diff options
Diffstat (limited to 'third_party/heimdal/lib/hcrypto/libtommath/pre_gen/mpi.c')
| -rw-r--r-- | third_party/heimdal/lib/hcrypto/libtommath/pre_gen/mpi.c | 9541 |
1 files changed, 9541 insertions, 0 deletions
diff --git a/third_party/heimdal/lib/hcrypto/libtommath/pre_gen/mpi.c b/third_party/heimdal/lib/hcrypto/libtommath/pre_gen/mpi.c new file mode 100644 index 00000000000..96f001d1fe5 --- /dev/null +++ b/third_party/heimdal/lib/hcrypto/libtommath/pre_gen/mpi.c @@ -0,0 +1,9541 @@ +/* Start: bn_cutoffs.c */ +#include "tommath_private.h" +#ifdef BN_CUTOFFS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#ifndef MP_FIXED_CUTOFFS +#include "tommath_cutoffs.h" +int KARATSUBA_MUL_CUTOFF = MP_DEFAULT_KARATSUBA_MUL_CUTOFF, + KARATSUBA_SQR_CUTOFF = MP_DEFAULT_KARATSUBA_SQR_CUTOFF, + TOOM_MUL_CUTOFF = MP_DEFAULT_TOOM_MUL_CUTOFF, + TOOM_SQR_CUTOFF = MP_DEFAULT_TOOM_SQR_CUTOFF; +#endif + +#endif + +/* End: bn_cutoffs.c */ + +/* Start: bn_deprecated.c */ +#include "tommath_private.h" +#ifdef BN_DEPRECATED_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#ifdef BN_MP_GET_BIT_C +int mp_get_bit(const mp_int *a, int b) +{ + if (b < 0) { + return MP_VAL; + } + return (s_mp_get_bit(a, (unsigned int)b) == MP_YES) ? MP_YES : MP_NO; +} +#endif +#ifdef BN_MP_JACOBI_C +mp_err mp_jacobi(const mp_int *a, const mp_int *n, int *c) +{ + if (a->sign == MP_NEG) { + return MP_VAL; + } + if (mp_cmp_d(n, 0uL) != MP_GT) { + return MP_VAL; + } + return mp_kronecker(a, n, c); +} +#endif +#ifdef BN_MP_PRIME_RANDOM_EX_C +mp_err mp_prime_random_ex(mp_int *a, int t, int size, int flags, private_mp_prime_callback cb, void *dat) +{ + return s_mp_prime_random_ex(a, t, size, flags, cb, dat); +} +#endif +#ifdef BN_MP_RAND_DIGIT_C +mp_err mp_rand_digit(mp_digit *r) +{ + mp_err err = s_mp_rand_source(r, sizeof(mp_digit)); + *r &= MP_MASK; + return err; +} +#endif +#ifdef BN_FAST_MP_INVMOD_C +mp_err fast_mp_invmod(const mp_int *a, const mp_int *b, mp_int *c) +{ + return s_mp_invmod_fast(a, b, c); +} +#endif +#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C +mp_err fast_mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho) +{ + return s_mp_montgomery_reduce_fast(x, n, rho); +} +#endif +#ifdef BN_FAST_S_MP_MUL_DIGS_C +mp_err fast_s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs) +{ + return s_mp_mul_digs_fast(a, b, c, digs); +} +#endif +#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C +mp_err fast_s_mp_mul_high_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs) +{ + return s_mp_mul_high_digs_fast(a, b, c, digs); +} +#endif +#ifdef BN_FAST_S_MP_SQR_C +mp_err fast_s_mp_sqr(const mp_int *a, mp_int *b) +{ + return s_mp_sqr_fast(a, b); +} +#endif +#ifdef BN_MP_BALANCE_MUL_C +mp_err mp_balance_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + return s_mp_balance_mul(a, b, c); +} +#endif +#ifdef BN_MP_EXPTMOD_FAST_C +mp_err mp_exptmod_fast(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode) +{ + return s_mp_exptmod_fast(G, X, P, Y, redmode); +} +#endif +#ifdef BN_MP_INVMOD_SLOW_C +mp_err mp_invmod_slow(const mp_int *a, const mp_int *b, mp_int *c) +{ + return s_mp_invmod_slow(a, b, c); +} +#endif +#ifdef BN_MP_KARATSUBA_MUL_C +mp_err mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + return s_mp_karatsuba_mul(a, b, c); +} +#endif +#ifdef BN_MP_KARATSUBA_SQR_C +mp_err mp_karatsuba_sqr(const mp_int *a, mp_int *b) +{ + return s_mp_karatsuba_sqr(a, b); +} +#endif +#ifdef BN_MP_TOOM_MUL_C +mp_err mp_toom_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + return s_mp_toom_mul(a, b, c); +} +#endif +#ifdef BN_MP_TOOM_SQR_C +mp_err mp_toom_sqr(const mp_int *a, mp_int *b) +{ + return s_mp_toom_sqr(a, b); +} +#endif +#ifdef S_MP_REVERSE_C +void bn_reverse(unsigned char *s, int len) +{ + if (len > 0) { + s_mp_reverse(s, (size_t)len); + } +} +#endif +#ifdef BN_MP_TC_AND_C +mp_err mp_tc_and(const mp_int *a, const mp_int *b, mp_int *c) +{ + return mp_and(a, b, c); +} +#endif +#ifdef BN_MP_TC_OR_C +mp_err mp_tc_or(const mp_int *a, const mp_int *b, mp_int *c) +{ + return mp_or(a, b, c); +} +#endif +#ifdef BN_MP_TC_XOR_C +mp_err mp_tc_xor(const mp_int *a, const mp_int *b, mp_int *c) +{ + return mp_xor(a, b, c); +} +#endif +#ifdef BN_MP_TC_DIV_2D_C +mp_err mp_tc_div_2d(const mp_int *a, int b, mp_int *c) +{ + return mp_signed_rsh(a, b, c); +} +#endif +#ifdef BN_MP_INIT_SET_INT_C +mp_err mp_init_set_int(mp_int *a, unsigned long b) +{ + return mp_init_u32(a, (uint32_t)b); +} +#endif +#ifdef BN_MP_SET_INT_C +mp_err mp_set_int(mp_int *a, unsigned long b) +{ + mp_set_u32(a, (uint32_t)b); + return MP_OKAY; +} +#endif +#ifdef BN_MP_SET_LONG_C +mp_err mp_set_long(mp_int *a, unsigned long b) +{ + mp_set_u64(a, b); + return MP_OKAY; +} +#endif +#ifdef BN_MP_SET_LONG_LONG_C +mp_err mp_set_long_long(mp_int *a, unsigned long long b) +{ + mp_set_u64(a, b); + return MP_OKAY; +} +#endif +#ifdef BN_MP_GET_INT_C +unsigned long mp_get_int(const mp_int *a) +{ + return (unsigned long)mp_get_mag_u32(a); +} +#endif +#ifdef BN_MP_GET_LONG_C +unsigned long mp_get_long(const mp_int *a) +{ + return (unsigned long)mp_get_mag_ul(a); +} +#endif +#ifdef BN_MP_GET_LONG_LONG_C +unsigned long long mp_get_long_long(const mp_int *a) +{ + return mp_get_mag_ull(a); +} +#endif +#ifdef BN_MP_PRIME_IS_DIVISIBLE_C +mp_err mp_prime_is_divisible(const mp_int *a, mp_bool *result) +{ + return s_mp_prime_is_divisible(a, result); +} +#endif +#ifdef BN_MP_EXPT_D_EX_C +mp_err mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast) +{ + (void)fast; + if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) { + return MP_VAL; + } + return mp_expt_u32(a, (uint32_t)b, c); +} +#endif +#ifdef BN_MP_EXPT_D_C +mp_err mp_expt_d(const mp_int *a, mp_digit b, mp_int *c) +{ + if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) { + return MP_VAL; + } + return mp_expt_u32(a, (uint32_t)b, c); +} +#endif +#ifdef BN_MP_N_ROOT_EX_C +mp_err mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast) +{ + (void)fast; + if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) { + return MP_VAL; + } + return mp_root_u32(a, (uint32_t)b, c); +} +#endif +#ifdef BN_MP_N_ROOT_C +mp_err mp_n_root(const mp_int *a, mp_digit b, mp_int *c) +{ + if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) { + return MP_VAL; + } + return mp_root_u32(a, (uint32_t)b, c); +} +#endif +#ifdef BN_MP_UNSIGNED_BIN_SIZE_C +int mp_unsigned_bin_size(const mp_int *a) +{ + return (int)mp_ubin_size(a); +} +#endif +#ifdef BN_MP_READ_UNSIGNED_BIN_C +mp_err mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c) +{ + return mp_from_ubin(a, b, (size_t) c); +} +#endif +#ifdef BN_MP_TO_UNSIGNED_BIN_C +mp_err mp_to_unsigned_bin(const mp_int *a, unsigned char *b) +{ + return mp_to_ubin(a, b, SIZE_MAX, NULL); +} +#endif +#ifdef BN_MP_TO_UNSIGNED_BIN_N_C +mp_err mp_to_unsigned_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen) +{ + size_t n = mp_ubin_size(a); + if (*outlen < (unsigned long)n) { + return MP_VAL; + } + *outlen = (unsigned long)n; + return mp_to_ubin(a, b, n, NULL); +} +#endif +#ifdef BN_MP_SIGNED_BIN_SIZE_C +int mp_signed_bin_size(const mp_int *a) +{ + return (int)mp_sbin_size(a); +} +#endif +#ifdef BN_MP_READ_SIGNED_BIN_C +mp_err mp_read_signed_bin(mp_int *a, const unsigned char *b, int c) +{ + return mp_from_sbin(a, b, (size_t) c); +} +#endif +#ifdef BN_MP_TO_SIGNED_BIN_C +mp_err mp_to_signed_bin(const mp_int *a, unsigned char *b) +{ + return mp_to_sbin(a, b, SIZE_MAX, NULL); +} +#endif +#ifdef BN_MP_TO_SIGNED_BIN_N_C +mp_err mp_to_signed_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen) +{ + size_t n = mp_sbin_size(a); + if (*outlen < (unsigned long)n) { + return MP_VAL; + } + *outlen = (unsigned long)n; + return mp_to_sbin(a, b, n, NULL); +} +#endif +#ifdef BN_MP_TORADIX_N_C +mp_err mp_toradix_n(const mp_int *a, char *str, int radix, int maxlen) +{ + if (maxlen < 0) { + return MP_VAL; + } + return mp_to_radix(a, str, (size_t)maxlen, NULL, radix); +} +#endif +#ifdef BN_MP_TORADIX_C +mp_err mp_toradix(const mp_int *a, char *str, int radix) +{ + return mp_to_radix(a, str, SIZE_MAX, NULL, radix); +} +#endif +#ifdef BN_MP_IMPORT_C +mp_err mp_import(mp_int *rop, size_t count, int order, size_t size, int endian, size_t nails, + const void *op) +{ + return mp_unpack(rop, count, order, size, endian, nails, op); +} +#endif +#ifdef BN_MP_EXPORT_C +mp_err mp_export(void *rop, size_t *countp, int order, size_t size, + int endian, size_t nails, const mp_int *op) +{ + return mp_pack(rop, SIZE_MAX, countp, order, size, endian, nails, op); +} +#endif +#endif + +/* End: bn_deprecated.c */ + +/* Start: bn_mp_2expt.c */ +#include "tommath_private.h" +#ifdef BN_MP_2EXPT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* computes a = 2**b + * + * Simple algorithm which zeroes the int, grows it then just sets one bit + * as required. + */ +mp_err mp_2expt(mp_int *a, int b) +{ + mp_err err; + + /* zero a as per default */ + mp_zero(a); + + /* grow a to accomodate the single bit */ + if ((err = mp_grow(a, (b / MP_DIGIT_BIT) + 1)) != MP_OKAY) { + return err; + } + + /* set the used count of where the bit will go */ + a->used = (b / MP_DIGIT_BIT) + 1; + + /* put the single bit in its place */ + a->dp[b / MP_DIGIT_BIT] = (mp_digit)1 << (mp_digit)(b % MP_DIGIT_BIT); + + return MP_OKAY; +} +#endif + +/* End: bn_mp_2expt.c */ + +/* Start: bn_mp_abs.c */ +#include "tommath_private.h" +#ifdef BN_MP_ABS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* b = |a| + * + * Simple function copies the input and fixes the sign to positive + */ +mp_err mp_abs(const mp_int *a, mp_int *b) +{ + mp_err err; + + /* copy a to b */ + if (a != b) { + if ((err = mp_copy(a, b)) != MP_OKAY) { + return err; + } + } + + /* force the sign of b to positive */ + b->sign = MP_ZPOS; + + return MP_OKAY; +} +#endif + +/* End: bn_mp_abs.c */ + +/* Start: bn_mp_add.c */ +#include "tommath_private.h" +#ifdef BN_MP_ADD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* high level addition (handles signs) */ +mp_err mp_add(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_sign sa, sb; + mp_err err; + + /* 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; + err = 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; + err = s_mp_sub(b, a, c); + } else { + c->sign = sa; + err = s_mp_sub(a, b, c); + } + } + return err; +} + +#endif + +/* End: bn_mp_add.c */ + +/* Start: bn_mp_add_d.c */ +#include "tommath_private.h" +#ifdef BN_MP_ADD_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* single digit addition */ +mp_err mp_add_d(const mp_int *a, mp_digit b, mp_int *c) +{ + mp_err err; + int ix, oldused; + mp_digit *tmpa, *tmpc; + + /* grow c as required */ + if (c->alloc < (a->used + 1)) { + if ((err = mp_grow(c, a->used + 1)) != MP_OKAY) { + return err; + } + } + + /* if a is negative and |a| >= b, call c = |a| - b */ + if ((a->sign == MP_NEG) && ((a->used > 1) || (a->dp[0] >= b))) { + mp_int a_ = *a; + /* temporarily fix sign of a */ + a_.sign = MP_ZPOS; + + /* c = |a| - b */ + err = mp_sub_d(&a_, b, c); + + /* fix sign */ + c->sign = MP_NEG; + + /* clamp */ + mp_clamp(c); + + return err; + } + + /* old number of used digits in c */ + oldused = c->used; + + /* source alias */ + tmpa = a->dp; + + /* destination alias */ + tmpc = c->dp; + + /* if a is positive */ + if (a->sign == MP_ZPOS) { + /* add digits, mu is carry */ + mp_digit mu = b; + for (ix = 0; ix < a->used; ix++) { + *tmpc = *tmpa++ + mu; + mu = *tmpc >> MP_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; + } + + /* sign always positive */ + c->sign = MP_ZPOS; + + /* now zero to oldused */ + MP_ZERO_DIGITS(tmpc, oldused - ix); + mp_clamp(c); + + return MP_OKAY; +} + +#endif + +/* End: bn_mp_add_d.c */ + +/* Start: bn_mp_addmod.c */ +#include "tommath_private.h" +#ifdef BN_MP_ADDMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* d = a + b (mod c) */ +mp_err mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) +{ + mp_err err; + mp_int t; + + if ((err = mp_init(&t)) != MP_OKAY) { + return err; + } + + if ((err = mp_add(a, b, &t)) != MP_OKAY) { + goto LBL_ERR; + } + err = mp_mod(&t, c, d); + +LBL_ERR: + mp_clear(&t); + return err; +} +#endif + +/* End: bn_mp_addmod.c */ + +/* Start: bn_mp_and.c */ +#include "tommath_private.h" +#ifdef BN_MP_AND_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* two complement and */ +mp_err mp_and(const mp_int *a, const mp_int *b, mp_int *c) +{ + int used = MP_MAX(a->used, b->used) + 1, i; + mp_err err; + mp_digit ac = 1, bc = 1, cc = 1; + mp_sign csign = ((a->sign == MP_NEG) && (b->sign == MP_NEG)) ? MP_NEG : MP_ZPOS; + + if (c->alloc < used) { + if ((err = mp_grow(c, used)) != MP_OKAY) { + return err; + } + } + + for (i = 0; i < used; i++) { + mp_digit x, y; + + /* convert to two complement if negative */ + if (a->sign == MP_NEG) { + ac += (i >= a->used) ? MP_MASK : (~a->dp[i] & MP_MASK); + x = ac & MP_MASK; + ac >>= MP_DIGIT_BIT; + } else { + x = (i >= a->used) ? 0uL : a->dp[i]; + } + + /* convert to two complement if negative */ + if (b->sign == MP_NEG) { + bc += (i >= b->used) ? MP_MASK : (~b->dp[i] & MP_MASK); + y = bc & MP_MASK; + bc >>= MP_DIGIT_BIT; + } else { + y = (i >= b->used) ? 0uL : b->dp[i]; + } + + c->dp[i] = x & y; + + /* convert to to sign-magnitude if negative */ + if (csign == MP_NEG) { + cc += ~c->dp[i] & MP_MASK; + c->dp[i] = cc & MP_MASK; + cc >>= MP_DIGIT_BIT; + } + } + + c->used = used; + c->sign = csign; + mp_clamp(c); + return MP_OKAY; +} +#endif + +/* End: bn_mp_and.c */ + +/* Start: bn_mp_clamp.c */ +#include "tommath_private.h" +#ifdef BN_MP_CLAMP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* 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] == 0u)) { + --(a->used); + } + + /* reset the sign flag if used == 0 */ + if (a->used == 0) { + a->sign = MP_ZPOS; + } +} +#endif + +/* End: bn_mp_clamp.c */ + +/* Start: bn_mp_clear.c */ +#include "tommath_private.h" +#ifdef BN_MP_CLEAR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* clear one (frees) */ +void mp_clear(mp_int *a) +{ + /* only do anything if a hasn't been freed previously */ + if (a->dp != NULL) { + /* free ram */ + MP_FREE_DIGITS(a->dp, a->alloc); + + /* reset members to make debugging easier */ + a->dp = NULL; + a->alloc = a->used = 0; + a->sign = MP_ZPOS; + } +} +#endif + +/* End: bn_mp_clear.c */ + +/* Start: bn_mp_clear_multi.c */ +#include "tommath_private.h" +#ifdef BN_MP_CLEAR_MULTI_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#include <stdarg.h> + +void mp_clear_multi(mp_int *mp, ...) +{ + mp_int *next_mp = mp; + va_list args; + va_start(args, mp); + while (next_mp != NULL) { + mp_clear(next_mp); + next_mp = va_arg(args, mp_int *); + } + va_end(args); +} +#endif + +/* End: bn_mp_clear_multi.c */ + +/* Start: bn_mp_cmp.c */ +#include "tommath_private.h" +#ifdef BN_MP_CMP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* compare two ints (signed)*/ +mp_ord mp_cmp(const mp_int *a, const 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 + +/* End: bn_mp_cmp.c */ + +/* Start: bn_mp_cmp_d.c */ +#include "tommath_private.h" +#ifdef BN_MP_CMP_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* compare a digit */ +mp_ord mp_cmp_d(const 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 + +/* End: bn_mp_cmp_d.c */ + +/* Start: bn_mp_cmp_mag.c */ +#include "tommath_private.h" +#ifdef BN_MP_CMP_MAG_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* compare maginitude of two ints (unsigned) */ +mp_ord mp_cmp_mag(const mp_int *a, const mp_int *b) +{ + int n; + const 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 + +/* End: bn_mp_cmp_mag.c */ + +/* Start: bn_mp_cnt_lsb.c */ +#include "tommath_private.h" +#ifdef BN_MP_CNT_LSB_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +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(const mp_int *a) +{ + int x; + mp_digit q, qq; + + /* easy out */ + if (MP_IS_ZERO(a)) { + return 0; + } + + /* scan lower digits until non-zero */ + for (x = 0; (x < a->used) && (a->dp[x] == 0u); x++) {} + q = a->dp[x]; + x *= MP_DIGIT_BIT; + + /* now scan this digit until a 1 is found */ + if ((q & 1u) == 0u) { + do { + qq = q & 15u; + x += lnz[qq]; + q >>= 4; + } while (qq == 0u); + } + return x; +} + +#endif + +/* End: bn_mp_cnt_lsb.c */ + +/* Start: bn_mp_complement.c */ +#include "tommath_private.h" +#ifdef BN_MP_COMPLEMENT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* b = ~a */ +mp_err mp_complement(const mp_int *a, mp_int *b) +{ + mp_err err = mp_neg(a, b); + return (err == MP_OKAY) ? mp_sub_d(b, 1uL, b) : err; +} +#endif + +/* End: bn_mp_complement.c */ + +/* Start: bn_mp_copy.c */ +#include "tommath_private.h" +#ifdef BN_MP_COPY_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* copy, b = a */ +mp_err mp_copy(const mp_int *a, mp_int *b) +{ + int n; + mp_digit *tmpa, *tmpb; + mp_err err; + + /* if dst == src do nothing */ + if (a == b) { + return MP_OKAY; + } + + /* grow dest */ + if (b->alloc < a->used) { + if ((err = mp_grow(b, a->used)) != MP_OKAY) { + return err; + } + } + + /* zero b and copy the parameters over */ + /* 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 */ + MP_ZERO_DIGITS(tmpb, b->used - n); + + /* copy used count and sign */ + b->used = a->used; + b->sign = a->sign; + return MP_OKAY; +} +#endif + +/* End: bn_mp_copy.c */ + +/* Start: bn_mp_count_bits.c */ +#include "tommath_private.h" +#ifdef BN_MP_COUNT_BITS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* returns the number of bits in an int */ +int mp_count_bits(const mp_int *a) +{ + int r; + mp_digit q; + + /* shortcut */ + if (MP_IS_ZERO(a)) { + return 0; + } + + /* get number of digits and add that */ + r = (a->used - 1) * MP_DIGIT_BIT; + + /* take the last digit and count the bits in it */ + q = a->dp[a->used - 1]; + while (q > 0u) { + ++r; + q >>= 1u; + } + return r; +} +#endif + +/* End: bn_mp_count_bits.c */ + +/* Start: bn_mp_decr.c */ +#include "tommath_private.h" +#ifdef BN_MP_DECR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Decrement "a" by one like "a--". Changes input! */ +mp_err mp_decr(mp_int *a) +{ + if (MP_IS_ZERO(a)) { + mp_set(a,1uL); + a->sign = MP_NEG; + return MP_OKAY; + } else if (a->sign == MP_NEG) { + mp_err err; + a->sign = MP_ZPOS; + if ((err = mp_incr(a)) != MP_OKAY) { + return err; + } + /* There is no -0 in LTM */ + if (!MP_IS_ZERO(a)) { + a->sign = MP_NEG; + } + return MP_OKAY; + } else if (a->dp[0] > 1uL) { + a->dp[0]--; + if (a->dp[0] == 0u) { + mp_zero(a); + } + return MP_OKAY; + } else { + return mp_sub_d(a, 1uL,a); + } +} +#endif + +/* End: bn_mp_decr.c */ + +/* Start: bn_mp_div.c */ +#include "tommath_private.h" +#ifdef BN_MP_DIV_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#ifdef BN_MP_DIV_SMALL + +/* slower bit-bang division... also smaller */ +mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d) +{ + mp_int ta, tb, tq, q; + int n, n2; + mp_err