Merge branch 'feature/timing_resist' into develop
This commit is contained in:
Steffen Jaeckel
commit
61d8c8aa42
@ -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);
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||||
return res;
|
||||
}
|
||||
}
|
||||
|
||||
/* square */
|
||||
if (b > 1 && (res = mp_sqr (&g, &g)) != MP_OKAY) {
|
||||
mp_clear (&g);
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||||
return res;
|
||||
}
|
||||
|
||||
/* shift to next bit */
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||||
b >>= 1;
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||||
}
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||||
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||||
mp_clear (&g);
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||||
return MP_OKAY;
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||||
return mp_expt_d_ex(a, b, c, 0);
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}
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||||
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||||
#endif
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||||
|
||||
/* $Source$ */
|
||||
|
||||
81
bn_mp_expt_d_ex.c
Normal file
81
bn_mp_expt_d_ex.c
Normal 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 */
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||||
int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
|
||||
{
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||||
int res;
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||||
unsigned int x;
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||||
|
||||
mp_int g;
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||||
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||||
if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
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||||
return res;
|
||||
}
|
||||
|
||||
/* set initial result */
|
||||
mp_set (c, 1);
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||||
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);
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||||
return res;
|
||||
}
|
||||
}
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||||
|
||||
/* square */
|
||||
if (b > 1 && (res = mp_sqr (&g, &g)) != MP_OKAY) {
|
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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);
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||||
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
110
bn_mp_n_root.c
@ -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
132
bn_mp_n_root_ex.c
Normal 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
|
||||
|
||||
/* $Source$ */
|
||||
/* $Revision$ */
|
||||
/* $Date$ */
|
||||
@ -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
2
makefile
@ -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)
|
||||
|
||||
@ -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);
|
||||
|
||||
@ -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
|
||||
|
||||
/* $Source$ */
|
||||
/* $Revision$ */
|
||||
/* $Date$ */
|
||||
|
||||
Loading…
Reference in New Issue
Block a user