a->used == 1) {\r
- return 1;\r
- } else if (a->used > 1) {\r
- iy = mp_count_bits(a);\r
- for (ix = DIGIT_BIT; ix < iy; ix++) {\r
- if ((a->dp[ix/DIGIT_BIT] & \r
- ((mp_digit)1 << (mp_digit)(ix % DIGIT_BIT))) == 0) {\r
- return 0;\r
- }\r
- }\r
- }\r
- return 1;\r
-}\r
-\r
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_IS_2K_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* determines if mp_reduce_2k can be used */
+int mp_reduce_is_2k(mp_int *a)
+{
+ int ix, iy, iw;
+ mp_digit iz;
+
+ if (a->used == 0) {
+ return MP_NO;
+ } else if (a->used == 1) {
+ return MP_YES;
+ } else if (a->used > 1) {
+ iy = mp_count_bits(a);
+ iz = 1;
+ iw = 1;
+
+ /* Test every bit from the second digit up, must be 1 */
+ for (ix = DIGIT_BIT; ix < iy; ix++) {
+ if ((a->dp[iw] & iz) == 0) {
+ return MP_NO;
+ }
+ iz <<= 1;
+ if (iz > (mp_digit)MP_MASK) {
+ ++iw;
+ iz = 1;
+ }
+ }
+ }
+ return MP_YES;
+}
+
+#endif
/* End: bn_mp_reduce_is_2k.c */
+/* Start: bn_mp_reduce_is_2k_l.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_IS_2K_L_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* determines if reduce_2k_l can be used */
+int mp_reduce_is_2k_l(mp_int *a)
+{
+ int ix, iy;
+
+ if (a->used == 0) {
+ return MP_NO;
+ } else if (a->used == 1) {
+ return MP_YES;
+ } else if (a->used > 1) {
+ /* if more than half of the digits are -1 we're sold */
+ for (iy = ix = 0; ix < a->used; ix++) {
+ if (a->dp[ix] == MP_MASK) {
+ ++iy;
+ }
+ }
+ return (iy >= (a->used/2)) ? MP_YES : MP_NO;
+
+ }
+ return MP_NO;
+}
+
+#endif
+
+/* End: bn_mp_reduce_is_2k_l.c */
+
/* Start: bn_mp_reduce_setup.c */
-/* LibTomMath, multiple-precision integer library -- Tom St Denis\r
- *\r
- * LibTomMath is library that provides for multiple-precision\r
- * integer arithmetic as well as number theoretic functionality.\r
- *\r
- * The library is designed directly after the MPI library by\r
- * Michael Fromberger but has been written from scratch with\r
- * additional optimizations in place.\r
- *\r
- * The library is free for all purposes without any express\r
- * guarantee it works.\r
- *\r
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org\r
- */\r
-#include <tommath.h>\r
-\r
-/* pre-calculate the value required for Barrett reduction\r
- * For a given modulus "b" it calulates the value required in "a"\r
- */\r
-int\r
-mp_reduce_setup (mp_int * a, mp_int * b)\r
-{\r
- int res;\r
- \r
- if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {\r
- return res;\r
- }\r
- return mp_div (a, b, a, NULL);\r
-}\r
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_SETUP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* pre-calculate the value required for Barrett reduction
+ * For a given modulus "b" it calulates the value required in "a"
+ */
+int mp_reduce_setup (mp_int * a, mp_int * b)
+{
+ int res;
+
+ if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
+ return res;
+ }
+ return mp_div (a, b, a, NULL);
+}
+#endif
/* End: bn_mp_reduce_setup.c */
/* Start: bn_mp_rshd.c */
+#include <tommath.h>
+#ifdef BN_MP_RSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift right a certain amount of digits */
-void
-mp_rshd (mp_int * a, int b)
+void mp_rshd (mp_int * a, int b)
{
int x;
/* remove excess digits */
a->used -= b;
}
+#endif
/* End: bn_mp_rshd.c */
/* Start: bn_mp_set.c */
+#include <tommath.h>
+#ifdef BN_MP_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* set to a digit */
-void
-mp_set (mp_int * a, mp_digit b)
+void mp_set (mp_int * a, mp_digit b)
{
mp_zero (a);
a->dp[0] = b & MP_MASK;
- a->used = (a->dp[0] != 0) ? 1 : 0;
+ a->used = (a->dp[0] != 0) ? 1 : 0;
}
+#endif
/* End: bn_mp_set.c */
/* Start: bn_mp_set_int.c */
+#include <tommath.h>
+#ifdef BN_MP_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* set a 32-bit const */
-int
-mp_set_int (mp_int * a, unsigned int b)
+int mp_set_int (mp_int * a, unsigned long b)
{
int x, res;
mp_zero (a);
+
/* set four bits at a time */
for (x = 0; x < 8; x++) {
/* shift the number up four bits */
mp_clamp (a);
return MP_OKAY;
}
+#endif
/* End: bn_mp_set_int.c */
/* Start: bn_mp_shrink.c */
+#include <tommath.h>
+#ifdef BN_MP_SHRINK_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shrink a bignum */
-int
-mp_shrink (mp_int * a)
+int mp_shrink (mp_int * a)
{
- if (a->alloc != a->used) {
- if ((a->dp = OPT_CAST realloc (a->dp, sizeof (mp_digit) * a->used)) == NULL) {
+ mp_digit *tmp;
+ if (a->alloc != a->used && a->used > 0) {
+ if ((tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * a->used)) == NULL) {
return MP_MEM;
}
+ a->dp = tmp;
a->alloc = a->used;
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_shrink.c */
/* Start: bn_mp_signed_bin_size.c */
+#include <tommath.h>
+#ifdef BN_MP_SIGNED_BIN_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* get the size for an signed equivalent */
-int
-mp_signed_bin_size (mp_int * a)
+int mp_signed_bin_size (mp_int * a)
{
return 1 + mp_unsigned_bin_size (a);
}
+#endif
/* End: bn_mp_signed_bin_size.c */
/* Start: bn_mp_sqr.c */
+#include <tommath.h>
+#ifdef BN_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes b = a*a */
int
mp_sqr (mp_int * a, mp_int * b)
{
int res;
+
+#ifdef BN_MP_TOOM_SQR_C
+ /* use Toom-Cook? */
if (a->used >= TOOM_SQR_CUTOFF) {
res = mp_toom_sqr(a, b);
- } else if (a->used >= KARATSUBA_SQR_CUTOFF) {
+ /* Karatsuba? */
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_SQR_C
+if (a->used >= KARATSUBA_SQR_CUTOFF) {
res = mp_karatsuba_sqr (a, b);
- } else {
-
- /* can we use the fast multiplier? */
+ } else
+#endif
+ {
+#ifdef BN_FAST_S_MP_SQR_C
+ /* can we use the fast comba multiplier? */
if ((a->used * 2 + 1) < MP_WARRAY &&
a->used <
(1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
res = fast_s_mp_sqr (a, b);
- } else {
+ } else
+#endif
+#ifdef BN_S_MP_SQR_C
res = s_mp_sqr (a, b);
- }
+#else
+ res = MP_VAL;
+#endif
}
b->sign = MP_ZPOS;
return res;
}
+#endif
/* End: bn_mp_sqr.c */
/* Start: bn_mp_sqrmod.c */
+#include <tommath.h>
+#ifdef BN_MP_SQRMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* c = a * a (mod b) */
int
int res;
mp_int t;
-
if ((res = mp_init (&t)) != MP_OKAY) {
return res;
}
mp_clear (&t);
return res;
}
+#endif
/* End: bn_mp_sqrmod.c */
-/* Start: bn_mp_sub.c */
+/* Start: bn_mp_sqrt.c */
+#include <tommath.h>
+#ifdef BN_MP_SQRT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* high level subtraction (handles signs) */
-int
-mp_sub (mp_int * a, mp_int * b, mp_int * c)
+/* this function is less generic than mp_n_root, simpler and faster */
+int mp_sqrt(mp_int *arg, mp_int *ret)
{
- int sa, sb, res;
+ int res;
+ mp_int t1,t2;
- sa = a->sign;
- sb = b->sign;
+ /* must be positive */
+ if (arg->sign == MP_NEG) {
