Skip to content

HTTPS clone URL

Subversion checkout URL

You can clone with HTTPS or Subversion.

Download ZIP
Fetching contributors…

Cannot retrieve contributors at this time

9529 lines (8136 sloc) 230.045 kb
/* 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@iahu.ca, http://math.libtomcrypt.org
*/
static const struct {
int code;
char *msg;
} msgs[] = {
{ MP_OKAY, "Successful" },
{ MP_MEM, "Out of heap" },
{ MP_VAL, "Value out of range" }
};
/* return a char * string for a given code */
char *mp_error_to_string(int code)
{
int x;
/* scan the lookup table for the given message */
for (x = 0; x < (int)(sizeof(msgs) / sizeof(msgs[0])); x++) {
if (msgs[x].code == code) {
return msgs[x].msg;
}
}
/* generic reply for invalid code */
return "Invalid error code";
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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);
}
/* store final carry */
W[ix] = (mp_digit)(_W & MP_MASK);
/* 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@iahu.ca, http://math.libtomcrypt.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);
}
/* store final carry */
W[ix] = (mp_digit)(_W & MP_MASK);
/* 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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.org
*/
#include <stdarg.h>
void mp_clear_multi(mp_int *mp, ...)
{
mp_int* next_mp = mp;
va_list args;
va_start(args, mp);
while (next_mp != NULL) {
mp_clear(next_mp);
next_mp = va_arg(args, mp_int*);
}
va_end(args);
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@iahu.ca, http://math.libtomcrypt.org
*/
/* compare two ints (signed)*/
int
mp_cmp (mp_int * a, mp_int * b)
{
/* compare based on sign */
if (a->sign != 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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.org
*/
static const int lnz[16] = {
4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
};
/* Counts the number of lsbs which are zero before the first zero bit */
int mp_cnt_lsb(mp_int *a)
{
int x;
mp_digit q, qq;
/* easy out */
if (mp_iszero(a) == 1) {
return 0;
}
/* scan lower digits until non-zero */
for (x = 0; x < a->used && a->dp[x] == 0; x++);
q = a->dp[x];
x *= DIGIT_BIT;
/* now scan this digit until a 1 is found */
if ((q & 1) == 0) {
do {
qq = q & 15;
x += lnz[qq];
q >>= 4;
} while (qq == 0);
}
return x;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.org
*/
/* divide by three (based on routine from MPI and the GMP manual) */
int
mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
{
mp_int q;
mp_word w, t;
mp_digit b;
int res, ix;
/* b = 2**DIGIT_BIT / 3 */
b = (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3);
if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
return res;
}
q.used = a->used;
q.sign = a->sign;
w = 0;
for (ix = a->used - 1; ix >= 0; ix--) {
w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
if (w >= 3) {
/* multiply w by [1/3] */
t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT);
/* now subtract 3 * [w/3] from w, to get the remainder */
w -= t+t+t;
/* fixup the remainder as required since
* the optimization is not exact.
*/
while (w >= 3) {
t += 1;
w -= 3;
}
} else {
t = 0;
}
q.dp[ix] = (mp_digit)t;
}
/* [optional] store the remainder */
if (d != NULL) {
*d = (mp_digit)w;
}
/* [optional] store the quotient */
if (c != NULL) {
mp_clamp(&q);
mp_exch(&q, c);
}
mp_clear(&q);
return res;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@iahu.ca, http://math.libtomcrypt.org
*/
static int s_is_power_of_two(mp_digit b, int *p)
{
int x;
for (x = 1; x < DIGIT_BIT; x++) {
if (b == (((mp_digit)1)<<x)) {
*p = x;
return 1;
}
}
return 0;
}
/* single digit division (based on routine from MPI) */
int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
{
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@iahu.ca, http://math.libtomcrypt.org
*/
/* determines if a number is a valid DR modulus */
int mp_dr_is_modulus(mp_int *a)
{
int ix;
/* must be at least two digits */
if (a->used < 2) {
return 0;
}
/* must be of the form b**k - a [a <= b] so all
* but the first digit must be equal to -1 (mod b).
*/
for (ix = 1; ix < a->used; ix++) {
if (a->dp[ix] != MP_MASK) {
return 0;
}
}
return 1;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.org
