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/* Start: bn_error.c */
#include <tommath.h>
#ifdef BN_ERROR_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@gmail.com, http://libtom.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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@gmail.com, http://libtom.org
*/
/* computes the modular inverse via binary extended euclidean algorithm,
* that is c = 1/a mod b
*
* 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)
{
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 LBL_ERR;
}
/* we need y = |a| */
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 LBL_ERR;
}
if ((res = mp_copy (&y, &v)) != MP_OKAY) {
goto LBL_ERR;
}
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 LBL_ERR;
}
/* 4.2 if B is odd then */
if (mp_isodd (&B) == 1) {
if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* B = B/2 */
if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
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 LBL_ERR;
}
/* 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 LBL_ERR;
}
}
/* D = D/2 */
if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* 6. if u >= v then */
if (mp_cmp (&u, &v) != MP_LT) {
/* u = u - v, B = B - D */
if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
goto LBL_ERR;
}
} else {
/* v - v - u, D = D - B */
if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* if not zero goto step 4 */
if (mp_iszero (&u) == 0) {
goto top;
}
/* now a = C, b = D, gcd == g*v */
/* if v != 1 then there is no inverse */
if (mp_cmp_d (&v, 1) != MP_EQ) {
res = MP_VAL;
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 LBL_ERR;
}
}
mp_exch (&D, c);
c->sign = neg;
res = MP_OKAY;
LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
return res;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* 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.
*
* 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 ix, res, olduse;
mp_word W[MP_WARRAY];
/* get old used count */
olduse = x->used;
/* grow a as required */
if (x->alloc < n->used + 1) {
if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
return res;
}
}
/* 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;
/* 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] */
for (ix = 0; ix < x->used; ix++) {
*_W++ = *tmpx++;
}
/* zero the high words of W[a->used..m->used*2] */
for (; ix < n->used * 2 + 1; ix++) {
*_W++ = 0;
}
}
/* 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
* 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);
/* a = a + mu * m * b**i
*
* This is computed in place and on the fly. The multiplication
* 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
* 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
* first m->used words of W[] have the carries fixed
*/
{
register int iy;
register mp_digit *tmpn;
register mp_word *_W;
/* alias for the digits of the modulus */
tmpn = n->dp;
/* Alias for the columns set by an offset of ix */
_W = W + ix;
/* inner loop */
for (iy = 0; iy < n->used; iy++) {
*_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
}
}
/* now fix carry for next digit, W[ix+1] */
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++) {
*_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
}
/* 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
* 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++) {
*tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
}
/* zero oldused digits, if the input a was larger than
* m->used+1 we'll have to clear the digits
*/
for (; ix < olduse; ix++) {
*tmpx++ = 0;
}
}
/* set the max used and clamp */
x->used = n->used + 1;
mp_clamp (x);
/* if A >= m then A = A - m */
if (mp_cmp_mag (x, n) != MP_LT) {
return s_mp_sub (x, n, x);
}
return MP_OKAY;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* Fast (comba) multiplier
*
* This is the fast column-array [comba] multiplier. It is
* designed to compute the columns of the product first
* then handle the carries afterwards. This has the effect
* of making the nested loops that compute the columns very
* simple and schedulable on super-scalar processors.
*
* This has been modified to produce a variable number of
* digits of output so if say only a half-product is required
* you don't have to compute the upper half (a feature
* required for fast Barrett reduction).
*
* 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 olduse, res, pa, ix, iz;
mp_digit W[MP_WARRAY];
register mp_word _W;
/* grow the destination as required */
if (c->alloc < digs) {
if ((res = mp_grow (c, digs)) != MP_OKAY) {
return res;
}
}
/* number of output digits to produce */
pa = MIN(digs, a->used + b->used);
/* clear the carry */
_W = 0;
for (ix = 0; ix < pa; ix++) {
int tx, ty;
int iy;
mp_digit *tmpx, *tmpy;
/* get offsets into the two bignums */
ty = MIN(b->used-1, ix);
tx = ix - ty;
/* setup temp aliases */
tmpx = a->dp + tx;
tmpy = b->dp + ty;
/* this is the number of times the loop will iterrate, essentially
while (tx++ < a->used && ty-- >= 0) { ... }
*/
iy = MIN(a->used-tx, ty+1);
/* 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);
}
/* setup dest */
olduse = c->used;
c->used = pa;
{
register mp_digit *tmpc;
tmpc = c->dp;
for (ix = 0; ix < pa+1; ix++) {
/* now extract the previous digit [below the carry] */
*tmpc++ = W[ix];
}
/* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
*tmpc++ = 0;
}
}
mp_clamp (c);
return MP_OKAY;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* 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
* only the higher digits were needed. This essentially halves the work.