err; + + /* is divisor zero ? */ + if (MP_IS_ZERO(b)) { + return MP_VAL; + } + + /* if a < b then q=0, r = a */ + if (mp_cmp_mag(a, b) == MP_LT) { + if (d != NULL) { + err = mp_copy(a, d); + } else { + err = MP_OKAY; + } + if (c != NULL) { + mp_zero(c); + } + return err; + } + + /* init our temps */ + if ((err = mp_init_multi(&ta, &tb, &tq, &q, NULL)) != MP_OKAY) { + return err; + } + + + mp_set(&tq, 1uL); + n = mp_count_bits(a) - mp_count_bits(b); + if ((err = mp_abs(a, &ta)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_abs(b, &tb)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_mul_2d(&tq, n, &tq)) != MP_OKAY) goto LBL_ERR; + + while (n-- >= 0) { + if (mp_cmp(&tb, &ta) != MP_GT) { + if ((err = mp_sub(&ta, &tb, &ta)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&q, &tq, &q)) != MP_OKAY) goto LBL_ERR; + } + if ((err = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) goto LBL_ERR; + if ((err = 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_IS_ZERO(c) ? MP_ZPOS : n2; + } + if (d != NULL) { + mp_exch(d, &ta); + d->sign = MP_IS_ZERO(d) ? MP_ZPOS : n; + } +LBL_ERR: + mp_clear_multi(&ta, &tb, &tq, &q, NULL); + return err; +} + +#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. +*/ +mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d) +{ + mp_int q, x, y, t1, t2; + int n, t, i, norm; + mp_sign neg; + mp_err err; + + /* is divisor zero ? */ + if (MP_IS_ZERO(b)) { + return MP_VAL; + } + + /* if a < b then q=0, r = a */ + if (mp_cmp_mag(a, b) == MP_LT) { + if (d != NULL) { + err = mp_copy(a, d); + } else { + err = MP_OKAY; + } + if (c != NULL) { + mp_zero(c); + } + return err; + } + + if ((err = mp_init_size(&q, a->used + 2)) != MP_OKAY) { + return err; + } + q.used = a->used + 2; + + if ((err = mp_init(&t1)) != MP_OKAY) goto LBL_Q; + + if ((err = mp_init(&t2)) != MP_OKAY) goto LBL_T1; + + if ((err = mp_init_copy(&x, a)) != MP_OKAY) goto LBL_T2; + + if ((err = 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**MP_DIGIT_BIT] */ + norm = mp_count_bits(&y) % MP_DIGIT_BIT; + if (norm < (MP_DIGIT_BIT - 1)) { + norm = (MP_DIGIT_BIT - 1) - norm; + if ((err = mp_mul_2d(&x, norm, &x)) != MP_OKAY) goto LBL_Y; + if ((err = 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} } */ + /* y = y*b**{n-t} */ + if ((err = mp_lshd(&y, n - t)) != MP_OKAY) goto LBL_Y; + + while (mp_cmp(&x, &y) != MP_LT) { + ++(q.dp[n - t]); + if ((err = 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 << (mp_digit)MP_DIGIT_BIT) - (mp_digit)1; + } else { + mp_word tmp; + tmp = (mp_word)x.dp[i] << (mp_word)MP_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] + 1uL) & (mp_digit)MP_MASK; + do { + q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1uL) & (mp_digit)MP_MASK; + + /* find left hand */ + mp_zero(&t1); + t1.dp[0] = ((t - 1) < 0) ? 0u : y.dp[t - 1]; + t1.dp[1] = y.dp[t]; + t1.used = 2; + if ((err = mp_mul_d(&t1, q.dp[(i - t) - 1], &t1)) != MP_OKAY) goto LBL_Y; + + /* find right hand */ + t2.dp[0] = ((i - 2) < 0) ? 0u : x.dp[i - 2]; + t2.dp[1] = x.dp[i - 1]; /* i >= 1 always holds */ + 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 ((err = mp_mul_d(&y, q.dp[(i - t) - 1], &t1)) != MP_OKAY) goto LBL_Y; + + if ((err = mp_lshd(&t1, (i - t) - 1)) != MP_OKAY) goto LBL_Y; + + if ((err = 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 ((err = mp_copy(&y, &t1)) != MP_OKAY) goto LBL_Y; + if ((err = mp_lshd(&t1, (i - t) - 1)) != MP_OKAY) goto LBL_Y; + if ((err = 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) { + if ((err = mp_div_2d(&x, norm, &x, NULL)) != MP_OKAY) goto LBL_Y; + mp_exch(&x, d); + } + + err = 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 err; +} + +#endif + +#endif + +/* End: bn_mp_div.c */ + +/* Start: bn_mp_div_2.c */ +#include "tommath_private.h" +#ifdef BN_MP_DIV_2_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* b = a/2 */ +mp_err mp_div_2(const mp_int *a, mp_int *b) +{ + int x, oldused; + mp_digit r, rr, *tmpa, *tmpb; + mp_err err; + + /* copy */ + if (b->alloc < a->used) { + if ((err = mp_grow(b, a->used)) != MP_OKAY) { + return err; + } + } + + oldused = b->used; + b->used = a->used; + + /* 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 & 1u; + + /* shift the current digit, add in carry and store */ + *tmpb-- = (*tmpa-- >> 1) | (r << (MP_DIGIT_BIT - 1)); + + /* forward carry to next iteration */ + r = rr; + } + + /* zero excess digits */ + MP_ZERO_DIGITS(b->dp + b->used, oldused - b->used); + + b->sign = a->sign; + mp_clamp(b); + return MP_OKAY; +} +#endif + +/* End: bn_mp_div_2.c */ + +/* Start: bn_mp_div_2d.c */ +#include "tommath_private.h" +#ifdef BN_MP_DIV_2D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* shift right by a certain bit count (store quotient in c, optional remainder in d) */ +mp_err mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d) +{ + mp_digit D, r, rr; + int x; + mp_err err; + + /* if the shift count is <= 0 then we do no work */ + if (b <= 0) { + err = mp_copy(a, c); + if (d != NULL) { + mp_zero(d); + } + return err; + } + + /* copy */ + if ((err = mp_copy(a, c)) != MP_OKAY) { + return err; + } + /* 'a' should not be used after here - it might be the same as d */ + + /* get the remainder */ + if (d != NULL) { + if ((err = mp_mod_2d(a, b, d)) != MP_OKAY) { + return err; + } + } + + /* shift by as many digits in the bit count */ + if (b >= MP_DIGIT_BIT) { + mp_rshd(c, b / MP_DIGIT_BIT); + } + + /* shift any bit count < MP_DIGIT_BIT */ + D = (mp_digit)(b % MP_DIGIT_BIT); + if (D != 0u) { + mp_digit *tmpc, mask, shift; + + /* mask */ + mask = ((mp_digit)1 << D) - 1uL; + + /* shift for lsb */ + shift = (mp_digit)MP_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); + return MP_OKAY; +} +#endif + +/* End: bn_mp_div_2d.c */ + +/* Start: bn_mp_div_3.c */ +#include "tommath_private.h" +#ifdef BN_MP_DIV_3_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* divide by three (based on routine from MPI and the GMP manual) */ +mp_err mp_div_3(const mp_int *a, mp_int *c, mp_digit *d) +{ + mp_int q; + mp_word w, t; + mp_digit b; + mp_err err; + int ix; + + /* b = 2**MP_DIGIT_BIT / 3 */ + b = ((mp_word)1 << (mp_word)MP_DIGIT_BIT) / (mp_word)3; + + if ((err = mp_init_size(&q, a->used)) != MP_OKAY) { + return err; + } + + q.used = a->used; + q.sign = a->sign; + w = 0; + for (ix = a->used - 1; ix >= 0; ix--) { + w = (w << (mp_word)MP_DIGIT_BIT) | (mp_word)a->dp[ix]; + + if (w >= 3u) { + /* multiply w by [1/3] */ + t = (w * (mp_word)b) >> (mp_word)MP_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 >= 3u) { + t += 1u; + w -= 3u; + } + } 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 err; +} + +#endif + +/* End: bn_mp_div_3.c */ + +/* Start: bn_mp_div_d.c */ +#include "tommath_private.h" +#ifdef BN_MP_DIV_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* single digit division (based on routine from MPI) */ +mp_err mp_div_d(const mp_int *a, mp_digit b, mp_int *c, mp_digit *d) +{ + mp_int q; + mp_word w; + mp_digit t; + mp_err err; + int ix; + + /* cannot divide by zero */ + if (b == 0u) { + return MP_VAL; + } + + /* quick outs */ + if ((b == 1u) || MP_IS_ZERO(a)) { + if (d != NULL) { + *d = 0; + } + if (c != NULL) { + return mp_copy(a, c); + } + return MP_OKAY; + } + + /* power of two ? */ + if ((b & (b - 1u)) == 0u) { + ix = 1; + while ((ix < MP_DIGIT_BIT) && (b != (((mp_digit)1)<<ix))) { + ix++; + } + if (d != NULL) { + *d = a->dp[0] & (((mp_digit)1<<(mp_digit)ix) - 1uL); + } + if (c != NULL) { + return mp_div_2d(a, ix, c, NULL); + } + return MP_OKAY; + } + + /* three? */ + if (MP_HAS(MP_DIV_3) && (b == 3u)) { + return mp_div_3(a, c, d); + } + + /* no easy answer [c'est la vie]. Just division */ + if ((err = mp_init_size(&q, a->used)) != MP_OKAY) { + return err; + } + + q.used = a->used; + q.sign = a->sign; + w = 0; + for (ix = a->used - 1; ix >= 0; ix--) { + w = (w << (mp_word)MP_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] = t; + } + + if (d != NULL) { + *d = (mp_digit)w; + } + + if (c != NULL) { + mp_clamp(&q); + mp_exch(&q, c); + } + mp_clear(&q); + + return err; +} + +#endif + +/* End: bn_mp_div_d.c */ + +/* Start: bn_mp_dr_is_modulus.c */ +#include "tommath_private.h" +#ifdef BN_MP_DR_IS_MODULUS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* determines if a number is a valid DR modulus */ +mp_bool mp_dr_is_modulus(const mp_int *a) +{ + int ix; + + /* must be at least two digits */ + if (a->used < 2) { + return MP_NO; + } + + /* 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 MP_NO; + } + } + return MP_YES; +} + +#endif + +/* End: bn_mp_dr_is_modulus.c */ + +/* Start: bn_mp_dr_reduce.c */ +#include "tommath_private.h" +#ifdef BN_MP_DR_REDUCE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* 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 + */ +mp_err mp_dr_reduce(mp_int *x, const mp_int *n, mp_digit k) +{ + mp_err err; + int 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)MP_DIGIT_BIT)); + } + + /* set final carry */ + *tmpx1++ = mu; + + /* zero words above m */ + MP_ZERO_DIGITS(tmpx1, (x->used - m) - 1); + + /* 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) { + if ((err = s_mp_sub(x, n, x)) != MP_OKAY) { + return err; + } + goto top; + } + return MP_OKAY; +} +#endif + +/* End: bn_mp_dr_reduce.c */ + +/* Start: bn_mp_dr_setup.c */ +#include "tommath_private.h" +#ifdef BN_MP_DR_SETUP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* determines the setup