*/
/* determines the setup value */
void mp_dr_setup(mp_int *a, mp_digit *d)
{
/* the casts are required if DIGIT_BIT is one less than
* the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
*/
*d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
((mp_word)a->dp[0]));
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.org
*/
/* Extended euclidean algorithm of (a, b) produces
a*u1 + b*u2 = u3
*/
int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
{
mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp;
int err;
if ((err = mp_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) {
return err;
}
/* initialize, (u1,u2,u3) = (1,0,a) */
mp_set(&u1, 1);
if ((err = mp_copy(a, &u3)) != MP_OKAY) { goto _ERR; }
/* initialize, (v1,v2,v3) = (0,1,b) */
mp_set(&v2, 1);
if ((err = mp_copy(b, &v3)) != MP_OKAY) { goto _ERR; }
/* loop while v3 != 0 */
while (mp_iszero(&v3) == MP_NO) {
/* q = u3/v3 */
if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY) { goto _ERR; }
/* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY) { goto _ERR; }
if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY) { goto _ERR; }
if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY) { goto _ERR; }
if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY) { goto _ERR; }
if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY) { goto _ERR; }
if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY) { goto _ERR; }
/* (u1,u2,u3) = (v1,v2,v3) */
if ((err = mp_copy(&v1, &u1)) != MP_OKAY) { goto _ERR; }
if ((err = mp_copy(&v2, &u2)) != MP_OKAY) { goto _ERR; }
if ((err = mp_copy(&v3, &u3)) != MP_OKAY) { goto _ERR; }
/* (v1,v2,v3) = (t1,t2,t3) */
if ((err = mp_copy(&t1, &v1)) != MP_OKAY) { goto _ERR; }
if ((err = mp_copy(&t2, &v2)) != MP_OKAY) { goto _ERR; }
if ((err = mp_copy(&t3, &v3)) != MP_OKAY) { goto _ERR; }
}
/* make sure U3 >= 0 */
if (u3.sign == MP_NEG) {
mp_neg(&u1, &u1);
mp_neg(&u2, &u2);
mp_neg(&u3, &u3);
}
/* copy result out */
if (U1 != NULL) { mp_exch(U1, &u1); }
if (U2 != NULL) { mp_exch(U2, &u2); }
if (U3 != NULL) { mp_exch(U3, &u3); }
err = MP_OKAY;
_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
return err;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@iahu.ca, http://math.libtomcrypt.org
*/
/* read a bigint from a file stream in ASCII */
int mp_fread(mp_int *a, int radix, FILE *stream)
{
int err, ch, neg, y;
/* clear a */
mp_zero(a);
/* if first digit is - then set negative */
ch = fgetc(stream);
if (ch == '-') {
neg = MP_NEG;
ch = fgetc(stream);
} else {
neg = MP_ZPOS;
}
for (;;) {
/* find y in the radix map */
for (y = 0; y < radix; y++) {
if (mp_s_rmap[y] == ch) {
break;
}
}
if (y == radix) {
break;
}
/* shift up and add */
if ((err = mp_mul_d(a, radix, a)) != MP_OKAY) {
return err;
}
if ((err = mp_add_d(a, y, a)) != MP_OKAY) {
return err;
}
ch = fgetc(stream);
}
if (mp_cmp_d(a, 0) != MP_EQ) {
a->sign = neg;
}
return MP_OKAY;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@iahu.ca, http://math.libtomcrypt.org
*/
int mp_fwrite(mp_int *a, int radix, FILE *stream)
{
char *buf;
int err, len, x;
if ((err = mp_radix_size(a, radix, &len)) != MP_OKAY) {
return err;
}
buf = OPT_CAST(char) XMALLOC (len);
if (buf == NULL) {
return MP_MEM;
}
if ((err = mp_toradix(a, buf, radix)) != MP_OKAY) {
XFREE (buf);
return err;
}
for (x = 0; x < len; x++) {
if (fputc(buf[x], stream) == EOF) {
XFREE (buf);
return MP_VAL;
}
}
XFREE (buf);
return MP_OKAY;
}
#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@iahu.ca, http://math.libtomcrypt.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) == 1 && mp_iszero (b) == 0) {
return mp_abs (b, c);
}
if (mp_iszero (a) == 0 && mp_iszero (b) == 1) {
return mp_abs (a, c);
}
/* optimized. At this point if a == 0 then
* b must equal zero too
*/
if (mp_iszero (a) == 1) {
mp_zero(c);
return MP_OKAY;
}
/* 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@iahu.ca, http://math.libtomcrypt.org
*/
/* get the lower 32-bits of an mp_int */
unsigned long mp_get_int(mp_int * a)
{
int i;
unsigned long res;
if (a->used == 0) {
return 0;
}
/* get number of digits of the lsb we have to read */
i = MIN(a->used,(int)((sizeof(unsigned long)*CHAR_BIT+DIGIT_BIT-1)/DIGIT_BIT))-1;
/* get most significant digit of result */