*
* 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 olduse, res, pa, ix, iz;
mp_digit W[MP_WARRAY];
mp_word _W;
/* grow the destination as required */
pa = a->used + b->used;
if (c->alloc < pa) {
if ((res = mp_grow (c, pa)) != MP_OKAY) {
return res;
}
}
/* 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;
/* get offsets into the two bignums */
ty = MIN(b->used-1, ix);
tx = ix - ty;
/* setup temp aliases */
tmpx = a->dp + tx;
tmpy = b->dp + ty;
/* this is the number of times the loop will iterrate, essentially its
while (tx++ < a->used && ty-- >= 0) { ... }
*/
iy = MIN(a->used-tx, ty+1);
/* 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);
}
/* setup dest */
olduse = c->used;
c->used = pa;
{
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];
}
/* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
*tmpc++ = 0;
}
}
mp_clamp (c);
return MP_OKAY;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* 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, res, pa, ix, iz;
mp_digit W[MP_WARRAY], *tmpx;
mp_word W1;
/* grow the destination as required */
pa = a->used + a->used;
if (b->alloc < pa) {
if ((res = mp_grow (b, pa)) != MP_OKAY) {
return res;
}
}
/* number of output digits to produce */
W1 = 0;
for (ix = 0; ix < pa; ix++) {
int tx, ty, iy;
mp_word _W;
mp_digit *tmpy;
/* clear counter */
_W = 0;
/* 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;
/* 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);
/* execute loop */
for (iz = 0; iz < iy; iz++) {
_W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
}
/* double the inner product and add carry */
_W = _W + _W + W1;
/* 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 = a->used+a->used;
{
mp_digit *tmpb;
tmpb = b->dp;
for (ix = 0; ix < pa; ix++) {
*tmpb++ = W[ix] & MP_MASK;
}
/* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
*tmpb++ = 0;
}
}
mp_clamp (b);
return MP_OKAY;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* computes a = 2**b
*
* Simple algorithm which zeroes the int, grows it then just sets one bit
* as required.
*/
int
mp_2expt (mp_int * a, int 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;
/* put the single bit in its place */
a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
return MP_OKAY;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* b = |a|
*
* Simple function copies the input and fixes the sign to positive
*/
int
mp_abs (mp_int * a, mp_int * b)
{
int 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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* high level addition (handles signs) */
int mp_add (mp_int * a, mp_int * b, mp_int * c)
{
int sa, sb, res;
/* get sign of both inputs */
sa = a->sign;
sb = b->sign;
/* handle two cases, not four */
if (sa == sb) {
/* both positive or both negative */
/* add their magnitudes, copy the sign */
c->sign = sa;
res = s_mp_add (a, b, c);
} else {
/* one positive, the other negative */
/* subtract the one with the greater magnitude from */
/* the one of the lesser magnitude. The result gets */
/* the sign of the one with the greater magnitude. */
if (mp_cmp_mag (a, b) == MP_LT) {
c->sign = sb;
res = s_mp_sub (b, a, c);
} else {
c->sign = sa;
res = s_mp_sub (a, b, c);
}
}
return res;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* single digit addition */
int
mp_add_d (mp_int * a, mp_digit b, mp_int * c)
{
int res, ix, oldused;
mp_digit *tmpa, *tmpc, mu;
/* grow c as required */
if (c->alloc < a->used + 1) {
if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
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;
/* clamp */
mp_clamp(c);
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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* d = a + b (mod c) */
int
mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
int res;
mp_int t;
if ((res = mp_init (&t)) != MP_OKAY) {
return res;
}
