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Merge branch 'feature/timing_resist' into develop

This commit is contained in:
Steffen Jaeckel 2014-09-28 13:59:17 +02:00
parent 8ed6043209 52bb535ff7
commit 61d8c8aa42
8 changed files with 241 additions and 146 deletions
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35
bn_mp_expt_d.c
View File

@ -15,41 +15,12 @@
* Tom St Denis, tomstdenis@gmail.com, http://libtom.org
*/
/* calculate c = a**b using a square-multiply algorithm */
/* wrapper function for mp_expt_d_ex() */
int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
{
int res;
mp_int g;
if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
return res;
}
/* set initial result */
mp_set (c, 1);
while (b > 0) {
/* if the bit is set multiply */
if (b & 1) {
if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
mp_clear (&g);
return res;
}
}
/* square */
if (b > 1 && (res = mp_sqr (&g, &g)) != MP_OKAY) {
mp_clear (&g);
return res;
}
/* shift to next bit */
b >>= 1;
}
mp_clear (&g);
return MP_OKAY;
return mp_expt_d_ex(a, b, c, 0);
}
#endif
/* $Source$ */

81
bn_mp_expt_d_ex.c Normal file
View File

@ -0,0 +1,81 @@
#include <tommath.h>
#ifdef BN_MP_EXPT_D_EX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@gmail.com, http://libtom.org
*/
/* calculate c = a**b using a square-multiply algorithm */
int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
{
int res;
unsigned int x;
mp_int g;
if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
return res;
}
/* set initial result */
mp_set (c, 1);
if (fast) {
while (b > 0) {
/* if the bit is set multiply */
if (b & 1) {
if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
mp_clear (&g);
return res;
}
}
/* square */
if (b > 1 && (res = mp_sqr (&g, &g)) != MP_OKAY) {
mp_clear (&g);
return res;
}
/* shift to next bit */
b >>= 1;
}
}
else {
for (x = 0; x < 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;
}
} /* if ... else */
mp_clear (&g);
return MP_OKAY;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */

110
bn_mp_n_root.c
View File

@ -15,116 +15,14 @@
* Tom St Denis, tomstdenis@gmail.com, http://libtom.org
*/
/* find the n'th root of an integer
*
* Result found such that (c)**b <= a and (c+1)**b > a
*
* This algorithm uses Newton's approximation
* x[i+1] = x[i] - f(x[i])/f'(x[i])
* which will find the root in log(N) time where
* each step involves a fair bit. This is not meant to
* find huge roots [square and cube, etc].
/* wrapper function for mp_n_root_ex()
* computes c = (a)**(1/b) such that (c)**b <= a and (c+1)**b > a
*/
int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
{
mp_int t1, t2, t3;
int res, neg;
/* input must be positive if b is even */
if ((b & 1) == 0 && a->sign == MP_NEG) {
return MP_VAL;
}
if ((res = mp_init (&t1)) != MP_OKAY) {
return res;
}
if ((res = mp_init (&t2)) != MP_OKAY) {
goto LBL_T1;
}
if ((res = mp_init (&t3)) != MP_OKAY) {
goto LBL_T2;
}
/* if a is negative fudge the sign but keep track */
neg = a->sign;
a->sign = MP_ZPOS;
/* t2 = 2 */
mp_set (&t2, 2);
do {
/* t1 = t2 */
if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
goto LBL_T3;
}
/* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
/* t3 = t1**(b-1) */
if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) {
goto LBL_T3;
}
/* numerator */
/* t2 = t1**b */
if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
goto LBL_T3;
}
/* t2 = t1**b - a */
if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
goto LBL_T3;
}
/* denominator */
/* t3 = t1**(b-1) * b */
if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
goto LBL_T3;
}
/* t3 = (t1**b - a)/(b * t1**(b-1)) */
if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
goto LBL_T3;
}
if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
goto LBL_T3;
}
} while (mp_cmp (&t1, &t2) != MP_EQ);
/* result can be off by a few so check */
for (;;) {
if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) {
goto LBL_T3;
}
if (mp_cmp (&t2, a) == MP_GT) {
if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
goto LBL_T3;
}
} else {
break;
}
}
/* reset the sign of a first */
a->sign = neg;
/* set the result */
mp_exch (&t1, c);
/* set the sign of the result */
c->sign = neg;
res = MP_OKAY;
LBL_T3:mp_clear (&t3);
LBL_T2:mp_clear (&t2);
LBL_T1:mp_clear (&t1);
return res;
return mp_n_root_ex(a, b, c, 0);
}
#endif
/* $Source$ */