res = DIGIT(a,i);
while (--i >= 0) {
res = (res << DIGIT_BIT) | DIGIT(a,i);
}
/* force result to 32-bits always so it is consistent on non 32-bit platforms */
return res & 0xFFFFFFFFUL;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.org
*/
#include <stdarg.h>
int mp_init_multi(mp_int *mp, ...)
{
mp_err res = MP_OKAY; /* Assume ok until proven otherwise */
int n = 0; /* Number of ok inits */
mp_int* cur_arg = mp;
va_list args;
va_start(args, mp); /* init args to next argument from caller */
while (cur_arg != NULL) {
if (mp_init(cur_arg) != MP_OKAY) {
/* Oops - error! Back-track and mp_clear what we already
succeeded in init-ing, then return error.
*/
va_list clean_args;
/* end the current list */
va_end(args);
/* now start cleaning up */
cur_arg = mp;
va_start(clean_args, mp);
while (n--) {
mp_clear(cur_arg);
cur_arg = va_arg(clean_args, mp_int*);
}
va_end(clean_args);
res = MP_MEM;
break;
}
n++;
cur_arg = va_arg(args, mp_int*);
}
va_end(args);
return res; /* Assumed ok, if error flagged above. */
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.org
*/
/* initialize and set a digit */
int mp_init_set_int (mp_int * a, unsigned long b)
{
int err;
if ((err = mp_init(a)) != MP_OKAY) {
return err;
}
return mp_set_int(a, b);
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@iahu.ca, http://math.libtomcrypt.org
*/
/* init an mp_init for a given size */
int mp_init_size (mp_int * a, int size)
{
int x;
/* pad size so there are always extra digits */
size += (MP_PREC * 2) - (size % MP_PREC);
/* 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@iahu.ca, http://math.libtomcrypt.org
*/
/* hac 14.61, pp608 */
int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
/* b cannot be negative */
if (b->sign == MP_NEG || mp_iszero(b) == 1) {
return MP_VAL;
}
#ifdef BN_FAST_MP_INVMOD_C
/* if the modulus is odd we can use a faster routine instead */
if (mp_isodd (b) == 1) {
return fast_mp_invmod (a, b, c);
}
#endif
#ifdef BN_MP_INVMOD_SLOW_C
return mp_invmod_slow(a, b, c);
#endif
return MP_VAL;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */
/* 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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.org
*/
/* Check if remainders are possible squares - fast exclude non-squares */
static const char rem_128[128] = {
0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1
};
static const char rem_105[105] = {
0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1,
0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1,
1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1,
1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1
};
/* Store non-zero to ret if arg is square, and zero if not */
int mp_is_square(mp_int *arg,int *ret)
{
int res;
mp_digit c;
mp_int t;
unsigned long r;
/* Default to Non-square :) */
*ret = MP_NO;
if (arg->sign == MP_NEG) {
return MP_VAL;
}
/* digits used? (TSD) */
if (arg->used == 0) {
return MP_OKAY;
}
/* First check mod 128 (suppose that DIGIT_BIT is at least 7) */
if (rem_128[127 & DIGIT(arg,0)] == 1) {
return MP_OKAY;
}
/* Next check mod 105 (3*5*7) */
if ((res = mp_mod_d(arg,105,&c)) != MP_OKAY) {
return res;
}
if (rem_105[c] == 1) {
return MP_OKAY;
}
if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) {
return res;
}
if ((res = mp_mod(arg,&t,&t)) != MP_OKAY) {
goto ERR;
}
r = mp_get_int(&t);
/* Check for other prime modules, note it's not an ERROR but we must
* free "t" so the easiest way is to goto ERR. We know that res
* is already equal to MP_OKAY from the mp_mod call
*/
if ( (1L<<(r%11)) & 0x5C4L ) goto ERR;
if ( (1L<<(r%13)) & 0x9E4L ) goto ERR;
if ( (1L<<(r%17)) & 0x5CE8L ) goto ERR;
if ( (1L<<(r%19)) & 0x4F50CL ) goto ERR;
if ( (1L<<(r%23)) & 0x7ACCA0L ) goto ERR;
if ( (1L<<(r%29)) & 0xC2EDD0CL ) goto ERR;
if ( (1L<<(r%31)) & 0x6DE2B848L ) goto ERR;
/* Final check - is sqr(sqrt(arg)) == arg ? */
if ((res = mp_sqrt(arg,&t)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sqr(&t,&t)) != MP_OKAY) {
goto ERR;
}
*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@iahu.ca, http://math.libtomcrypt.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@iahu.ca, http://math.libtomcrypt.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.
*