if ((res = mp_add (a, b, &t)) != MP_OKAY) {
mp_clear (&t);
return res;
}
res = mp_mod (&t, c, d);
mp_clear (&t);
return res;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* AND two ints together */
int
mp_and (mp_int * a, mp_int * b, mp_int * c)
{
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];
}
/* zero digits above the last from the smallest mp_int */
for (; ix < t.used; ix++) {
t.dp[ix] = 0;
}
mp_clamp (&t);
mp_exch (c, &t);
mp_clear (&t);
return MP_OKAY;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* trim unused digits
*
* This is used to ensure that leading zero digits are
* trimed and the leading "used" digit will be non-zero
* Typically very fast. Also fixes the sign if there
* are no more leading 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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* clear one (frees) */
void
mp_clear (mp_int * a)
{
int i;
/* only do anything if a hasn't been freed previously */
if (a->dp != NULL) {
/* first zero the digits */
for (i = 0; i < a->used; i++) {
a->dp[i] = 0;
}
/* free ram */
XFREE(a->dp);
/* reset members to make debugging easier */
a->dp = NULL;
a->alloc = a->used = 0;
a->sign = MP_ZPOS;
}
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* End: bn_mp_clear.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 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@gmail.com, http://libtom.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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@gmail.com, http://libtom.org
*/
/* compare two ints (signed)*/
int
mp_cmp (mp_int * a, mp_int * b)
{
/* compare based on sign */
if (a->sign != b->sign) {
if (a->sign == MP_NEG) {
return MP_LT;
} else {
return MP_GT;
}
}
/* compare digits */
if (a->sign == MP_NEG) {
/* if negative compare opposite direction */
return mp_cmp_mag(b, a);
} else {
return mp_cmp_mag(a, b);
}
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* compare a digit */
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_LT;
} else {
return MP_EQ;
}
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* compare maginitude of two ints (unsigned) */
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 = 0; n < a->used; ++n, --tmpa, --tmpb) {
if (*tmpa > *tmpb) {
return MP_GT;
}
if (*tmpa < *tmpb) {
return MP_LT;
}
}
return MP_EQ;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* End: bn_mp_cmp_mag.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 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@gmail.com, http://libtom.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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@gmail.com, http://libtom.org
*/
/* copy, b = a */
int
mp_copy (mp_int * a, mp_int * b)
{
int res, n;
/* if dst == src do nothing */
if (a == b) {
return MP_OKAY;
}
/* grow dest */
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 */
for (n = 0; n < a->used; n++) {
*tmpb++ = *tmpa++;
}
/* clear high digits */
for (; n < b->used; n++) {
*tmpb++ = 0;
}
}
/* copy used count and sign */
b->used = a->used;
b->sign = a->sign;
return MP_OKAY;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* returns the number of bits in an int */
int
mp_count_bits (mp_int * a)
{
int r;
mp_digit q;
/* shortcut */
if (a->used == 0) {
return 0;
}
/* get number of digits and add that */
r = (a->used - 1) * DIGIT_BIT;
/* take the last digit and count the bits in it */
q = a->dp[a->used - 1];
while (q > ((mp_digit) 0)) {
++r;
q >>= ((mp_digit) 1);
}
return r;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
#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]
* HAC pp.598 Algorithm 14.20
*
* Note that the description in HAC is horribly
* incomplete. For example, it doesn't consider
* the case where digits are removed from 'x' in
* the inner loop. It also doesn't consider the
* case that y has fewer than three digits, etc..