+ return MP_VAL;
+ }
- if (sa != sb) {
- /* subtract a negative from a positive, OR */
- /* subtract a positive from a negative. */
+ /* easy out */
+ if (mp_iszero(arg) == MP_YES) {
+ mp_zero(ret);
+ return MP_OKAY;
+ }
+
+ if ((res = mp_init_copy(&t1, arg)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init(&t2)) != MP_OKAY) {
+ goto E2;
+ }
+
+ /* First approx. (not very bad for large arg) */
+ mp_rshd (&t1,t1.used/2);
+
+ /* t1 > 0 */
+ if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ /* And now t1 > sqrt(arg) */
+ do {
+ if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ /* t1 >= sqrt(arg) >= t2 at this point */
+ } while (mp_cmp_mag(&t1,&t2) == MP_GT);
+
+ mp_exch(&t1,ret);
+
+E1: mp_clear(&t2);
+E2: mp_clear(&t1);
+ return res;
+}
+
+#endif
+
+/* End: bn_mp_sqrt.c */
+
+/* Start: bn_mp_sub.c */
+#include <tommath.h>
+#ifdef BN_MP_SUB_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* high level subtraction (handles signs) */
+int
+mp_sub (mp_int * a, mp_int * b, mp_int * c)
+{
+ int sa, sb, res;
+
+ sa = a->sign;
+ sb = b->sign;
+
+ if (sa != sb) {
+ /* subtract a negative from a positive, OR */
+ /* subtract a positive from a negative. */
/* In either case, ADD their magnitudes, */
/* and use the sign of the first number. */
c->sign = sa;
return res;
}
+#endif
/* End: bn_mp_sub.c */
/* Start: bn_mp_sub_d.c */
+#include <tommath.h>
+#ifdef BN_MP_SUB_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* single digit subtraction */
int
mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
{
- mp_int t;
- int res;
+ mp_digit *tmpa, *tmpc, mu;
+ int res, ix, oldused;
+ /* grow c as required */
+ if (c->alloc < a->used + 1) {
+ if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
- if ((res = mp_init (&t)) != MP_OKAY) {
- return res;
+ /* if a is negative just do an unsigned
+ * addition [with fudged signs]
+ */
+ if (a->sign == MP_NEG) {
+ a->sign = MP_ZPOS;
+ res = mp_add_d(a, b, c);
+ a->sign = c->sign = MP_NEG;
+ return res;
}
- mp_set (&t, b);
- res = mp_sub (a, &t, c);
- mp_clear (&t);
- return res;
+ /* setup regs */
+ oldused = c->used;
+ tmpa = a->dp;
+ tmpc = c->dp;
+
+ /* if a <= b simply fix the single digit */
+ if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) {
+ if (a->used == 1) {
+ *tmpc++ = b - *tmpa;
+ } else {
+ *tmpc++ = b;
+ }
+ ix = 1;
+
+ /* negative/1digit */
+ c->sign = MP_NEG;
+ c->used = 1;
+ } else {
+ /* positive/size */
+ c->sign = MP_ZPOS;
+ c->used = a->used;
+
+ /* subtract first digit */
+ *tmpc = *tmpa++ - b;
+ mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
+ *tmpc++ &= MP_MASK;
+
+ /* handle rest of the digits */
+ for (ix = 1; ix < a->used; ix++) {
+ *tmpc = *tmpa++ - mu;
+ mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
+ *tmpc++ &= MP_MASK;
+ }
+ }
+
+ /* zero excess digits */
+ while (ix++ < oldused) {
+ *tmpc++ = 0;
+ }
+ mp_clamp(c);
+ return MP_OKAY;
}
+#endif
+
/* End: bn_mp_sub_d.c */
/* Start: bn_mp_submod.c */
+#include <tommath.h>
+#ifdef BN_MP_SUBMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* d = a - b (mod c) */
int
mp_clear (&t);
return res;
}
+#endif
/* End: bn_mp_submod.c */
/* Start: bn_mp_to_signed_bin.c */
+#include <tommath.h>
+#ifdef BN_MP_TO_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* store in signed [big endian] format */
-int
-mp_to_signed_bin (mp_int * a, unsigned char *b)
+int mp_to_signed_bin (mp_int * a, unsigned char *b)
{
int res;
b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1);
return MP_OKAY;
}
+#endif
/* End: bn_mp_to_signed_bin.c */
-/* Start: bn_mp_to_unsigned_bin.c */
+/* Start: bn_mp_to_signed_bin_n.c */
+#include <tommath.h>
+#ifdef BN_MP_TO_SIGNED_BIN_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
+
+/* store in signed [big endian] format */
+int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
+{
+ if (*outlen < (unsigned long)mp_signed_bin_size(a)) {
+ return MP_VAL;
+ }
+ *outlen = mp_signed_bin_size(a);
+ return mp_to_signed_bin(a, b);
+}
+#endif
+
+/* End: bn_mp_to_signed_bin_n.c */
+
+/* Start: bn_mp_to_unsigned_bin.c */
#include <tommath.h>
+#ifdef BN_MP_TO_UNSIGNED_BIN_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
/* store in unsigned [big endian] format */
-int
-mp_to_unsigned_bin (mp_int * a, unsigned char *b)
+int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
{
int x, res;
mp_int t;
x = 0;
while (mp_iszero (&t) == 0) {
- if (DIGIT_BIT != 7) {
+#ifndef MP_8BIT
b[x++] = (unsigned char) (t.dp[0] & 255);
- } else {
+#else
b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
- }
+#endif
if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
mp_clear (&t);
return res;
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_mp_to_unsigned_bin.c */
-/* Start: bn_mp_toom_mul.c */
-/* LibTomMath, multiple-precision integer library -- Tom St Denis\r
- *\r
- * LibTomMath is library that provides for multiple-precision\r
- * integer arithmetic as well as number theoretic functionality.\r
- *\r
- * The library is designed directly after the MPI library by\r
- * Michael Fromberger but has been written from scratch with\r
- * additional optimizations in place.\r
- *\r
- * The library is free for all purposes without any express\r
- * guarantee it works.\r
- *\r
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org\r
- */\r
-#include <tommath.h>\r
-\r
-/* multiplication using the Toom-Cook 3-way algorithm */\r
-int \r
-mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)\r
-{\r
- mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;\r
- int res, B;\r
- \r
- /* init temps */\r
- if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, \r
- &a0, &a1, &a2, &b0, &b1, \r
- &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {\r
- return res;\r
- }\r
- \r
- /* B */\r
- B = MIN(a->used, b->used) / 3;\r
- \r
- /* a = a2 * B**2 + a1 * B + a0 */\r
- if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
-\r
- if ((res = mp_copy(a, &a1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- mp_rshd(&a1, B);\r
- mp_mod_2d(&a1, DIGIT_BIT * B, &a1);\r
-\r
- if ((res = mp_copy(a, &a2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- mp_rshd(&a2, B*2);\r
- \r
- /* b = b2 * B**2 + b1 * B + b0 */\r
- if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
-\r
- if ((res = mp_copy(b, &b1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- mp_rshd(&b1, B);\r
- mp_mod_2d(&b1, DIGIT_BIT * B, &b1);\r
-\r
- if ((res = mp_copy(b, &b2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- mp_rshd(&b2, B*2);\r
- \r
- /* w0 = a0*b0 */\r
- if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- /* w4 = a2 * b2 */\r
- if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */\r