132
bn_mp_n_root_ex.c Normal file
View File

@ -0,0 +1,132 @@
#include <tommath.h>
#ifdef BN_MP_N_ROOT_EX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@gmail.com, http://libtom.org
*/
/* find the n'th root of an integer
*
* Result found such that (c)**b <= a and (c+1)**b > a
*
* This algorithm uses Newton's approximation
* x[i+1] = x[i] - f(x[i])/f'(x[i])
* which will find the root in log(N) time where
* each step involves a fair bit. This is not meant to
* find huge roots [square and cube, etc].
*/
int mp_n_root_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
{
mp_int t1, t2, t3;
int res, neg;
/* input must be positive if b is even */
if ((b & 1) == 0 && a->sign == MP_NEG) {
return MP_VAL;
}
if ((res = mp_init (&t1)) != MP_OKAY) {
return res;
}
if ((res = mp_init (&t2)) != MP_OKAY) {
goto LBL_T1;
}
if ((res = mp_init (&t3)) != MP_OKAY) {
goto LBL_T2;
}
/* if a is negative fudge the sign but keep track */
neg = a->sign;
a->sign = MP_ZPOS;
/* t2 = 2 */
mp_set (&t2, 2);
do {
/* t1 = t2 */
if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
goto LBL_T3;
}
/* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
/* t3 = t1**(b-1) */
if ((res = mp_expt_d_ex (&t1, b - 1, &t3, fast)) != MP_OKAY) {
goto LBL_T3;
}
/* numerator */
/* t2 = t1**b */
if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
goto LBL_T3;
}
/* t2 = t1**b - a */
if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
goto LBL_T3;
}
/* denominator */
/* t3 = t1**(b-1) * b */
if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
goto LBL_T3;
}
/* t3 = (t1**b - a)/(b * t1**(b-1)) */
if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
goto LBL_T3;
}
if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
goto LBL_T3;
}
} while (mp_cmp (&t1, &t2) != MP_EQ);
/* result can be off by a few so check */
for (;;) {
if ((res = mp_expt_d_ex (&t1, b, &t2, fast)) != MP_OKAY) {
goto LBL_T3;
}
if (mp_cmp (&t2, a) == MP_GT) {
if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
goto LBL_T3;
}
} else {
break;
}
}
/* reset the sign of a first */
a->sign = neg;
/* set the result */
mp_exch (&t1, c);
/* set the sign of the result */
c->sign = neg;
res = MP_OKAY;
LBL_T3:mp_clear (&t3);
LBL_T2:mp_clear (&t2);
LBL_T1:mp_clear (&t1);
return res;
}
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */

9
demo/demo.c
View File

@ -179,8 +179,13 @@ printf("compare no compare!\n"); return EXIT_FAILURE; }
printf("\nmp_sqrt() error!");
return EXIT_FAILURE;
}
mp_n_root(&a, 2, &a);
if (mp_cmp_mag(&b, &a) != MP_EQ) {
mp_n_root_ex(&a, 2, &c, 0);
mp_n_root_ex(&a, 2, &d, 1);
if (mp_cmp_mag(&c, &d) != MP_EQ) {
printf("\nmp_n_root_ex() bad result!");
return EXIT_FAILURE;
}
if (mp_cmp_mag(&b, &c) != MP_EQ) {
printf("mp_sqrt() bad result!\n");
return 1;
}

2
makefile
View File

@ -96,7 +96,7 @@ bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \
bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o bn_mp_import.o bn_mp_export.o \
bn_mp_balance_mul.o
bn_mp_balance_mul.o bn_mp_expt_d_ex.o bn_mp_n_root_ex.o
$(LIBNAME): $(OBJECTS)
$(AR) $(ARFLAGS) $@ $(OBJECTS)

2
tommath.h
View File

@ -364,6 +364,7 @@ int mp_div_3(mp_int *a, mp_int *c, mp_digit *d);
/* c = a**b */
int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast);
/* c = a mod b, 0 <= c < b */
int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
@ -399,6 +400,7 @@ int mp_lcm(mp_int *a, mp_int *b, mp_int *c);
* returns error if a < 0 and b is even
*/
int mp_n_root(mp_int *a, mp_digit b, mp_int *c);
int mp_n_root_ex (mp_int * a, mp_digit b, mp_int * c, int fast);
/* special sqrt algo */
int mp_sqrt(mp_int *arg, mp_int *ret);

16
tommath_class.h
View File

@ -41,6 +41,7 @@
#define BN_MP_EXCH_C
#define BN_MP_EXPORT_C
#define BN_MP_EXPT_D_C
#define BN_MP_EXPT_D_EX_C
#define BN_MP_EXPTMOD_C
#define BN_MP_EXPTMOD_FAST_C
#define BN_MP_EXTEUCLID_C
@ -76,6 +77,7 @@
#define BN_MP_MUL_D_C
#define BN_MP_MULMOD_C
#define BN_MP_N_ROOT_C
#define BN_MP_N_ROOT_EX_C
#define BN_MP_NEG_C
#define BN_MP_OR_C
#define BN_MP_PRIME_FERMAT_C
@ -333,6 +335,10 @@
#endif
#if defined(BN_MP_EXPT_D_C)
#define BN_MP_EXPT_D_EX_C
#endif
#if defined(BN_MP_EXPT_D_EX_C)
#define BN_MP_INIT_COPY_C
#define BN_MP_SET_C
#define BN_MP_MUL_C
@ -609,10 +615,14 @@
#endif
#if defined(BN_MP_N_ROOT_C)
#define BN_MP_N_ROOT_EX_C
#endif
#if defined(BN_MP_N_ROOT_EX_C)
#define BN_MP_INIT_C
#define BN_MP_SET_C
#define BN_MP_COPY_C
#define BN_MP_EXPT_D_C
#define BN_MP_EXPT_D_EX_C
#define BN_MP_MUL_C
#define BN_MP_SUB_C
#define BN_MP_MUL_D_C
@ -1018,7 +1028,3 @@
#else
#define LTM_LAST
#endif
/* $Source$ */
/* $Revision$ */
/* $Date$ */