value */ +void mp_dr_setup(const mp_int *a, mp_digit *d) +{ + /* the casts are required if MP_DIGIT_BIT is one less than + * the number of bits in a mp_digit [e.g. MP_DIGIT_BIT==31] + */ + *d = (mp_digit)(((mp_word)1 << (mp_word)MP_DIGIT_BIT) - (mp_word)a->dp[0]); +} + +#endif + +/* End: bn_mp_dr_setup.c */ + +/* Start: bn_mp_error_to_string.c */ +#include "tommath_private.h" +#ifdef BN_MP_ERROR_TO_STRING_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* return a char * string for a given code */ +const char *mp_error_to_string(mp_err code) +{ + switch (code) { + case MP_OKAY: + return "Successful"; + case MP_ERR: + return "Unknown error"; + case MP_MEM: + return "Out of heap"; + case MP_VAL: + return "Value out of range"; + case MP_ITER: + return "Max. iterations reached"; + case MP_BUF: + return "Buffer overflow"; + default: + return "Invalid error code"; + } +} + +#endif + +/* End: bn_mp_error_to_string.c */ + +/* Start: bn_mp_exch.c */ +#include "tommath_private.h" +#ifdef BN_MP_EXCH_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* 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 + +/* End: bn_mp_exch.c */ + +/* Start: bn_mp_expt_u32.c */ +#include "tommath_private.h" +#ifdef BN_MP_EXPT_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* calculate c = a**b using a square-multiply algorithm */ +mp_err mp_expt_u32(const mp_int *a, uint32_t b, mp_int *c) +{ + mp_err err; + + mp_int g; + + if ((err = mp_init_copy(&g, a)) != MP_OKAY) { + return err; + } + + /* set initial result */ + mp_set(c, 1uL); + + while (b > 0u) { + /* if the bit is set multiply */ + if ((b & 1u) != 0u) { + if ((err = mp_mul(c, &g, c)) != MP_OKAY) { + goto LBL_ERR; + } + } + + /* square */ + if (b > 1u) { + if ((err = mp_sqr(&g, &g)) != MP_OKAY) { + goto LBL_ERR; + } + } + + /* shift to next bit */ + b >>= 1; + } + + err = MP_OKAY; + +LBL_ERR: + mp_clear(&g); + return err; +} + +#endif + +/* End: bn_mp_expt_u32.c */ + +/* Start: bn_mp_exptmod.c */ +#include "tommath_private.h" +#ifdef BN_MP_EXPTMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* 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) + */ +mp_err mp_exptmod(const mp_int *G, const mp_int *X, const 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) { + mp_int tmpG, tmpX; + mp_err err; + + if (!MP_HAS(MP_INVMOD)) { + return MP_VAL; + } + + if ((err = mp_init_multi(&tmpG, &tmpX, NULL)) != MP_OKAY) { + return err; + } + + /* first compute 1/G mod P */ + if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) { + goto LBL_ERR; + } + + /* now get |X| */ + if ((err = mp_abs(X, &tmpX)) != MP_OKAY) { + goto LBL_ERR; + } + + /* and now compute (1/G)**|X| instead of G**X [X < 0] */ + err = mp_exptmod(&tmpG, &tmpX, P, Y); +LBL_ERR: + mp_clear_multi(&tmpG, &tmpX, NULL); + return err; + } + + /* modified diminished radix reduction */ + if (MP_HAS(MP_REDUCE_IS_2K_L) && MP_HAS(MP_REDUCE_2K_L) && MP_HAS(S_MP_EXPTMOD) && + (mp_reduce_is_2k_l(P) == MP_YES)) { + return s_mp_exptmod(G, X, P, Y, 1); + } + + /* is it a DR modulus? default to no */ + dr = (MP_HAS(MP_DR_IS_MODULUS) && (mp_dr_is_modulus(P) == MP_YES)) ? 1 : 0; + + /* if not, is it a unrestricted DR modulus? */ + if (MP_HAS(MP_REDUCE_IS_2K) && (dr == 0)) { + dr = (mp_reduce_is_2k(P) == MP_YES) ? 2 : 0; + } + + /* if the modulus is odd or dr != 0 use the montgomery method */ + if (MP_HAS(S_MP_EXPTMOD_FAST) && (MP_IS_ODD(P) || (dr != 0))) { + return s_mp_exptmod_fast(G, X, P, Y, dr); + } else if (MP_HAS(S_MP_EXPTMOD)) { + /* 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 + +/* End: bn_mp_exptmod.c */ + +/* Start: bn_mp_exteuclid.c */ +#include "tommath_private.h" +#ifdef BN_MP_EXTEUCLID_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Extended euclidean algorithm of (a, b) produces + a*u1 + b*u2 = u3 + */ +mp_err mp_exteuclid(const mp_int *a, const 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; + mp_err 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, 1uL); + if ((err = mp_copy(a, &u3)) != MP_OKAY) goto LBL_ERR; + + /* initialize, (v1,v2,v3) = (0,1,b) */ + mp_set(&v2, 1uL); + if ((err = mp_copy(b, &v3)) != MP_OKAY) goto LBL_ERR; + + /* loop while v3 != 0 */ + while (!MP_IS_ZERO(&v3)) { + /* q = u3/v3 */ + if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY) goto LBL_ERR; + + /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */ + if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY) goto LBL_ERR; + + /* (u1,u2,u3) = (v1,v2,v3) */ + if ((err = mp_copy(&v1, &u1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&v2, &u2)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&v3, &u3)) != MP_OKAY) goto LBL_ERR; + + /* (v1,v2,v3) = (t1,t2,t3) */ + if ((err = mp_copy(&t1, &v1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&t2, &v2)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&t3, &v3)) != MP_OKAY) goto LBL_ERR; + } + + /* make sure U3 >= 0 */ + if (u3.sign == MP_NEG) { + if ((err = mp_neg(&u1, &u1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_neg(&u2, &u2)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_neg(&u3, &u3)) != MP_OKAY) goto LBL_ERR; + } + + /* 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; +LBL_ERR: + mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL); + return err; +} +#endif + +/* End: bn_mp_exteuclid.c */ + +/* Start: bn_mp_fread.c */ +#include "tommath_private.h" +#ifdef BN_MP_FREAD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#ifndef MP_NO_FILE +/* read a bigint from a file stream in ASCII */ +mp_err mp_fread(mp_int *a, int radix, FILE *stream) +{ + mp_err err; + mp_sign neg; + + /* if first digit is - then set negative */ + int ch = fgetc(stream); + if (ch == (int)'-') { + neg = MP_NEG; + ch = fgetc(stream); + } else { + neg = MP_ZPOS; + } + + /* no digits, return error */ + if (ch == EOF) { + return MP_ERR; + } + + /* clear a */ + mp_zero(a); + + do { + int y; + unsigned pos = (unsigned)(ch - (int)'('); + if (mp_s_rmap_reverse_sz < pos) { + break; + } + + y = (int)mp_s_rmap_reverse[pos]; + + if ((y == 0xff) || (y >= radix)) { + break; + } + + /* shift up and add */ + if ((err = mp_mul_d(a, (mp_digit)radix, a)) != MP_OKAY) { + return err; + } + if ((err = mp_add_d(a, (mp_digit)y, a)) != MP_OKAY) { + return err; + } + } while ((ch = fgetc(stream)) != EOF); + + if (a->used != 0) { + a->sign = neg; + } + + return MP_OKAY; +} +#endif + +#endif + +/* End: bn_mp_fread.c */ + +/* Start: bn_mp_from_sbin.c */ +#include "tommath_private.h" +#ifdef BN_MP_FROM_SBIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* read signed bin, big endian, first byte is 0==positive or 1==negative */ +mp_err mp_from_sbin(mp_int *a, const unsigned char *buf, size_t size) +{ + mp_err err; + + /* read magnitude */ + if ((err = mp_from_ubin(a, buf + 1, size - 1u)) != MP_OKAY) { + return err; + } + + /* first byte is 0 for positive, non-zero for negative */ + if (buf[0] == (unsigned char)0) { + a->sign = MP_ZPOS; + } else { + a->sign = MP_NEG; + } + + return MP_OKAY; +} +#endif + +/* End: bn_mp_from_sbin.c */ + +/* Start: bn_mp_from_ubin.c */ +#include "tommath_private.h" +#ifdef BN_MP_FROM_UBIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* reads a unsigned char array, assumes the msb is stored first [big endian] */ +mp_err mp_from_ubin(mp_int *a, const unsigned char *buf, size_t size) +{ + mp_err err; + + /* make sure there are at least two digits */ + if (a->alloc < 2) { + if ((err = mp_grow(a, 2)) != MP_OKAY) { + return err; + } + } + + /* zero the int */ + mp_zero(a); + + /* read the bytes in */ + while (size-- > 0u) { + if ((err = mp_mul_2d(a, 8, a)) != MP_OKAY) { + return err; + } + +#ifndef MP_8BIT + a->dp[0] |= *buf++; + a->used += 1; +#else + a->dp[0] = (*buf & MP_MASK); + a->dp[1] |= ((*buf++ >> 7) & 1u); + a->used += 2; +#endif + } + mp_clamp(a); + return MP_OKAY; +} +#endif + +/* End: bn_mp_from_ubin.c */ + +/* Start: bn_mp_fwrite.c */ +#include "tommath_private.h" +#ifdef BN_MP_FWRITE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#ifndef MP_NO_FILE +mp_err mp_fwrite(const mp_int *a, int radix, FILE *stream) +{ + char *buf; + mp_err err; + int len; + size_t written; + + /* TODO: this function is not in this PR */ + if (MP_HAS(MP_RADIX_SIZE_OVERESTIMATE)) { + /* if ((err = mp_radix_size_overestimate(&t, base, &len)) != MP_OKAY) goto LBL_ERR; */ + } else { + if ((err = mp_radix_size(a, radix, &len)) != MP_OKAY) { + return err; + } + } + + buf = (char *) MP_MALLOC((size_t)len); + if (buf == NULL) { + return MP_MEM; + } + + if ((err = mp_to_radix(a, buf, (size_t)len, &written, radix)) != MP_OKAY) { + goto LBL_ERR; + } + + if (fwrite(buf, written, 1uL, stream) != 1uL) { + err = MP_ERR; + goto LBL_ERR; + } + err = MP_OKAY; + + +LBL_ERR: + MP_FREE_BUFFER(buf, (size_t)len); + return err; +} +#endif + +#endif + +/* End: bn_mp_fwrite.c */ + +/* Start: bn_mp_gcd.c */ +#include "tommath_private.h" +#ifdef BN_MP_GCD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Greatest Common Divisor using the binary method */ +mp_err mp_gcd(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_int u, v; + int k, u_lsb, v_lsb; + mp_err err; + + /* either zero than gcd is the largest */ + if (MP_IS_ZERO(a)) { + return mp_abs(b, c); + } + if (MP_IS_ZERO(b)) { + return mp_abs(a, c); + } + + /* get copies of a and b we can modify */ + if ((err = mp_init_copy(&u, a)) != MP_OKAY) { + return err; + } + + if ((err = 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 = MP_MIN(u_lsb, v_lsb); + + if (k > 0) { + /* divide the power of two out */ + if ((err = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) { + goto LBL_V; + } + + if ((err = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) { + goto LBL_V; + } + } + + /* divide any remaining factors of two out */ + if (u_lsb != k) { + if ((err = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) { + goto LBL_V; + } + } + + if (v_lsb != k) { + if ((err = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) { + goto LBL_V; + } + } + + while (!MP_IS_ZERO(&v)) { + /* 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 ((err = s_mp_sub(&v, &u, &v)) != MP_OKAY) { + goto LBL_V; + } + + /* Divide out all factors of two */ + if ((err = 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 ((err = mp_mul_2d(&u, k, c)) != MP_OKAY) { + goto LBL_V; + } + c->sign = MP_ZPOS; + err = MP_OKAY; +LBL_V: + mp_clear(&u); +LBL_U: + mp_clear(&v); + return err; +} +#endif + +/* End: bn_mp_gcd.c */ + +/* Start: bn_mp_get_double.