- if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */\r
- if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
-\r
- /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */\r
- if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- /* now solve the matrix \r
- \r
- 0 0 0 0 1\r
- 1 2 4 8 16\r
- 1 1 1 1 1\r
- 16 8 4 2 1\r
- 1 0 0 0 0\r
- \r
- using 12 subtractions, 4 shifts, \r
- 2 small divisions and 1 small multiplication \r
- */\r
- \r
- /* r1 - r4 */\r
- if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r3 - r0 */\r
- if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r1/2 */\r
- if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r3/2 */\r
- if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r2 - r0 - r4 */\r
- if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r1 - r2 */\r
- if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r3 - r2 */\r
- if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r1 - 8r0 */\r
- if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r3 - 8r4 */\r
- if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* 3r2 - r1 - r3 */\r
- if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r1 - r2 */\r
- if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r3 - r2 */\r
- if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r1/3 */\r
- if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r3/3 */\r
- if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- /* at this point shift W[n] by B*n */\r
- if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {\r
- goto ERR;\r
- } \r
- \r
- if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {\r
- goto ERR;\r
- } \r
- \r
-ERR:\r
- mp_clear_multi(&w0, &w1, &w2, &w3, &w4, \r
- &a0, &a1, &a2, &b0, &b1, \r
- &b2, &tmp1, &tmp2, NULL);\r
- return res;\r
-} \r
- \r
-
-/* End: bn_mp_toom_mul.c */
-
-/* Start: bn_mp_toom_sqr.c */
-/* LibTomMath, multiple-precision integer library -- Tom St Denis\r
- *\r
- * LibTomMath is library that provides for multiple-precision\r
- * integer arithmetic as well as number theoretic functionality.\r
- *\r
- * The library is designed directly after the MPI library by\r
- * Michael Fromberger but has been written from scratch with\r
- * additional optimizations in place.\r
- *\r
- * The library is free for all purposes without any express\r
- * guarantee it works.\r
- *\r
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org\r
- */\r
-#include <tommath.h>\r
-\r
-/* squaring using Toom-Cook 3-way algorithm */\r
-int \r
-mp_toom_sqr(mp_int *a, mp_int *b)\r
-{\r
- mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2;\r
- int res, B;\r
- \r
- /* init temps */\r
- if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL)) != MP_OKAY) {\r
- return res;\r
- }\r
-\r
- /* B */\r
- B = a->used / 3;\r
- \r
- /* a = a2 * B^2 + a1 * B + a0 */\r
- if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
-\r
- if ((res = mp_copy(a, &a1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- mp_rshd(&a1, B);\r
- mp_mod_2d(&a1, DIGIT_BIT * B, &a1);\r
-\r
- if ((res = mp_copy(a, &a2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- mp_rshd(&a2, B*2);\r
- \r
- /* w0 = a0*a0 */\r
- if ((res = mp_sqr(&a0, &w0)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- /* w4 = a2 * a2 */\r
- if ((res = mp_sqr(&a2, &w4)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- /* w1 = (a2 + 2(a1 + 2a0))**2 */\r
- if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- if ((res = mp_sqr(&tmp1, &w1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- /* w3 = (a0 + 2(a1 + 2a2))**2 */\r
- if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- if ((res = mp_sqr(&tmp1, &w3)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
-\r
- /* w2 = (a2 + a1 + a0)**2 */\r
- if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_sqr(&tmp1, &w2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- /* now solve the matrix \r
- \r
- 0 0 0 0 1\r
- 1 2 4 8 16\r
- 1 1 1 1 1\r
- 16 8 4 2 1\r
- 1 0 0 0 0\r
- \r
- using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication.\r
- */\r
- \r
- /* r1 - r4 */\r
- if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r3 - r0 */\r
- if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r1/2 */\r
- if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r3/2 */\r
- if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r2 - r0 - r4 */\r
- if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r1 - r2 */\r
- if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r3 - r2 */\r
- if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r1 - 8r0 */\r
- if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r3 - 8r4 */\r
- if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* 3r2 - r1 - r3 */\r
- if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r1 - r2 */\r
- if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r3 - r2 */\r
- if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r1/3 */\r
- if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- /* r3/3 */\r
- if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- \r
- /* at this point shift W[n] by B*n */\r
- if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {\r
- goto ERR;\r
- } \r
- \r
- if ((res = mp_add(&w0, &w1, b)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {\r
- goto ERR;\r
- }\r
- if ((res = mp_add(&tmp1, b, b)) != MP_OKAY) {\r
- goto ERR;\r
- } \r
- \r
-ERR:\r
- mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL);\r
- return res;\r
-} \r
- \r
-
-/* End: bn_mp_toom_sqr.c */
-
-/* Start: bn_mp_unsigned_bin_size.c */
+/* Start: bn_mp_to_unsigned_bin_n.c */
+#include <tommath.h>
+#ifdef BN_MP_TO_UNSIGNED_BIN_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* get the size for an unsigned equivalent */
-int
-mp_unsigned_bin_size (mp_int * a)
+/* store in unsigned [big endian] format */
+int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
{
- int size = mp_count_bits (a);
- return (size / 8 + ((size & 7) != 0 ? 1 : 0));
+ if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) {
+ return MP_VAL;
+ }
+ *outlen = mp_unsigned_bin_size(a);
+ return mp_to_unsigned_bin(a, b);
}
+#endif
-/* End: bn_mp_unsigned_bin_size.c */
+/* End: bn_mp_to_unsigned_bin_n.c */
-/* Start: bn_mp_xor.c */
+/* Start: bn_mp_toom_mul.c */
+#include <tommath.h>
+#ifdef BN_MP_TOOM_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* XOR two ints together */
-int
-mp_xor (mp_int * a, mp_int * b, mp_int * c)
+/* multiplication using the Toom-Cook 3-way algorithm
+ *
+ * Much more complicated than Karatsuba but has a lower
+ * asymptotic running time of O(N**1.464). This algorithm is
+ * only particularly useful on VERY large inputs
+ * (we're talking 1000s of digits here...).