*
* 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)
{
mp_int q, x, y, t1, t2;
int res, n, t, i, norm, neg;
/* 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;
}
if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
return res;
}
q.used = a->used + 2;
if ((res = mp_init (&t1)) != MP_OKAY) {
goto LBL_Q;
}
if ((res = mp_init (&t2)) != MP_OKAY) {
goto LBL_T1;
}
if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
goto LBL_T2;
}
if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
goto LBL_X;
}
/* fix the sign */
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
x.sign = y.sign = MP_ZPOS;
/* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
norm = mp_count_bits(&y) % DIGIT_BIT;
if (norm < (int)(DIGIT_BIT-1)) {
norm = (DIGIT_BIT-1) - norm;
if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
goto LBL_Y;
}
if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
goto LBL_Y;
}
} else {
norm = 0;
}
/* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
n = x.used - 1;
t = y.used - 1;
/* 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 LBL_Y;
}
while (mp_cmp (&x, &y) != MP_LT) {
++(q.dp[n - t]);
if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
goto LBL_Y;
}
}
/* reset y by shifting it back down */
mp_rshd (&y, n - t);
/* step 3. for i from n down to (t + 1) */
for (i = n; i >= (t + 1); i--) {
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 */
if (x.dp[i] == y.dp[t]) {
q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
} else {
mp_word tmp;
tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
tmp |= ((mp_word) x.dp[i - 1]);
tmp /= ((mp_word) y.dp[t]);
if (tmp > (mp_word) MP_MASK)
tmp = MP_MASK;
q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
}
/* while (q{i-t-1} * (yt * b + y{t-1})) >
xi * b**2 + xi-1 * b + xi-2
do q{i-t-1} -= 1;
*/
q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
do {
q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
/* find left hand */
mp_zero (&t1);
t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
t1.dp[1] = y.dp[t];
t1.used = 2;
if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
goto LBL_Y;
}
/* find right hand */
t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
t2.dp[2] = x.dp[i];
t2.used = 3;
} while (mp_cmp_mag(&t1, &t2) == MP_GT);
/* 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 LBL_Y;
}
if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
goto LBL_Y;
}
if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
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 LBL_Y;
}
if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
goto LBL_Y;
}
if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
goto LBL_Y;
}
q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
}
}
/* now q is the quotient and x is the remainder
* [which we have to normalize]
*/
/* get sign before writing to c */
x.sign = x.used == 0 ? MP_ZPOS : a->sign;
if (c != NULL) {
mp_clamp (&q);
mp_exch (&q, c);
c->sign = neg;
}
if (d != NULL) {
mp_div_2d (&x, norm, &x, NULL);
mp_exch (&x, d);
}
res = MP_OKAY;
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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* b = a/2 */
int mp_div_2(mp_int * a, mp_int * b)
{
int x, res, oldused;
/* copy */
if (b->alloc < a->used) {
if ((res = mp_grow (b, a->used)) != MP_OKAY) {
return res;
}
}
oldused = b->used;
b->used = a->used;
{
register mp_digit r, rr, *tmpa, *tmpb;
/* source alias */
tmpa = a->dp + b->used - 1;
/* dest alias */
tmpb = b->dp + b->used - 1;
/* carry */
r = 0;
for (x = b->used - 1; x >= 0; x--) {
/* get the carry for the next iteration */
rr = *tmpa & 1;
/* shift the current digit, add in carry and store */
*tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
/* forward carry to next iteration */
r = rr;
}
/* zero excess digits */
tmpb = b->dp + b->used;
for (x = b->used; x < oldused; x++) {
*tmpb++ = 0;
}
}
b->sign = a->sign;
mp_clamp (b);
return MP_OKAY;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* 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)
{
mp_digit D, r, rr;
int x, res;
mp_int t;
/* if the shift count is <= 0 then we do no work */
if (b <= 0) {
res = mp_copy (a, c);
if (d != NULL) {
mp_zero (d);
}
return res;
}
if ((res = mp_init (&t)) != MP_OKAY) {
return res;
}
/* get the remainder */
if (d != NULL) {
if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
mp_clear (&t);
return res;
}
}
/* copy */
if ((res = mp_copy (a, c)) != MP_OKAY) {
mp_clear (&t);
return res;
}
/* shift by as many digits in the bit count */
if (b >= (int)DIGIT_BIT) {
mp_rshd (c, b / DIGIT_BIT);
}
/* shift any bit count < DIGIT_BIT */
D = (mp_digit) (b % DIGIT_BIT);
if (D != 0) {
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);
/* carry */
r = 0;
for (x = c->used - 1; x >= 0; x--) {
/* get the lower bits of this word in a temp */
rr = *tmpc & mask;
/* shift the current word and mix in the carry bits from the previous word */
*tmpc = (*tmpc >> D) | (r << shift);
--tmpc;
/* set the carry to the carry bits of the current word found above */
r = rr;
}
}
mp_clamp (c);
if (d != NULL) {
mp_exch (&t, d);
}
mp_clear (&t);
return MP_OKAY;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* End: bn_mp_div_2d.c */
/* Start: bn_mp_div_3.c */
#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@gmail.com, http://libtom.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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
static int s_is_power_of_two(mp_digit b, int *p)
{
int x;
/* fast return if no power of two */
if ((b==0) || (b & (b-1))) {
return 0;
}
for (x = 0; 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)
{
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;
}
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 >= b) {
t = (mp_digit)(w / b);
w -= ((mp_word)t) * ((mp_word)b);
} else {
t = 0;
}
q.dp[ix] = (mp_digit)t;
}
if (d != NULL) {
*d = (mp_digit)w;
}
if (c != NULL) {
mp_clamp(&q);
mp_exch(&q, c);
}
mp_clear(&q);
return res;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* End: bn_mp_div_d.c */
/* Start: bn_mp_dr_is_modulus.c */
#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@gmail.com, http://libtom.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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* 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 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) {
return err;
}
}
/* 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) + 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
* Each successive "recursion" makes the input smaller and smaller.