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_DOUBLE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +double mp_get_double(const mp_int *a) +{ + int i; + double d = 0.0, fac = 1.0; + for (i = 0; i < MP_DIGIT_BIT; ++i) { + fac *= 2.0; + } + for (i = a->used; i --> 0;) { + d = (d * fac) + (double)a->dp[i]; + } + return (a->sign == MP_NEG) ? -d : d; +} +#endif + +/* End: bn_mp_get_double.c */ + +/* Start: bn_mp_get_i32.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_I32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_SIGNED(mp_get_i32, mp_get_mag_u32, int32_t, uint32_t) +#endif + +/* End: bn_mp_get_i32.c */ + +/* Start: bn_mp_get_i64.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_I64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_SIGNED(mp_get_i64, mp_get_mag_u64, int64_t, uint64_t) +#endif + +/* End: bn_mp_get_i64.c */ + +/* Start: bn_mp_get_l.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_SIGNED(mp_get_l, mp_get_mag_ul, long, unsigned long) +#endif + +/* End: bn_mp_get_l.c */ + +/* Start: bn_mp_get_ll.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_LL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_SIGNED(mp_get_ll, mp_get_mag_ull, long long, unsigned long long) +#endif + +/* End: bn_mp_get_ll.c */ + +/* Start: bn_mp_get_mag_u32.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_MAG_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_MAG(mp_get_mag_u32, uint32_t) +#endif + +/* End: bn_mp_get_mag_u32.c */ + +/* Start: bn_mp_get_mag_u64.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_MAG_U64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_MAG(mp_get_mag_u64, uint64_t) +#endif + +/* End: bn_mp_get_mag_u64.c */ + +/* Start: bn_mp_get_mag_ul.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_MAG_UL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_MAG(mp_get_mag_ul, unsigned long) +#endif + +/* End: bn_mp_get_mag_ul.c */ + +/* Start: bn_mp_get_mag_ull.c */ +#include "tommath_private.h" +#ifdef BN_MP_GET_MAG_ULL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_GET_MAG(mp_get_mag_ull, unsigned long long) +#endif + +/* End: bn_mp_get_mag_ull.c */ + +/* Start: bn_mp_grow.c */ +#include "tommath_private.h" +#ifdef BN_MP_GROW_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* grow as required */ +mp_err 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) { + /* 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 = (mp_digit *) MP_REALLOC(a->dp, + (size_t)a->alloc * sizeof(mp_digit), + (size_t)size * sizeof(mp_digit)); + 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; + MP_ZERO_DIGITS(a->dp + i, a->alloc - i); + } + return MP_OKAY; +} +#endif + +/* End: bn_mp_grow.c */ + +/* Start: bn_mp_incr.c */ +#include "tommath_private.h" +#ifdef BN_MP_INCR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Increment "a" by one like "a++". Changes input! */ +mp_err mp_incr(mp_int *a) +{ + if (MP_IS_ZERO(a)) { + mp_set(a,1uL); + return MP_OKAY; + } else if (a->sign == MP_NEG) { + mp_err err; + a->sign = MP_ZPOS; + if ((err = mp_decr(a)) != MP_OKAY) { + return err; + } + /* There is no -0 in LTM */ + if (!MP_IS_ZERO(a)) { + a->sign = MP_NEG; + } + return MP_OKAY; + } else if (a->dp[0] < MP_DIGIT_MAX) { + a->dp[0]++; + return MP_OKAY; + } else { + return mp_add_d(a, 1uL,a); + } +} +#endif + +/* End: bn_mp_incr.c */ + +/* Start: bn_mp_init.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* init a new mp_int */ +mp_err mp_init(mp_int *a) +{ + /* allocate memory required and clear it */ + a->dp = (mp_digit *) MP_CALLOC((size_t)MP_PREC, sizeof(mp_digit)); + if (a->dp == NULL) { + return MP_MEM; + } + + /* 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 + +/* End: bn_mp_init.c */ + +/* Start: bn_mp_init_copy.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_COPY_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* creates "a" then copies b into it */ +mp_err mp_init_copy(mp_int *a, const mp_int *b) +{ + mp_err err; + + if ((err = mp_init_size(a, b->used)) != MP_OKAY) { + return err; + } + + if ((err = mp_copy(b, a)) != MP_OKAY) { + mp_clear(a); + } + + return err; +} +#endif + +/* End: bn_mp_init_copy.c */ + +/* Start: bn_mp_init_i32.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_I32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_i32, mp_set_i32, int32_t) +#endif + +/* End: bn_mp_init_i32.c */ + +/* Start: bn_mp_init_i64.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_I64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_i64, mp_set_i64, int64_t) +#endif + +/* End: bn_mp_init_i64.c */ + +/* Start: bn_mp_init_l.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_l, mp_set_l, long) +#endif + +/* End: bn_mp_init_l.c */ + +/* Start: bn_mp_init_ll.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_LL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_ll, mp_set_ll, long long) +#endif + +/* End: bn_mp_init_ll.c */ + +/* Start: bn_mp_init_multi.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_MULTI_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#include <stdarg.h> + +mp_err mp_init_multi(mp_int *mp, ...) +{ + mp_err err = 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; + + /* now start cleaning up */ + cur_arg = mp; + va_start(clean_args, mp); + while (n-- != 0) { + mp_clear(cur_arg); + cur_arg = va_arg(clean_args, mp_int *); + } + va_end(clean_args); + err = MP_MEM; + break; + } + n++; + cur_arg = va_arg(args, mp_int *); + } + va_end(args); + return err; /* Assumed ok, if error flagged above. */ +} + +#endif + +/* End: bn_mp_init_multi.c */ + +/* Start: bn_mp_init_set.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_SET_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* initialize and set a digit */ +mp_err mp_init_set(mp_int *a, mp_digit b) +{ + mp_err err; + if ((err = mp_init(a)) != MP_OKAY) { + return err; + } + mp_set(a, b); + return err; +} +#endif + +/* End: bn_mp_init_set.c */ + +/* Start: bn_mp_init_size.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_SIZE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* init an mp_init for a given size */ +mp_err mp_init_size(mp_int *a, int size) +{ + size = MP_MAX(MP_MIN_PREC, size); + + /* alloc mem */ + a->dp = (mp_digit *) MP_CALLOC((size_t)size, sizeof(mp_digit)); + if (a->dp == NULL) { + return MP_MEM; + } + + /* set the members */ + a->used = 0; + a->alloc = size; + a->sign = MP_ZPOS; + + return MP_OKAY; +} +#endif + +/* End: bn_mp_init_size.c */ + +/* Start: bn_mp_init_u32.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_u32, mp_set_u32, uint32_t) +#endif + +/* End: bn_mp_init_u32.c */ + +/* Start: bn_mp_init_u64.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_U64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_u64, mp_set_u64, uint64_t) +#endif + +/* End: bn_mp_init_u64.c */ + +/* Start: bn_mp_init_ul.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_UL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_ul, mp_set_ul, unsigned long) +#endif + +/* End: bn_mp_init_ul.c */ + +/* Start: bn_mp_init_ull.c */ +#include "tommath_private.h" +#ifdef BN_MP_INIT_ULL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_INIT_INT(mp_init_ull, mp_set_ull, unsigned long long) +#endif + +/* End: bn_mp_init_ull.c */ + +/* Start: bn_mp_invmod.c */ +#include "tommath_private.h" +#ifdef BN_MP_INVMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* hac 14.61, pp608 */ +mp_err mp_invmod(const mp_int *a, const mp_int *b, mp_int *c) +{ + /* b cannot be negative and has to be >1 */ + if ((b->sign == MP_NEG) || (mp_cmp_d(b, 1uL) != MP_GT)) { + return MP_VAL; + } + + /* if the modulus is odd we can use a faster routine instead */ + if (MP_HAS(S_MP_INVMOD_FAST) && MP_IS_ODD(b)) { + return s_mp_invmod_fast(a, b, c); + } + + return MP_HAS(S_MP_INVMOD_SLOW) + ? s_mp_invmod_slow(a, b, c) + : MP_VAL; +} +#endif + +/* End: bn_mp_invmod.c */ + +/* Start: bn_mp_is_square.c */ +#include "tommath_private.h" +#ifdef BN_MP_IS_SQUARE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* 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 */ +mp_err mp_is_square(const mp_int *arg, mp_bool *ret) +{ + mp_err err; + mp_digit c; + mp_int t; + unsigned long r; + + /* Default to Non-square :) */ + *ret = MP_NO; + + if (arg->sign == MP_NEG) { + return MP_VAL; + } + + if (MP_IS_ZERO(arg)) { + return MP_OKAY; + } + + /* First check mod 128 (suppose