+*/
+int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
{
- int res, ix, px;
- mp_int t, *x;
+ mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
+ int res, B;
+
+ /* init temps */
+ if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
+ &a0, &a1, &a2, &b0, &b1,
+ &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* B */
+ B = MIN(a->used, b->used) / 3;
+
+ /* a = a2 * B**2 + a1 * B + a0 */
+ if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
+ goto ERR;
+ }
- if (a->used > b->used) {
- if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
- return res;
+ if ((res = mp_copy(a, &a1)) != MP_OKAY) {
+ goto ERR;
}
- px = b->used;
- x = b;
- } else {
- if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
- return res;
+ mp_rshd(&a1, B);
+ mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
+
+ if ((res = mp_copy(a, &a2)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&a2, B*2);
+
+ /* b = b2 * B**2 + b1 * B + b0 */
+ if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
+ goto ERR;
}
- px = a->used;
- x = a;
- }
- for (ix = 0; ix < px; ix++) {
- t.dp[ix] ^= x->dp[ix];
- }
- mp_clamp (&t);
- mp_exch (c, &t);
- mp_clear (&t);
- return MP_OKAY;
-}
+ if ((res = mp_copy(b, &b1)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&b1, B);
+ mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
-/* End: bn_mp_xor.c */
+ if ((res = mp_copy(b, &b2)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&b2, B*2);
+
+ /* w0 = a0*b0 */
+ if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w4 = a2 * b2 */
+ if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
+ if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
+ if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+
-/* Start: bn_mp_zero.c */
+ /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
+ if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* now solve the matrix
+
+ 0 0 0 0 1
+ 1 2 4 8 16
+ 1 1 1 1 1
+ 16 8 4 2 1
+ 1 0 0 0 0
+
+ using 12 subtractions, 4 shifts,
+ 2 small divisions and 1 small multiplication
+ */
+
+ /* r1 - r4 */
+ if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r0 */
+ if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1/2 */
+ if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3/2 */
+ if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r2 - r0 - r4 */
+ if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - r2 */
+ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r2 */
+ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - 8r0 */
+ if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - 8r4 */
+ if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* 3r2 - r1 - r3 */
+ if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - r2 */
+ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r2 */
+ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1/3 */
+ if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3/3 */
+ if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* at this point shift W[n] by B*n */
+ if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ERR:
+ mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
+ &a0, &a1, &a2, &b0, &b1,
+ &b2, &tmp1, &tmp2, NULL);
+ return res;
+}
+
+#endif
+
+/* End: bn_mp_toom_mul.c */
+
+/* Start: bn_mp_toom_sqr.c */
+#include <tommath.h>
+#ifdef BN_MP_TOOM_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* set to zero */
-void
-mp_zero (mp_int * a)
+/* squaring using Toom-Cook 3-way algorithm */
+int
+mp_toom_sqr(mp_int *a, mp_int *b)
{
- a->sign = MP_ZPOS;
- a->used = 0;
- memset (a->dp, 0, sizeof (mp_digit) * a->alloc);
-}
+ mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2;
+ int res, B;
-/* End: bn_mp_zero.c */
+ /* init temps */
+ if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL)) != MP_OKAY) {
+ return res;
+ }
-/* Start: bn_prime_tab.c */
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is library that provides for multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library is designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-#include <tommath.h>
-const mp_digit __prime_tab[] = {
- 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
- 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
- 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
- 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
-#ifndef MP_8BIT
- 0x0083,
- 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
- 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
- 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
- 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
+ /* B */
+ B = a->used / 3;
- 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
- 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
- 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
- 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
- 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
- 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
- 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
- 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
+ /* a = a2 * B**2 + a1 * B + a0 */
+ if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
+ goto ERR;
+ }
- 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
- 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
- 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
- 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
- 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
- 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
- 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
- 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
+ if ((res = mp_copy(a, &a1)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&a1, B);
+ mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
+
+ if ((res = mp_copy(a, &a2)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&a2, B*2);
+
+ /* w0 = a0*a0 */
+ if ((res = mp_sqr(&a0, &w0)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w4 = a2 * a2 */
+ if ((res = mp_sqr(&a2, &w4)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w1 = (a2 + 2(a1 + 2a0))**2 */
+ if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_sqr(&tmp1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w3 = (a0 + 2(a1 + 2a2))**2 */
+ if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_sqr(&tmp1, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+
+
+ /* w2 = (a2 + a1 + a0)**2 */
+ if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sqr(&tmp1, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* now solve the matrix
+
+ 0 0 0 0 1
+ 1 2 4 8 16
+ 1 1 1 1 1
+ 16 8 4 2 1
+ 1 0 0 0 0
+
+ using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication.