*/
if (mp_cmp_mag (x, n) != MP_LT) {
s_mp_sub(x, n, x);
goto top;
}
return MP_OKAY;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* End: bn_mp_dr_reduce.c */
/* Start: bn_mp_dr_setup.c */
#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@gmail.com, http://libtom.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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* swap the elements of two integers, for cases where you can't simply swap the
* mp_int pointers around
*/
void
mp_exch (mp_int * a, mp_int * b)
{
mp_int t;
t = *a;
*a = *b;
*b = t;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* calculate c = a**b using a square-multiply algorithm */
int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
{
int res, x;
mp_int g;
if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
return res;
}
/* set initial result */
mp_set (c, 1);
for (x = 0; x < (int) DIGIT_BIT; x++) {
/* square */
if ((res = mp_sqr (c, c)) != MP_OKAY) {
mp_clear (&g);
return res;
}
/* if the bit is set multiply */
if ((b & (mp_digit) (((mp_digit)1) << (DIGIT_BIT - 1))) != 0) {
if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
mp_clear (&g);
return res;
}
}
/* shift to next bit */
b <<= 1;
}
mp_clear (&g);
return MP_OKAY;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* this is a shell function that calls either the normal or Montgomery
* exptmod functions. Originally the call to the montgomery code was
* 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 dr;
/* modulus P must be positive */
if (P->sign == MP_NEG) {
return MP_VAL;
}
/* 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;
/* first compute 1/G mod P */
if ((err = mp_init(&tmpG)) != MP_OKAY) {
return err;
}
if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
mp_clear(&tmpG);
return err;
}
/* now get |X| */
if ((err = mp_init(&tmpX)) != MP_OKAY) {
mp_clear(&tmpG);
return err;
}
if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
mp_clear_multi(&tmpG, &tmpX, NULL);
return err;
}
/* and now compute (1/G)**|X| instead of G**X [X < 0] */
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) && defined(BN_S_MP_EXPTMOD_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 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 {
#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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* 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]
*/
#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[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.