that MP_DIGIT_BIT is at least 7) */ + if (rem_128[127u & arg->dp[0]] == (char)1) { + return MP_OKAY; + } + + /* Next check mod 105 (3*5*7) */ + if ((err = mp_mod_d(arg, 105uL, &c)) != MP_OKAY) { + return err; + } + if (rem_105[c] == (char)1) { + return MP_OKAY; + } + + + if ((err = mp_init_u32(&t, 11u*13u*17u*19u*23u*29u*31u)) != MP_OKAY) { + return err; + } + if ((err = mp_mod(arg, &t, &t)) != MP_OKAY) { + goto LBL_ERR; + } + r = mp_get_u32(&t); + /* Check for other prime modules, note it's not an ERROR but we must + * free "t" so the easiest way is to goto LBL_ERR. We know that err + * is already equal to MP_OKAY from the mp_mod call + */ + if (((1uL<<(r%11uL)) & 0x5C4uL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%13uL)) & 0x9E4uL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%17uL)) & 0x5CE8uL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%19uL)) & 0x4F50CuL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%23uL)) & 0x7ACCA0uL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%29uL)) & 0xC2EDD0CuL) != 0uL) goto LBL_ERR; + if (((1uL<<(r%31uL)) & 0x6DE2B848uL) != 0uL) goto LBL_ERR; + + /* Final check - is sqr(sqrt(arg)) == arg ? */ + if ((err = mp_sqrt(arg, &t)) != MP_OKAY) { + goto LBL_ERR; + } + if ((err = mp_sqr(&t, &t)) != MP_OKAY) { + goto LBL_ERR; + } + + *ret = (mp_cmp_mag(&t, arg) == MP_EQ) ? MP_YES : MP_NO; +LBL_ERR: + mp_clear(&t); + return err; +} +#endif + +/* End: bn_mp_is_square.c */ + +/* Start: bn_mp_iseven.c */ +#include "tommath_private.h" +#ifdef BN_MP_ISEVEN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +mp_bool mp_iseven(const mp_int *a) +{ + return MP_IS_EVEN(a) ? MP_YES : MP_NO; +} +#endif + +/* End: bn_mp_iseven.c */ + +/* Start: bn_mp_isodd.c */ +#include "tommath_private.h" +#ifdef BN_MP_ISODD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +mp_bool mp_isodd(const mp_int *a) +{ + return MP_IS_ODD(a) ? MP_YES : MP_NO; +} +#endif + +/* End: bn_mp_isodd.c */ + +/* Start: bn_mp_kronecker.c */ +#include "tommath_private.h" +#ifdef BN_MP_KRONECKER_C + +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* + Kronecker symbol (a|p) + Straightforward implementation of algorithm 1.4.10 in + Henri Cohen: "A Course in Computational Algebraic Number Theory" + + @book{cohen2013course, + title={A course in computational algebraic number theory}, + author={Cohen, Henri}, + volume={138}, + year={2013}, + publisher={Springer Science \& Business Media} + } + */ +mp_err mp_kronecker(const mp_int *a, const mp_int *p, int *c) +{ + mp_int a1, p1, r; + mp_err err; + int v, k; + + static const int table[8] = {0, 1, 0, -1, 0, -1, 0, 1}; + + if (MP_IS_ZERO(p)) { + if ((a->used == 1) && (a->dp[0] == 1u)) { + *c = 1; + } else { + *c = 0; + } + return MP_OKAY; + } + + if (MP_IS_EVEN(a) && MP_IS_EVEN(p)) { + *c = 0; + return MP_OKAY; + } + + if ((err = mp_init_copy(&a1, a)) != MP_OKAY) { + return err; + } + if ((err = mp_init_copy(&p1, p)) != MP_OKAY) { + goto LBL_KRON_0; + } + + v = mp_cnt_lsb(&p1); + if ((err = mp_div_2d(&p1, v, &p1, NULL)) != MP_OKAY) { + goto LBL_KRON_1; + } + + if ((v & 1) == 0) { + k = 1; + } else { + k = table[a->dp[0] & 7u]; + } + + if (p1.sign == MP_NEG) { + p1.sign = MP_ZPOS; + if (a1.sign == MP_NEG) { + k = -k; + } + } + + if ((err = mp_init(&r)) != MP_OKAY) { + goto LBL_KRON_1; + } + + for (;;) { + if (MP_IS_ZERO(&a1)) { + if (mp_cmp_d(&p1, 1uL) == MP_EQ) { + *c = k; + goto LBL_KRON; + } else { + *c = 0; + goto LBL_KRON; + } + } + + v = mp_cnt_lsb(&a1); + if ((err = mp_div_2d(&a1, v, &a1, NULL)) != MP_OKAY) { + goto LBL_KRON; + } + + if ((v & 1) == 1) { + k = k * table[p1.dp[0] & 7u]; + } + + if (a1.sign == MP_NEG) { + /* + * Compute k = (-1)^((a1)*(p1-1)/4) * k + * a1.dp[0] + 1 cannot overflow because the MSB + * of the type mp_digit is not set by definition + */ + if (((a1.dp[0] + 1u) & p1.dp[0] & 2u) != 0u) { + k = -k; + } + } else { + /* compute k = (-1)^((a1-1)*(p1-1)/4) * k */ + if ((a1.dp[0] & p1.dp[0] & 2u) != 0u) { + k = -k; + } + } + + if ((err = mp_copy(&a1, &r)) != MP_OKAY) { + goto LBL_KRON; + } + r.sign = MP_ZPOS; + if ((err = mp_mod(&p1, &r, &a1)) != MP_OKAY) { + goto LBL_KRON; + } + if ((err = mp_copy(&r, &p1)) != MP_OKAY) { + goto LBL_KRON; + } + } + +LBL_KRON: + mp_clear(&r); +LBL_KRON_1: + mp_clear(&p1); +LBL_KRON_0: + mp_clear(&a1); + + return err; +} + +#endif + +/* End: bn_mp_kronecker.c */ + +/* Start: bn_mp_lcm.c */ +#include "tommath_private.h" +#ifdef BN_MP_LCM_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* computes least common multiple as |a*b|/(a, b) */ +mp_err mp_lcm(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_err err; + mp_int t1, t2; + + + if ((err = mp_init_multi(&t1, &t2, NULL)) != MP_OKAY) { + return err; + } + + /* t1 = get the GCD of the two inputs */ + if ((err = mp_gcd(a, b, &t1)) != MP_OKAY) { + goto LBL_T; + } + + /* divide the smallest by the GCD */ + if (mp_cmp_mag(a, b) == MP_LT) { + /* store quotient in t2 such that t2 * b is the LCM */ + if ((err = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) { + goto LBL_T; + } + err = mp_mul(b, &t2, c); + } else { + /* store quotient in t2 such that t2 * a is the LCM */ + if ((err = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) { + goto LBL_T; + } + err = mp_mul(a, &t2, c); + } + + /* fix the sign to positive */ + c->sign = MP_ZPOS; + +LBL_T: + mp_clear_multi(&t1, &t2, NULL); + return err; +} +#endif + +/* End: bn_mp_lcm.c */ + +/* Start: bn_mp_log_u32.c */ +#include "tommath_private.h" +#ifdef BN_MP_LOG_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Compute log_{base}(a) */ +static mp_word s_pow(mp_word base, mp_word exponent) +{ + mp_word result = 1uLL; + while (exponent != 0u) { + if ((exponent & 1u) == 1u) { + result *= base; + } + exponent >>= 1; + base *= base; + } + + return result; +} + +static mp_digit s_digit_ilogb(mp_digit base, mp_digit n) +{ + mp_word bracket_low = 1uLL, bracket_mid, bracket_high, N; + mp_digit ret, high = 1uL, low = 0uL, mid; + + if (n < base) { + return 0uL; + } + if (n == base) { + return 1uL; + } + + bracket_high = (mp_word) base ; + N = (mp_word) n; + + while (bracket_high < N) { + low = high; + bracket_low = bracket_high; + high <<= 1; + bracket_high *= bracket_high; + } + + while (((mp_digit)(high - low)) > 1uL) { + mid = (low + high) >> 1; + bracket_mid = bracket_low * s_pow(base, (mp_word)(mid - low)); + + if (N < bracket_mid) { + high = mid ; + bracket_high = bracket_mid ; + } + if (N > bracket_mid) { + low = mid ; + bracket_low = bracket_mid ; + } + if (N == bracket_mid) { + return (mp_digit) mid; + } + } + + if (bracket_high == N) { + ret = high; + } else { + ret = low; + } + + return ret; +} + +/* TODO: output could be "int" because the output of mp_radix_size is int, too, + as is the output of mp_bitcount. + With the same problem: max size is INT_MAX * MP_DIGIT not INT_MAX only! +*/ +mp_err mp_log_u32(const mp_int *a, uint32_t base, uint32_t *c) +{ + mp_err err; + mp_ord cmp; + uint32_t high, low, mid; + mp_int bracket_low, bracket_high, bracket_mid, t, bi_base; + + err = MP_OKAY; + + if (a->sign == MP_NEG) { + return MP_VAL; + } + + if (MP_IS_ZERO(a)) { + return MP_VAL; + } + + if (base < 2u) { + return MP_VAL; + } + + /* A small shortcut for bases that are powers of two. */ + if ((base & (base - 1u)) == 0u) { + int y, bit_count; + for (y=0; (y < 7) && ((base & 1u) == 0u); y++) { + base >>= 1; + } + bit_count = mp_count_bits(a) - 1; + *c = (uint32_t)(bit_count/y); + return MP_OKAY; + } + + if (a->used == 1) { + *c = (uint32_t)s_digit_ilogb(base, a->dp[0]); + return err; + } + + cmp = mp_cmp_d(a, base); + if ((cmp == MP_LT) || (cmp == MP_EQ)) { + *c = cmp == MP_EQ; + return err; + } + + if ((err = + mp_init_multi(&bracket_low, &bracket_high, + &bracket_mid, &t, &bi_base, NULL)) != MP_OKAY) { + return err; + } + + low = 0u; + mp_set(&bracket_low, 1uL); + high = 1u; + + mp_set(&bracket_high, base); + + /* + A kind of Giant-step/baby-step algorithm. + Idea shamelessly stolen from https://programmingpraxis.com/2010/05/07/integer-logarithms/2/ + The effect is asymptotic, hence needs benchmarks to test if the Giant-step should be skipped + for small n. + */ + while (mp_cmp(&bracket_high, a) == MP_LT) { + low = high; + if ((err = mp_copy(&bracket_high, &bracket_low)) != MP_OKAY) { + goto LBL_ERR; + } + high <<= 1; + if ((err = mp_sqr(&bracket_high, &bracket_high)) != MP_OKAY) { + goto LBL_ERR; + } + } + mp_set(&bi_base, base); + + while ((high - low) > 1u) { + mid = (high + low) >> 1; + + if ((err = mp_expt_u32(&bi_base, (uint32_t)(mid - low), &t)) != MP_OKAY) { + goto LBL_ERR; + } + if ((err = mp_mul(&bracket_low, &t, &bracket_mid)) != MP_OKAY) { + goto LBL_ERR; + } + cmp = mp_cmp(a, &bracket_mid); + if (cmp == MP_LT) { + high = mid; + mp_exch(&bracket_mid, &bracket_high); + } + if (cmp == MP_GT) { + low = mid; + mp_exch(&bracket_mid, &bracket_low); + } + if (cmp == MP_EQ) { + *c = mid; + goto LBL_END; + } + } + + *c = (mp_cmp(&bracket_high, a) == MP_EQ) ? high : low; + +LBL_END: +LBL_ERR: + mp_clear_multi(&bracket_low, &bracket_high, &bracket_mid, + &t, &bi_base, NULL); + return err; +} + + +#endif + +/* End: bn_mp_log_u32.c */ + +/* Start: bn_mp_lshd.c */ +#include "tommath_private.h" +#ifdef BN_MP_LSHD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* shift left a certain amount of digits */ +mp_err mp_lshd(mp_int *a, int b) +{ + int x; + mp_err err; + mp_digit *top, *bottom; + + /* if its less