+ */
+
+ /* r1 - r4 */
+ if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r0 */
+ if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1/2 */
+ if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3/2 */
+ if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r2 - r0 - r4 */
+ if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - r2 */
+ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r2 */
+ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - 8r0 */
+ if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - 8r4 */
+ if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* 3r2 - r1 - r3 */
+ if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - r2 */
+ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r2 */
+ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1/3 */
+ if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3/3 */
+ if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* at this point shift W[n] by B*n */
+ if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_add(&w0, &w1, b)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, b, b)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ERR:
+ mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL);
+ return res;
+}
- 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
- 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
- 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
- 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
- 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
- 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
- 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
- 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
#endif
-};
-/* End: bn_prime_tab.c */
+/* End: bn_mp_toom_sqr.c */
-/* Start: bn_radix.c */
+/* Start: bn_mp_toradix.c */
+#include <tommath.h>
+#ifdef BN_MP_TORADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-
-/* chars used in radix conversions */
-static const char *s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
-
-/* read a string [ASCII] in a given radix */
-int
-mp_read_radix (mp_int * a, char *str, int radix)
-{
- int y, res, neg;
- char ch;
-
- if (radix < 2 || radix > 64) {
- return MP_VAL;
- }
-
- if (*str == '-') {
- ++str;
- neg = MP_NEG;
- } else {
- neg = MP_ZPOS;
- }
-
- mp_zero (a);
- while (*str) {
- ch = (char) ((radix < 36) ? toupper (*str) : *str);
- for (y = 0; y < 64; y++) {
- if (ch == s_rmap[y]) {
- break;
- }
- }
-
- if (y < radix) {
- if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) {
- return res;
- }
- if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) {
- return res;
- }
- } else {
- break;
- }
- ++str;
- }
- if (mp_iszero(a) != 1) {
- a->sign = neg;
- }
- return MP_OKAY;
-}
/* stores a bignum as a ASCII string in a given radix (2..64) */
-int
-mp_toradix (mp_int * a, char *str, int radix)
+int mp_toradix (mp_int * a, char *str, int radix)
{
int res, digs;
mp_int t;
mp_digit d;
char *_s = str;
+ /* check range of the radix */
if (radix < 2 || radix > 64) {
return MP_VAL;
}
-
+
/* quick out if its zero */
if (mp_iszero(a) == 1) {
*str++ = '0';
*str = '\0';
return MP_OKAY;
}
-
if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
return res;
}
+ /* if it is negative output a - */
if (t.sign == MP_NEG) {
++_s;
*str++ = '-';
mp_clear (&t);
return res;
}
- *str++ = s_rmap[d];
+ *str++ = mp_s_rmap[d];
++digs;
}
+
+ /* reverse the digits of the string. In this case _s points
+ * to the first digit [exluding the sign] of the number]
+ */
bn_reverse ((unsigned char *)_s, digs);
- *str++ = '\0';
+
+ /* append a NULL so the string is properly terminated */
+ *str = '\0';
+
mp_clear (&t);
return MP_OKAY;
}
-/* returns size of ASCII reprensentation */
-int
-mp_radix_size (mp_int * a, int radix)
+#endif
+
+/* End: bn_mp_toradix.c */
+
+/* Start: bn_mp_toradix_n.c */
+#include <tommath.h>
+#ifdef BN_MP_TORADIX_N_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* stores a bignum as a ASCII string in a given radix (2..64)
+ *
+ * Stores upto maxlen-1 chars and always a NULL byte
+ */
+int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
{
int res, digs;
mp_int t;
mp_digit d;
+ char *_s = str;
- /* special case for binary */
- if (radix == 2) {
- return mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1;
+ /* check range of the maxlen, radix */
+ if (maxlen < 3 || radix < 2 || radix > 64) {
+ return MP_VAL;
}
- if (radix < 2 || radix > 64) {
- return 0;
+ /* quick out if its zero */
+ if (mp_iszero(a) == 1) {
+ *str++ = '0';
+ *str = '\0';
+ return MP_OKAY;
}
if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
- return 0;
+ return res;
}
- digs = 0;
+ /* if it is negative output a - */
if (t.sign == MP_NEG) {
- ++digs;
+ /* we have to reverse our digits later... but not the - sign!! */
+ ++_s;
+
+ /* store the flag and mark the number as positive */
+ *str++ = '-';
t.sign = MP_ZPOS;
+
+ /* subtract a char */
+ --maxlen;
}
+ digs = 0;
while (mp_iszero (&t) == 0) {
if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
mp_clear (&t);
- return 0;
+ return res;
}
+ *str++ = mp_s_rmap[d];
++digs;
+
+ if (--maxlen == 1) {
+ /* no more room */
+ break;
+ }
}
+
+ /* reverse the digits of the string. In this case _s points
+ * to the first digit [exluding the sign] of the number]
+ */
+ bn_reverse ((unsigned char *)_s, digs);
+
+ /* append a NULL so the string is properly terminated */
+ *str = '\0';
+
mp_clear (&t);
- return digs + 1;
+ return MP_OKAY;
}
-/* read a bigint from a file stream in ASCII */
-int mp_fread(mp_int *a, int radix, FILE *stream)
+#endif
+
+/* End: bn_mp_toradix_n.c */
+
+/* Start: bn_mp_unsigned_bin_size.c */
+#include <tommath.h>
+#ifdef BN_MP_UNSIGNED_BIN_SIZE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* get the size for an unsigned equivalent */
+int mp_unsigned_bin_size (mp_int * a)
{
- int err, ch, neg, y;
-
- /* clear a */
- mp_zero(a);
-
- /* if first digit is - then set negative */
- ch = fgetc(stream);
- if (ch == '-') {
- neg = MP_NEG;
- ch = fgetc(stream);
- } else {
- neg = MP_ZPOS;
- }
-
- for (;;) {
- /* find y in the radix map */
- for (y = 0; y < radix; y++) {
- if (s_rmap[y] == ch) {
- break;
- }
- }
- if (y == radix) {
- break;
- }
-
- /* shift up and add */
- if ((err = mp_mul_d(a, radix, a)) != MP_OKAY) {
- return err;
- }
- if ((err = mp_add_d(a, y, a)) != MP_OKAY) {
- return err;
- }
-
- ch = fgetc(stream);
- }
- if (mp_cmp_d(a, 0) != MP_EQ) {
- a->sign = neg;
- }
-
- return MP_OKAY;
+ int size = mp_count_bits (a);
+ return (size / 8 + ((size & 7) != 0 ? 1 : 0));
}
+#endif
-int mp_fwrite(mp_int *a, int radix, FILE *stream)
+/* End: bn_mp_unsigned_bin_size.c */
+
+/* Start: bn_mp_xor.c */
+#include <tommath.h>
+#ifdef BN_MP_XOR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* XOR two ints together */
+int
+mp_xor (mp_int * a, mp_int * b, mp_int * c)
{
- char *buf;