*/
int (*redux)(mp_int*,mp_int*,mp_digit);
/* 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;
}
}
/* 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 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
#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) {
#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 {
#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 LBL_M;
}
redux = mp_reduce_2k;
#else
err = MP_VAL;
goto LBL_M;
#endif
}
/* setup result */
if ((err = mp_init (&res)) != MP_OKAY) {
goto LBL_M;
}
/* create M table
*
*
* 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 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 LBL_RES;
}
} else {
mp_set(&res, 1);
if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
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 LBL_RES;
}
for (x = 0; x < (winsize - 1); x++) {
if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
goto LBL_RES;
}
if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
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 LBL_RES;
}
if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
goto LBL_RES;
}
}
/* 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 so break */
if (digidx == -1) {
break;
}
/* 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;
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, mp)) != 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, mp)) != 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, mp)) != 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, mp)) != MP_OKAY) {
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 LBL_RES;
}
if ((err = redux (&res, P, mp)) != MP_OKAY) {
goto LBL_RES;
}
}
}
}
if (redmode == 0) {
/* 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;
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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* End: bn_mp_exptmod_fast.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@gmail.com, http://libtom.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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@gmail.com, http://libtom.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;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@gmail.com, http://libtom.org
*/
/* Greatest Common Divisor using the binary method */
int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
{
mp_int u, v;
int k, u_lsb, v_lsb, res;
/* either zero than gcd is the largest */
if (mp_iszero (a) == MP_YES) {
return mp_abs (b, c);
}
if (mp_iszero (b) == MP_YES) {
return mp_abs (a, c);
}
/* 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 LBL_U;
}
/* must be positive for the remainder of the algorithm */
u.sign = v.sign = MP_ZPOS;
/* 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);
if (k > 0) {
/* divide the power of two out */
if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
goto LBL_V;
}
if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
goto LBL_V;
}
}
/* 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;
}
}
if (v_lsb != k) {
if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
goto LBL_V;
}
}
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, c)) != MP_OKAY) {
goto LBL_V;
}
c->sign = MP_ZPOS;
res = MP_OKAY;
LBL_V:mp_clear (&u);
LBL_U:mp_clear (&v);
return res;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* End: bn_mp_gcd.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 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@gmail.com, http://libtom.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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@gmail.com, http://libtom.org
*/
/* grow as required */
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);
/* 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;
for (; i < a->alloc; i++) {
a->dp[i] = 0;
}
}
return MP_OKAY;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* init a new mp_int */
int mp_init (mp_int * a)
{
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;
a->alloc = MP_PREC;
a->sign = MP_ZPOS;
return MP_OKAY;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* creates "a" then copies b into it */
int mp_init_copy (mp_int * a, mp_int * b)
{
int res;
if ((res = mp_init (a)) != MP_OKAY) {
return res;
}
return mp_copy (b, a);
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* End: bn_mp_init_copy.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 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@gmail.com, http://libtom.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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@gmail.com, http://libtom.org
*/
/* 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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@gmail.com, http://libtom.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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@gmail.com, http://libtom.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);
/* alloc mem */
a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
if (a->dp == NULL) {
return MP_MEM;
}
/* set the members */
a->used = 0;
a->alloc = size;
a->sign = MP_ZPOS;
/* zero the digits */
for (x = 0; x < size; x++) {
a->dp[x] = 0;
}
return MP_OKAY;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@gmail.com, http://libtom.org
*/
/* 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 || mp_iszero(b) == 1) {
return MP_VAL;
}
/* init temps */
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_mod(a, b, &x)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_copy (b, &y)) != MP_OKAY) {
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 LBL_ERR;
}
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
if ((res = mp_copy (&x, &u)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_copy (&y, &v)) != MP_OKAY) {
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 LBL_ERR;
}
/* 4.2 if A or B is odd then */
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 LBL_ERR;
}
if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* A = A/2, B = B/2 */
if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
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 LBL_ERR;
}
/* 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 LBL_ERR;
}
if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* C = C/2, D = D/2 */
if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* 6. if u >= v then */
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 LBL_ERR;
}
if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
goto LBL_ERR;
}
} else {
/* v - v - u, C = C - A, D = D - B */
if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* if not zero goto step 4 */
if (mp_iszero (&u) == 0)
goto top;
/* now a = C, b = D, gcd == g*v */
/* if v != 1 then there is no inverse */
if (mp_cmp_d (&v, 1) != MP_EQ) {
res = MP_VAL;
goto LBL_ERR;
}
/* 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
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@gmail.com, http://libtom.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;
}
*ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO;
ERR:mp_clear(&t);
return res;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* 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 * p, int *c)
{
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;
return MP_OKAY;
}
/* step 2. if a == 1, return 1 */
if (mp_cmp_d (a, 1) == MP_EQ) {
*c = 1;
return MP_OKAY;
}
/* default */
s = 0;
/* step 3. write a = a1 * 2**k */
if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
return res;
}
if ((res = mp_init (&p1)) != MP_OKAY) {
goto LBL_A1;
}
/* 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 ((k & 1) == 0) {
s = 1;
} else {
/* 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;
} else if (residue == 3 || residue == 5) {
s = -1;
}
}
/* 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 */
if (mp_cmp_d (&a1, 1) == MP_EQ) {
*c = s;
} else {
/* n1 = n mod a1 */
if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) {
goto LBL_P1;
}
if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
goto LBL_P1;
}
*c = s * r;
}
/* done */
res = MP_OKAY;
LBL_P1:mp_clear (&p1);
LBL_A1:mp_clear (&a1);
return res;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* c = |a| * |b| using Karatsuba Multiplication using
* three half size multiplications
*
* Let B represent the radix [e.g. 2**DIGIT_BIT] and
* let n represent half of the number of digits in
* the min(a,b)
*
* a = a1 * B**n + a0
* b = b1 * B**n + b0
*
* Then, a * b =>
a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
*
* Note that a1b1 and a0b0 are used twice and only need to be
* computed once. So in total three half size (half # of
* digit) multiplications are performed, a0b0, a1b1 and
* (a1+b1)(a0+b0)
*
* Note that a multiplication of half the digits requires
* 1/4th the number of single precision multiplications so in
* total after one call 25% of the single precision multiplications
* are saved. Note also that the call to mp_mul can end up back
* in this function if the a0, a1, b0, or b1 are above the threshold.