- int err, len, x;
-
- len = mp_radix_size(a, radix);
- if (len == 0) {
- return MP_VAL;
- }
-
- buf = malloc(len);
- if (buf == NULL) {
- return MP_MEM;
- }
-
- if ((err = mp_toradix(a, buf, radix)) != MP_OKAY) {
- free(buf);
- return err;
- }
-
- for (x = 0; x < len; x++) {
- if (fputc(buf[x], stream) == EOF) {
- free(buf);
- return MP_VAL;
- }
- }
-
- free(buf);
- return MP_OKAY;
+ int res, ix, px;
+ mp_int t, *x;
+
+ if (a->used > b->used) {
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+ px = b->used;
+ x = b;
+ } else {
+ if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
+ return res;
+ }
+ px = a->used;
+ x = a;
+ }
+
+ for (ix = 0; ix < px; ix++) {
+ t.dp[ix] ^= x->dp[ix];
+ }
+ mp_clamp (&t);
+ mp_exch (c, &t);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* End: bn_mp_xor.c */
+
+/* Start: bn_mp_zero.c */
+#include <tommath.h>
+#ifdef BN_MP_ZERO_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* set to zero */
+void mp_zero (mp_int * a)
+{
+ int n;
+ mp_digit *tmp;
+
+ a->sign = MP_ZPOS;
+ a->used = 0;
+
+ tmp = a->dp;
+ for (n = 0; n < a->alloc; n++) {
+ *tmp++ = 0;
+ }
}
+#endif
+
+/* End: bn_mp_zero.c */
+
+/* Start: bn_prime_tab.c */
+#include <tommath.h>
+#ifdef BN_PRIME_TAB_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+const mp_digit ltm_prime_tab[] = {
+ 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
+ 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
+ 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
+ 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
+#ifndef MP_8BIT
+ 0x0083,
+ 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
+ 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
+ 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
+ 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
+
+ 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
+ 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
+ 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
+ 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
+ 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
+ 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
+ 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
+ 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
+
+ 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
+ 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
+ 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
+ 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
+ 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
+ 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
+ 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
+ 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
+ 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
+ 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
+ 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
+ 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
+ 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
+ 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
+ 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
+ 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
+#endif
+};
+#endif
-/* End: bn_radix.c */
+/* End: bn_prime_tab.c */
/* Start: bn_reverse.c */
+#include <tommath.h>
+#ifdef BN_REVERSE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reverse an array, used for radix code */
void
--iy;
}
}
+#endif
/* End: bn_reverse.c */
/* Start: bn_s_mp_add.c */
+#include <tommath.h>
+#ifdef BN_S_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* low level addition, based on HAC pp.594, Algorithm 14.7 */
int
mp_clamp (c);
return MP_OKAY;
}
+#endif
/* End: bn_s_mp_add.c */
/* Start: bn_s_mp_exptmod.c */
-/* LibTomMath, multiple-precision integer library -- Tom St Denis\r
- *\r
- * LibTomMath is library that provides for multiple-precision\r
- * integer arithmetic as well as number theoretic functionality.\r
- *\r
- * The library is designed directly after the MPI library by\r
- * Michael Fromberger but has been written from scratch with\r
- * additional optimizations in place.\r
- *\r
- * The library is free for all purposes without any express\r
- * guarantee it works.\r
- *\r
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org\r
- */\r
-#include <tommath.h>\r
-\r
-int\r
-s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)\r
-{\r
- mp_int M[256], res, mu;\r
- mp_digit buf;\r
- int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;\r
-\r
- /* find window size */\r
- x = mp_count_bits (X);\r
- if (x <= 7) {\r
- winsize = 2;\r
- } else if (x <= 36) {\r
- winsize = 3;\r
- } else if (x <= 140) {\r
- winsize = 4;\r
- } else if (x <= 450) {\r
- winsize = 5;\r
- } else if (x <= 1303) {\r
- winsize = 6;\r
- } else if (x <= 3529) {\r
- winsize = 7;\r
- } else {\r
- winsize = 8;\r
- }\r
-\r
-#ifdef MP_LOW_MEM\r
- if (winsize > 5) {\r
- winsize = 5;\r
- }\r
-#endif\r
-\r
- /* init M array */\r
- for (x = 0; x < (1 << winsize); x++) {\r
- if ((err = mp_init_size (&M[x], 1)) != MP_OKAY) {\r
- for (y = 0; y < x; y++) {\r
- mp_clear (&M[y]);\r
- }\r
- return err;\r
- }\r
- }\r
-\r
- /* create mu, used for Barrett reduction */\r
- if ((err = mp_init (&mu)) != MP_OKAY) {\r
- goto __M;\r
- }\r
- if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {\r
- goto __MU;\r
- }\r
-\r
- /* create M table\r
- *\r
- * The M table contains powers of the base, \r
- * e.g. M[x] = G**x mod P\r
- *\r
- * The first half of the table is not \r
- * computed though accept for M[0] and M[1]\r
- */\r
- if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {\r
- goto __MU;\r
- }\r
-\r
- /* compute the value at M[1<<(winsize-1)] by squaring \r
- * M[1] (winsize-1) times \r
- */\r
- if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {\r
- goto __MU;\r
- }\r
-\r
- for (x = 0; x < (winsize - 1); x++) {\r
- if ((err = mp_sqr (&M[1 << (winsize - 1)], \r
- &M[1 << (winsize - 1)])) != MP_OKAY) {\r
- goto __MU;\r
- }\r
- if ((err = mp_reduce (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {\r
- goto __MU;\r
- }\r
- }\r
-\r
- /* create upper table */\r
- for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {\r
- if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {\r
- goto __MU;\r
- }\r
- if ((err = mp_reduce (&M[x], P, &mu)) != MP_OKAY) {\r
- goto __MU;\r
- }\r
- }\r
-\r
- /* setup result */\r
- if ((err = mp_init (&res)) != MP_OKAY) {\r
- goto __MU;\r
- }\r
- mp_set (&res, 1);\r
-\r
- /* set initial mode and bit cnt */\r
- mode = 0;\r
- bitcnt = 1;\r
- buf = 0;\r
- digidx = X->used - 1;\r
- bitcpy = 0;\r
- bitbuf = 0;\r
-\r
- for (;;) {\r
- /* grab next digit as required */\r
- if (--bitcnt == 0) {\r
- if (digidx == -1) {\r
- break;\r
- }\r
- buf = X->dp[digidx--];\r
- bitcnt = (int) DIGIT_BIT;\r
- }\r
-\r
- /* grab the next msb from the exponent */\r
- y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;\r
- buf <<= (mp_digit)1;\r
-\r
- /* if the bit is zero and mode == 0 then we ignore it\r
- * These represent the leading zero bits before the first 1 bit\r
- * in the exponent. Technically this opt is not required but it\r
- * does lower the # of trivial squaring/reductions used\r
- */\r
- if (mode == 0 && y == 0)\r
- continue;\r
-\r
- /* if the bit is zero and mode == 1 then we square */\r
- if (mode == 1 && y == 0) {\r
- if ((err = mp_sqr (&res, &res)) != MP_OKAY) {\r
- goto __RES;\r
- }\r
- if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {\r
- goto __RES;\r
- }\r
- continue;\r
- }\r
-\r
- /* else we add it to the window */\r
- bitbuf |= (y << (winsize - ++bitcpy));\r
- mode = 2;\r
-\r
- if (bitcpy == winsize) {\r
- /* ok window is filled so square as required and multiply */\r
- /* square first */\r
- for (x = 0; x < winsize; x++) {\r
- if ((err = mp_sqr (&res, &res)) != MP_OKAY) {\r
- goto __RES;\r
- }\r
- if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {\r
- goto __RES;\r
- }\r
- }\r
-\r
- /* then multiply */\r
- if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {\r
- goto __MU;\r
- }\r
- if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {\r
- goto __MU;\r
- }\r
-\r
- /* empty window and reset */\r
- bitcpy = 0;\r
- bitbuf = 0;\r
- mode = 1;\r
- }\r
- }\r
-\r
- /* if bits remain then square/multiply */\r
- if (mode == 2 && bitcpy > 0) {\r
- /* square then multiply if the bit is set */\r
- for (x = 0; x < bitcpy; x++) {\r
- if ((err = mp_sqr (&res, &res)) != MP_OKAY) {\r
- goto __RES;\r
- }\r
- if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {\r
- goto __RES;\r
- }\r
-\r
- bitbuf <<= 1;\r
- if ((bitbuf & (1 << winsize)) != 0) {\r
- /* then multiply */\r
- if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {\r
- goto __RES;\r
- }\r
- if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {\r
- goto __RES;\r
- }\r
- }\r
- }\r
- }\r
-\r
- mp_exch (&res, Y);\r
- err = MP_OKAY;\r
-__RES:mp_clear (&res);\r
-__MU:mp_clear (&mu);\r
-__M:\r
- for (x = 0; x < (1 << winsize); x++) {\r
- mp_clear (&M[x]);\r
- }\r
- return err;\r
-}\r
+#include <tommath.h>
+#ifdef BN_S_MP_EXPTMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+#ifdef MP_LOW_MEM
+ #define TAB_SIZE 32
+#else
+ #define TAB_SIZE 256
+#endif
+
+int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
+{
+ mp_int M[TAB_SIZE], res, mu;
+ mp_digit buf;
+ int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
+ int (*redux)(mp_int*,mp_int*,mp_int*);
+
+ /* find window size */
+ x = mp_count_bits (X);
+ if (x <= 7) {
+ winsize = 2;
+ } else if (x <= 36) {
+ winsize = 3;
+ } else if (x <= 140) {
+ winsize = 4;
+ } else if (x <= 450) {
+ winsize = 5;
+ } else if (x <= 1303) {
+ winsize = 6;
+ } else if (x <= 3529) {
+ winsize = 7;
+ } else {
+ winsize = 8;
+ }
+
+#ifdef MP_LOW_MEM
+ if (winsize > 5) {
+ winsize = 5;
+ }
+#endif
+
+ /* init M array */
+ /* init first cell */
+ if ((err = mp_init(&M[1])) != MP_OKAY) {
+ return err;
+ }
+
+ /* now init the second half of the array */
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+ if ((err = mp_init(&M[x])) != MP_OKAY) {
+ for (y = 1<<(winsize-1); y < x; y++) {
+ mp_clear (&M[y]);
+ }
+ mp_clear(&M[1]);
+ return err;
+ }
+ }
+
+ /* create mu, used for Barrett reduction */
+ if ((err = mp_init (&mu)) != MP_OKAY) {
+ goto LBL_M;
+ }
+
+ if (redmode == 0) {
+ if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ redux = mp_reduce;
+ } else {
+ if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ redux = mp_reduce_2k_l;
+ }
+
+ /* create M table
+ *
+ * The M table contains powers of the base,
+ * e.g. M[x] = G**x mod P
+ *
+ * The first half of the table is not
+ * computed though accept for M[0] and M[1]
+ */
+ if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
+ goto LBL_MU;
+ }
+
+ /* compute the value at M[1<<(winsize-1)] by squaring
+ * M[1] (winsize-1) times
+ */
+ if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
+ goto LBL_MU;
+ }
+
+ for (x = 0; x < (winsize - 1); x++) {
+ /* square it */
+ if ((err = mp_sqr (&M[1 << (winsize - 1)],
+ &M[1 << (winsize - 1)])) != MP_OKAY) {
+ goto LBL_MU;
+ }
+
+ /* reduce modulo P */
+ if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ }
+
+ /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
+ * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
+ */
+ for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
+ if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ }
+
+ /* setup result */
+ if ((err = mp_init (&res)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ mp_set (&res, 1);
+
+ /* set initial mode and bit cnt */
+ mode = 0;
+ bitcnt = 1;
+ buf = 0;
+ digidx = X->used - 1;
+ bitcpy = 0;
+ bitbuf = 0;
+
+ for (;;) {
+ /* grab next digit as required */
+ if (--bitcnt == 0) {
+ /* if digidx == -1 we are out of digits */
+ if (digidx == -1) {
+ break;
+ }
+ /* read next digit and reset the bitcnt */
+ buf = X->dp[digidx--];
+ bitcnt = (int) DIGIT_BIT;
+ }
+
+ /* grab the next msb from the exponent */
+ y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
+ buf <<= (mp_digit)1;
+
+ /* if the bit is zero and mode == 0 then we ignore it
+ * These represent the leading zero bits before the first 1 bit
+ * in the exponent. Technically this opt is not required but it
+ * does lower the # of trivial squaring/reductions used
+ */
+ if (mode == 0 && y == 0) {
+ continue;
+ }
+
+ /* if the bit is zero and mode == 1 then we square */
+ if (mode == 1 && y == 0) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ continue;
+ }
+
+ /* else we add it to the window */
+ bitbuf |= (y << (winsize - ++bitcpy));
+ mode = 2;
+
+ if (bitcpy == winsize) {
+ /* ok window is filled so square as required and multiply */
+ /* square first */
+ for (x = 0; x < winsize; x++) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* then multiply */
+ if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ /* empty window and reset */
+ bitcpy = 0;
+ bitbuf = 0;
+ mode = 1;
+ }
+ }
+
+ /* if bits remain then square/multiply */
+ if (mode == 2 && bitcpy > 0) {
+ /* square then multiply if the bit is set */
+ for (x = 0; x < bitcpy; x++) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ bitbuf <<= 1;
+ if ((bitbuf & (1 << winsize)) != 0) {
+ /* then multiply */
+ if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+ }
+ }
+
+ mp_exch (&res, Y);
+ err = MP_OKAY;
+LBL_RES:mp_clear (&res);
+LBL_MU:mp_clear (&mu);
+LBL_M:
+ mp_clear(&M[1]);
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+ mp_clear (&M[x]);
+ }
+ return err;
+}
+#endif
/* End: bn_s_mp_exptmod.c */
/* Start: bn_s_mp_mul_digs.c */
+#include <tommath.h>
+#ifdef BN_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* multiplies |a| * |b| and only computes upto digs digits of result
* HAC pp. 595, Algorithm 14.12 Modified so you can control how
* many digits of output are created.