* This is known as divide-and-conquer and leads to the famous
* O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
* the standard O(N**2) that the baseline/comba methods use.
* 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)
{
mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
int B, err;
/* default the return code to an error */
err = MP_MEM;
/* min # of digits */
B = MIN (a->used, b->used);
/* now divide in two */
B = B >> 1;
/* init copy all the temps */
if (mp_init_size (&x0, B) != MP_OKAY)
goto ERR;
if (mp_init_size (&x1, a->used - B) != MP_OKAY)
goto X0;
if (mp_init_size (&y0, B) != MP_OKAY)
goto X1;
if (mp_init_size (&y1, b->used - B) != MP_OKAY)
goto Y0;
/* init temps */
if (mp_init_size (&t1, B * 2) != MP_OKAY)
goto Y1;
if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
goto T1;
if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
goto X0Y0;
/* now shift the digits */
x0.used = y0.used = B;
x1.used = a->used - B;
y1.used = b->used - B;
{
register int x;
register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
/* we copy the digits directly instead of using higher level functions
* since we also need to shift the digits
*/
tmpa = a->dp;
tmpb = b->dp;
tmpx = x0.dp;
tmpy = y0.dp;
for (x = 0; x < B; x++) {
*tmpx++ = *tmpa++;
*tmpy++ = *tmpb++;
}
tmpx = x1.dp;
for (x = B; x < a->used; x++) {
*tmpx++ = *tmpa++;
}
tmpy = y1.dp;
for (x = B; x < b->used; x++) {
*tmpy++ = *tmpb++;
}
}
/* only need to clamp the lower words since by definition the
* upper words x1/y1 must have a known number of digits
*/
mp_clamp (&x0);
mp_clamp (&y0);
/* now calc the products x0y0 and x1y1 */
/* after this x0 is no longer required, free temp [x0==t2]! */
if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
goto X1Y1; /* x0y0 = x0*y0 */
if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
goto X1Y1; /* x1y1 = x1*y1 */
/* now calc x1+x0 and y1+y0 */
if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
goto X1Y1; /* t1 = x1 - x0 */
if (s_mp_add (&y1, &y0, &x0) != MP_OKAY)
goto X1Y1; /* t2 = y1 - y0 */
if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */
/* add x0y0 */
if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
goto X1Y1; /* t2 = x0y0 + x1y1 */
if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY)
goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
/* shift by B */
if (mp_lshd (&t1, B) != MP_OKAY)
goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
goto X1Y1; /* x1y1 = x1y1 << 2*B */
if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
goto X1Y1; /* t1 = x0y0 + t1 */
if (mp_add (&t1, &x1y1, c) != MP_OKAY)
goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
/* Algorithm succeeded set the return code to MP_OKAY */
err = MP_OKAY;
X1Y1:mp_clear (&x1y1);
X0Y0:mp_clear (&x0y0);
T1:mp_clear (&t1);
Y1:mp_clear (&y1);
Y0:mp_clear (&y0);
X1:mp_clear (&x1);
X0:mp_clear (&x0);
ERR:
return err;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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 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@gmail.com, http://libtom.org
*/
/* Karatsuba squaring, computes b = a*a using three
</