*/
-int
-s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
mp_int t;
int res, pa, pb, ix, iy;
/* compute the columns of the output and propagate the carry */
for (iy = 0; iy < pb; iy++) {
/* compute the column as a mp_word */
- r = ((mp_word) *tmpt) +
- ((mp_word) tmpx) * ((mp_word) * tmpy++) +
- ((mp_word) u);
+ r = ((mp_word)*tmpt) +
+ ((mp_word)tmpx) * ((mp_word)*tmpy++) +
+ ((mp_word) u);
/* the new column is the lower part of the result */
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
/* get the carry word from the result */
- u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
+ u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
}
/* set carry if it is placed below digs */
if (ix + iy < digs) {
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_s_mp_mul_digs.c */
/* Start: bn_s_mp_mul_high_digs.c */
+#include <tommath.h>
+#ifdef BN_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* multiplies |a| * |b| and does not compute the lower digs digits
* [meant to get the higher part of the product]
mp_word r;
mp_digit tmpx, *tmpt, *tmpy;
-
/* can we use the fast multiplier? */
+#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
if (((a->used + b->used + 1) < MP_WARRAY)
&& MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
return fast_s_mp_mul_high_digs (a, b, c, digs);
}
+#endif
if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
return res;
for (iy = digs - ix; iy < pb; iy++) {
/* calculate the double precision result */
- r = ((mp_word) * tmpt) + ((mp_word) tmpx) * ((mp_word) * tmpy++) + ((mp_word) u);
+ r = ((mp_word)*tmpt) +
+ ((mp_word)tmpx) * ((mp_word)*tmpy++) +
+ ((mp_word) u);
/* get the lower part */
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
/* carry the carry */
- u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
+ u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
}
*tmpt = u;
}
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_s_mp_mul_high_digs.c */
/* Start: bn_s_mp_sqr.c */
+#include <tommath.h>
+#ifdef BN_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
-int
-s_mp_sqr (mp_int * a, mp_int * b)
+int s_mp_sqr (mp_int * a, mp_int * b)
{
mp_int t;
int res, ix, iy, pa;
if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
return res;
}
+
+ /* default used is maximum possible size */
t.used = 2*pa + 1;
for (ix = 0; ix < pa; ix++) {
/* first calculate the digit at 2*ix */
/* calculate double precision result */
- r = ((mp_word) t.dp[2*ix]) +
- ((mp_word) a->dp[ix]) * ((mp_word) a->dp[ix]);
+ r = ((mp_word) t.dp[2*ix]) +
+ ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
/* store lower part in result */
- t.dp[2*ix] = (mp_digit) (r & ((mp_word) MP_MASK));
+ t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
/* get the carry */
- u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
/* left hand side of A[ix] * A[iy] */
- tmpx = a->dp[ix];
+ tmpx = a->dp[ix];
/* alias for where to store the results */
- tmpt = t.dp + (2*ix + 1);
+ tmpt = t.dp + (2*ix + 1);
for (iy = ix + 1; iy < pa; iy++) {
/* first calculate the product */
- r = ((mp_word) tmpx) * ((mp_word) a->dp[iy]);
+ r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
/* now calculate the double precision result, note we use
* addition instead of *2 since it's easier to optimize
*/
- r = ((mp_word) * tmpt) + r + r + ((mp_word) u);
+ r = ((mp_word) *tmpt) + r + r + ((mp_word) u);
/* store lower part */
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
/* get carry */
- u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
}
/* propagate upwards */
while (u != ((mp_digit) 0)) {
- r = ((mp_word) * tmpt) + ((mp_word) u);
+ r = ((mp_word) *tmpt) + ((mp_word) u);
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
- u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
}
}
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_s_mp_sqr.c */
/* Start: bn_s_mp_sub.c */
+#include <tommath.h>
+#ifdef BN_S_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
int
return MP_OKAY;
}
+#endif
/* End: bn_s_mp_sub.c */
/* Start: bncore.c */
+#include <tommath.h>
+#ifdef BNCORE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Known optimal configurations
CPU /Compiler /MUL CUTOFF/SQR CUTOFF
-------------------------------------------------------------
- Intel P4 /GCC v3.2 / 70/ 108
- AMD Athlon XP /GCC v3.2 / 109/ 127
-
+ Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-)
+ AMD Athlon64 /GCC v3.4.4 / 74/ 124/LTM 0.34
+
*/
-/* configured for a AMD XP Thoroughbred core with etc/tune.c */
-int KARATSUBA_MUL_CUTOFF = 109, /* Min. number of digits before Karatsuba multiplication is used. */
- KARATSUBA_SQR_CUTOFF = 127, /* Min. number of digits before Karatsuba squaring is used. */
+int KARATSUBA_MUL_CUTOFF = 74, /* Min. number of digits before Karatsuba multiplication is used. */
+ KARATSUBA_SQR_CUTOFF = 124, /* Min. number of digits before Karatsuba squaring is used. */
TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */
TOOM_SQR_CUTOFF = 400;
+#endif
/* End: bncore.c */
projects / bcm963xx.git / blobdiff