than zero return */ + if (b <= 0) { + return MP_OKAY; + } + /* no need to shift 0 around */ + if (MP_IS_ZERO(a)) { + return MP_OKAY; + } + + /* grow to fit the new digits */ + if (a->alloc < (a->used + b)) { + if ((err = mp_grow(a, a->used + b)) != MP_OKAY) { + return err; + } + } + + /* increment the used by the shift amount then copy upwards */ + a->used += b; + + /* top */ + top = a->dp + a->used - 1; + + /* base */ + bottom = (a->dp + a->used - 1) - b; + + /* much like mp_rshd this is implemented using a sliding window + * except the window goes the otherway around. Copying from + * the bottom to the top. see bn_mp_rshd.c for more info. + */ + for (x = a->used - 1; x >= b; x--) { + *top-- = *bottom--; + } + + /* zero the lower digits */ + MP_ZERO_DIGITS(a->dp, b); + + return MP_OKAY; +} +#endif + +/* End: bn_mp_lshd.c */ + +/* Start: bn_mp_mod.c */ +#include "tommath_private.h" +#ifdef BN_MP_MOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* c = a mod b, 0 <= c < b if b > 0, b < c <= 0 if b < 0 */ +mp_err mp_mod(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_int t; + mp_err err; + + if ((err = mp_init_size(&t, b->used)) != MP_OKAY) { + return err; + } + + if ((err = mp_div(a, b, NULL, &t)) != MP_OKAY) { + goto LBL_ERR; + } + + if (MP_IS_ZERO(&t) || (t.sign == b->sign)) { + err = MP_OKAY; + mp_exch(&t, c); + } else { + err = mp_add(b, &t, c); + } + +LBL_ERR: + mp_clear(&t); + return err; +} +#endif + +/* End: bn_mp_mod.c */ + +/* Start: bn_mp_mod_2d.c */ +#include "tommath_private.h" +#ifdef BN_MP_MOD_2D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* calc a value mod 2**b */ +mp_err mp_mod_2d(const mp_int *a, int b, mp_int *c) +{ + int x; + mp_err err; + + /* if b is <= 0 then zero the int */ + if (b <= 0) { + mp_zero(c); + return MP_OKAY; + } + + /* if the modulus is larger than the value than return */ + if (b >= (a->used * MP_DIGIT_BIT)) { + return mp_copy(a, c); + } + + /* copy */ + if ((err = mp_copy(a, c)) != MP_OKAY) { + return err; + } + + /* zero digits above the last digit of the modulus */ + x = (b / MP_DIGIT_BIT) + (((b % MP_DIGIT_BIT) == 0) ? 0 : 1); + MP_ZERO_DIGITS(c->dp + x, c->used - x); + + /* clear the digit that is not completely outside/inside the modulus */ + c->dp[b / MP_DIGIT_BIT] &= + ((mp_digit)1 << (mp_digit)(b % MP_DIGIT_BIT)) - (mp_digit)1; + mp_clamp(c); + return MP_OKAY; +} +#endif + +/* End: bn_mp_mod_2d.c */ + +/* Start: bn_mp_mod_d.c */ +#include "tommath_private.h" +#ifdef BN_MP_MOD_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +mp_err mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c) +{ + return mp_div_d(a, b, NULL, c); +} +#endif + +/* End: bn_mp_mod_d.c */ + +/* Start: bn_mp_montgomery_calc_normalization.c */ +#include "tommath_private.h" +#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* + * shifts with subtractions when the result is greater than b. + * + * The method is slightly modified to shift B unconditionally upto just under + * the leading bit of b. This saves alot of multiple precision shifting. + */ +mp_err mp_montgomery_calc_normalization(mp_int *a, const mp_int *b) +{ + int x, bits; + mp_err err; + + /* how many bits of last digit does b use */ + bits = mp_count_bits(b) % MP_DIGIT_BIT; + + if (b->used > 1) { + if ((err = mp_2expt(a, ((b->used - 1) * MP_DIGIT_BIT) + bits - 1)) != MP_OKAY) { + return err; + } + } else { + mp_set(a, 1uL); + bits = 1; + } + + + /* now compute C = A * B mod b */ + for (x = bits - 1; x < (int)MP_DIGIT_BIT; x++) { + if ((err = mp_mul_2(a, a)) != MP_OKAY) { + return err; + } + if (mp_cmp_mag(a, b) != MP_LT) { + if ((err = s_mp_sub(a, b, a)) != MP_OKAY) { + return err; + } + } + } + + return MP_OKAY; +} +#endif + +/* End: bn_mp_montgomery_calc_normalization.c */ + +/* Start: bn_mp_montgomery_reduce.c */ +#include "tommath_private.h" +#ifdef BN_MP_MONTGOMERY_REDUCE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* computes xR**-1 == x (mod N) via Montgomery Reduction */ +mp_err mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho) +{ + int ix, digs; + mp_err err; + mp_digit mu; + + /* can the fast reduction [comba] method be used? + * + * Note that unlike in mul you're safely allowed *less* + * than the available columns [255 per default] since carries + * are fixed up in the inner loop. + */ + digs = (n->used * 2) + 1; + if ((digs < MP_WARRAY) && + (x->used <= MP_WARRAY) && + (n->used < MP_MAXFAST)) { + return s_mp_montgomery_reduce_fast(x, n, rho); + } + + /* grow the input as required */ + if (x->alloc < digs) { + if ((err = mp_grow(x, digs)) != MP_OKAY) { + return err; + } + } + x->used = digs; + + for (ix = 0; ix < n->used; ix++) { + /* mu = ai * rho mod b + * + * The value of rho must be precalculated via + * montgomery_setup() such that + * it equals -1/n0 mod b this allows the + * following inner loop to reduce the + * input one digit at a time + */ + mu = (mp_digit)(((mp_word)x->dp[ix] * (mp_word)rho) & MP_MASK); + + /* a = a + mu * m * b**i */ + { + int iy; + mp_digit *tmpn, *tmpx, u; + mp_word r; + + /* alias for digits of the modulus */ + tmpn = n->dp; + + /* alias for the digits of x [the input] */ + tmpx = x->dp + ix; + + /* set the carry to zero */ + u = 0; + + /* Multiply and add in place */ + for (iy = 0; iy < n->used; iy++) { + /* compute product and sum */ + r = ((mp_word)mu * (mp_word)*tmpn++) + + (mp_word)u + (mp_word)*tmpx; + + /* get carry */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + + /* fix digit */ + *tmpx++ = (mp_digit)(r & (mp_word)MP_MASK); + } + /* At this point the ix'th digit of x should be zero */ + + + /* propagate carries upwards as required*/ + while (u != 0u) { + *tmpx += u; + u = *tmpx >> MP_DIGIT_BIT; + *tmpx++ &= MP_MASK; + } + } + } + + /* at this point the n.used'th least + * significant digits of x are all zero + * which means we can shift x to the + * right by n.used digits and the + * residue is unchanged. + */ + + /* x = x/b**n.used */ + mp_clamp(x); + mp_rshd(x, n->used); + + /* if x >= n then x = x - n */ + if (mp_cmp_mag(x, n) != MP_LT) { + return s_mp_sub(x, n, x); + } + + return MP_OKAY; +} +#endif + +/* End: bn_mp_montgomery_reduce.c */ + +/* Start: bn_mp_montgomery_setup.c */ +#include "tommath_private.h" +#ifdef BN_MP_MONTGOMERY_SETUP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* setups the montgomery reduction stuff */ +mp_err mp_montgomery_setup(const mp_int *n, mp_digit *rho) +{ + mp_digit x, b; + + /* fast inversion mod 2**k + * + * Based on the fact that + * + * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n) + * => 2*X*A - X*X*A*A = 1 + * => 2*(1) - (1) = 1 + */ + b = n->dp[0]; + + if ((b & 1u) == 0u) { + return MP_VAL; + } + + x = (((b + 2u) & 4u) << 1) + b; /* here x*a==1 mod 2**4 */ + x *= 2u - (b * x); /* here x*a==1 mod 2**8 */ +#if !defined(MP_8BIT) + x *= 2u - (b * x); /* here x*a==1 mod 2**16 */ +#endif +#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT)) + x *= 2u - (b * x); /* here x*a==1 mod 2**32 */ +#endif +#ifdef MP_64BIT + x *= 2u - (b * x); /* here x*a==1 mod 2**64 */ +#endif + + /* rho = -1/m mod b */ + *rho = (mp_digit)(((mp_word)1 << (mp_word)MP_DIGIT_BIT) - x) & MP_MASK; + + return MP_OKAY; +} +#endif + +/* End: bn_mp_montgomery_setup.c */ + +/* Start: bn_mp_mul.c */ +#include "tommath_private.h" +#ifdef BN_MP_MUL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* high level multiplication (handles sign) */ +mp_err mp_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_err err; + int min_len = MP_MIN(a->used, b->used), + max_len = MP_MAX(a->used, b->used), + digs = a->used + b->used + 1; + mp_sign neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; + + if (MP_HAS(S_MP_BALANCE_MUL) && + /* Check sizes. The smaller one needs to be larger than the Karatsuba cut-off. + * The bigger one needs to be at least about one MP_KARATSUBA_MUL_CUTOFF bigger + * to make some sense, but it depends on architecture, OS, position of the + * stars... so YMMV. + * Using it to cut the input into slices small enough for fast_s_mp_mul_digs + * was actually slower on the author's machine, but YMMV. + */ + (min_len >= MP_KARATSUBA_MUL_CUTOFF) && + ((max_len / 2) >= MP_KARATSUBA_MUL_CUTOFF) && + /* Not much effect was observed below a ratio of 1:2, but again: YMMV. */ + (max_len >= (2 * min_len))) { + err = s_mp_balance_mul(a,b,c); + } else if (MP_HAS(S_MP_TOOM_MUL) && + (min_len >= MP_TOOM_MUL_CUTOFF)) { + err = s_mp_toom_mul(a, b, c); + } else if (MP_HAS(S_MP_KARATSUBA_MUL) && + (min_len >= MP_KARATSUBA_MUL_CUTOFF)) { + err = s_mp_karatsuba_mul(a, b, c); + } else if (MP_HAS(S_MP_MUL_DIGS_FAST) && + /* can we use the fast multiplier? + * + * The fast multiplier can be used if the output will + * have less than MP_WARRAY digits and the number of + * digits won't affect carry propagation + */ + (digs < MP_WARRAY) && + (min_len <= MP_MAXFAST)) { + err = s_mp_mul_digs_fast(a, b, c, digs); + } else if (MP_HAS(S_MP_MUL_DIGS)) { + err = s_mp_mul_digs(a, b, c, digs); + } else { + err = MP_VAL; + } + c->sign = (c->used > 0) ? neg : MP_ZPOS; + return err; +} +#endif + +/* End: bn_mp_mul.c */ + +/* Start: bn_mp_mul_2.c */ +#include "tommath_private.h" +#ifdef BN_MP_MUL_2_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* b = a*2 */ +mp_err mp_mul_2(const mp_int *a, mp_int *b) +{ + int x, oldused; + mp_err err; + + /* grow to accomodate result */ + if (b->alloc < (a->used + 1)) { + if ((err = mp_grow(b, a->used + 1)) != MP_OKAY) { + return err; + } + } + + oldused = b->used; + b->used = a->used; + + { + mp_digit r, rr, *tmpa, *tmpb; + + /* alias for source */ + tmpa = a->dp; + + /* alias for dest */ + tmpb = b->dp; + + /* carry */ + r = 0; + for (x = 0; x < a->used; x++) { + + /* get what will be the *next* carry bit from the + * MSB of the current digit + */ + rr = *tmpa >> (mp_digit)(MP_DIGIT_BIT - 1); + + /* now shift up this digit, add in the carry [from the previous] */ + *tmpb++ = ((*tmpa++ << 1uL) | r) & MP_MASK; + + /* copy the carry that would be from the source + * digit into the next iteration + */ + r = rr; + } + + /* new leading digit? */ + if (r != 0u) { + /* add a MSB which is always 1 at this point */ + *tmpb = 1; + ++(b->used); + } + + /* now zero any excess digits on the destination + * that we didn't write to + */ + MP_ZERO_DIGITS(b->dp + b->used, oldused - b->used); + } + b->sign = a->sign; + return MP_OKAY; +} +#endif + +/* End: bn_mp_mul_2.c */ + +/* Start: bn_mp_mul_2d.c */ +#include "tommath_private.h" +#ifdef BN_MP_MUL_2D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* shift left by a certain bit count */ +mp_err mp_mul_2d(const mp_int *a, int b, mp_int *c) +{ + mp_digit d; + mp_err err; + + /* copy */ + if (a != c) { + if ((err = mp_copy(a, c)) != MP_OKAY) { + return err; + } + } + + if (c->alloc < (c->used + (b / MP_DIGIT_BIT) + 1)) { + if ((err = mp_grow(c, c->used + (b / MP_DIGIT_BIT) + 1)) != MP_OKAY) { + return err; + } + } + + /* shift by as many digits in the bit count */ + if (b >= MP_DIGIT_BIT) { + if ((err = mp_lshd(c, b / MP_DIGIT_BIT)) != MP_OKAY) { + return err; + } + } + + /* shift any bit count < MP_DIGIT_BIT */ + d = (mp_digit)(b % MP_DIGIT_BIT); + if (d != 0u) { + mp_digit *tmpc, shift, mask, r, rr; + int x; + + /* bitmask for carries */ + mask = ((mp_digit)1 << d) - (mp_digit)1; + + /* shift for msbs */ + shift = (mp_digit)MP_DIGIT_BIT - d; + + /* alias */ + tmpc = c->dp; + + /* carry */ + r = 0; + for (x = 0; x < c->used; x++) { + /* get the higher bits of the current word */ + rr = (*tmpc >> shift) & mask; + + /* shift the current word and OR in the carry */ + *tmpc = ((*tmpc << d) | r) & MP_MASK; + ++tmpc; + + /* set the carry to the carry bits of the current word */ + r = rr; + } + + /* set final carry */ + if (r != 0u) { + c->dp[(c->used)++] = r; + } + } + mp_clamp(c); + return MP_OKAY; +} +#endif + +/* End: bn_mp_mul_2d.c */ + +/* Start: bn_mp_mul_d.c */ +#include "tommath_private.h" +#ifdef BN_MP_MUL_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* multiply by a digit */ +mp_err mp_mul_d(const mp_int *a, mp_digit b, mp_int *c) +{ + mp_digit u, *tmpa, *tmpc; + mp_word r; + mp_err err; + int ix, olduse; + + /* make sure c is big enough to hold a*b */ + if (c->alloc < (a->used + 1)) { + if ((err = mp_grow(c, a->used + 1)) != MP_OKAY) { + return err; + } + } + + /* get the original destinations used count */ + olduse = c->used; + + /* set the sign */ + c->sign = a->sign; + + /* alias for a->dp [source] */ + tmpa = a->dp; + + /* alias for c->dp [dest] */ + tmpc = c->dp; + + /* zero carry */ + u = 0; + + /* compute columns */ + for (ix = 0; ix < a->used; ix++) { + /* compute product and carry sum for this term */ + r = (mp_word)u + ((mp_word)*tmpa++ * (mp_word)b); + + /* mask off higher bits to get a single digit */ + *tmpc++ = (mp_digit)(r & (mp_word)MP_MASK); + + /* send carry into next iteration */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + } + + /* store final carry [if any] and increment ix offset */ + *tmpc++ = u; + ++ix; + + /* now zero digits above the top */ + MP_ZERO_DIGITS(tmpc, olduse - ix); + + /* set used count */ + c->used = a->used + 1; + mp_clamp(c); + + return MP_OKAY; +} +#endif + +/* End: bn_mp_mul_d.c */ + +/* Start: bn_mp_mulmod.c */ +#include "tommath_private.h" +#ifdef BN_MP_MULMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* d = a * b (mod c) */ +mp_err mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) +{ + mp_err err; + mp_int t; + + if ((err = mp_init_size(&t, c->used)) != MP_OKAY) { + return err; + } + + if ((err = mp_mul(a, b, &t)) != MP_OKAY) { + goto LBL_ERR; + } + err = mp_mod(&t, c, d); + +LBL_ERR: + mp_clear(&t); + return err; +} +#endif + +/* End: bn_mp_mulmod.c */ + +/* Start: bn_mp_neg.c */ +#include "tommath_private.h" +#ifdef BN_MP_NEG_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* b = -a */ +mp_err mp_neg(const mp_int *a, mp_int *b) +{ + mp_err err; + if (a != b) { + if ((err = mp_copy(a, b)) != MP_OKAY) { + return err; + } + } + + if (!MP_IS_ZERO(b)) { + b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS; + } else { + b->sign = MP_ZPOS; + } + + return MP_OKAY; +} +#endif + +/* End: bn_mp_neg.c */ + +/* Start: bn_mp_or.c */ +#include "tommath_private.h" +#ifdef BN_MP_OR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* two complement or */ +mp_err mp_or(const mp_int *a, const mp_int *b, mp_int *c) +{ + int used = MP_MAX(a->used, b->used) + 1, i; + mp_err err; + mp_digit ac = 1, bc = 1, cc = 1; + mp_sign csign = ((a->sign == MP_NEG) || (b->sign == MP_NEG)) ? MP_NEG : MP_ZPOS; + + if (c->alloc < used) { + if ((err = mp_grow(c, used)) != MP_OKAY) { + return err; + } + } + + for (i = 0; i < used; i++) { + mp_digit x, y; + + /* convert to two complement if negative */ + if (a->sign == MP_NEG) { + ac += (i >= a->used) ? MP_MASK : (~a->dp[i] & MP_MASK); + x = ac & MP_MASK; + ac >>= MP_DIGIT_BIT; + } else { + x = (i >= a->used) ? 0uL : a->dp[i]; + } + + /* convert to two complement if negative */ + if (b->sign == MP_NEG) { + bc += (i >= b->used) ? MP_MASK : (~b->dp[i] & MP_MASK); + y = bc & MP_MASK; + bc >>= MP_DIGIT_BIT; + } else { + y = (i >= b->used) ? 0uL : b->dp[i]; + } + + c->dp[i] = x | y; + + /* convert to to sign-magnitude if negative */ + if (csign == MP_NEG) { + cc += ~c->dp[i] & MP_MASK; + c->dp[i] = cc & MP_MASK; + cc >>= MP_DIGIT_BIT; + } + } + + c->used = used; + c->sign = csign; + mp_clamp(c); + return MP_OKAY; +} +#endif + +/* End: bn_mp_or.c */ + +/* Start: bn_mp_pack.c */ +#include "tommath_private.h" +#ifdef BN_MP_PACK_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* based on gmp's mpz_export. + * see http://gmplib.org/manual/Integer-Import-and-Export.html + */ +mp_err mp_pack(void *rop, size_t maxcount, size_t *written, mp_order order, size_t size, + mp_endian endian, size_t nails, const mp_int *op) +{ + mp_err err; + size_t odd_nails, nail_bytes, i, j, count; + unsigned char odd_nail_mask; + + mp_int t; + + count = mp_pack_count(op, nails, size); + + if (count > maxcount) { + return MP_BUF; + } + + if ((err = mp_init_copy(&t, op)) != MP_OKAY) { + return err; + } + + if (endian == MP_NATIVE_ENDIAN) { + MP_GET_ENDIANNESS(endian); + } + + odd_nails = (nails % 8u); + odd_nail_mask = 0xff; + for (i = 0u; i < odd_nails; ++i) { + odd_nail_mask ^= (unsigned char)(1u << (7u - i)); + } + nail_bytes = nails / 8u; + + for (i = 0u; i < count; ++i) { + for (j = 0u; j < size; ++j) { + unsigned char *byte = (unsigned char *)rop + + (((order == MP_LSB_FIRST) ? i : ((count - 1u) - i)) * size) + + ((endian == MP_LITTLE_ENDIAN) ? j : ((size - 1u) - j)); + + if (j >= (size - nail_bytes)) { + *byte = 0; + continue; + } + + *byte = (unsigned char)((j == ((size - nail_bytes) - 1u)) ? (t.dp[0] & odd_nail_mask) : (t.dp[0] & 0xFFuL)); + + if ((err = mp_div_2d(&t, (j == ((size - nail_bytes) - 1u)) ? (int)(8u - odd_nails) : 8, &t, NULL)) != MP_OKAY) { + goto LBL_ERR; + } + + } + } + + if (written != NULL) { + *written = count; + } + err = MP_OKAY; + +LBL_ERR: + mp_clear(&t); + return err; +} + +#endif + +/* End: bn_mp_pack.c */ + +/* Start: bn_mp_pack_count.c */ +#include "tommath_private.h" +#ifdef BN_MP_PACK_COUNT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +size_t mp_pack_count(const mp_int *a, size_t nails, size_t size) +{ + size_t bits = (size_t)mp_count_bits(a); + return ((bits / ((size * 8u) - nails)) + (((bits % ((size * 8u) - nails)) != 0u) ? 1u : 0u)); +} + +#endif + +/* End: bn_mp_pack_count.c */ + +/* Start: bn_mp_prime_fermat.c */ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_FERMAT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* performs one Fermat test. + * + * If "a" were prime then b**a == b (mod a) since the order of + * the multiplicative sub-group would be phi(a) = a-1. That means + * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a). + * + * Sets result to 1 if the congruence holds, or zero otherwise. + */ +mp_err mp_prime_fermat(const mp_int *a, const mp_int *b, mp_bool *result) +{ + mp_int t; + mp_err err; + + /* default to composite */ + *result = MP_NO; + + /* ensure b > 1 */ + if (mp_cmp_d(b, 1uL) != MP_GT) { + return MP_VAL; + } + + /* init t */ + if ((err = mp_init(&t)) != MP_OKAY) { + return err; + } + + /* compute t = b**a mod a */ + if ((err = mp_exptmod(b, a, a, &t)) != MP_OKAY) { + goto LBL_T; + } + + /* is it equal to b? */ + if (mp_cmp(&t, b) == MP_EQ) { + *result = MP_YES; + } + + err = MP_OKAY; +LBL_T: + mp_clear(&t); + return err; +} +#endif + +/* End: bn_mp_prime_fermat.c */ + +/* Start: bn_mp_prime_frobenius_underwood.c */ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_FROBENIUS_UNDERWOOD_C + +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* + * See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details + */ +#ifndef LTM_USE_ONLY_MR + +#ifdef MP_8BIT +/* + * floor of positive solution of + * (2^16)-1 = (a+4)*(2*a+5) + * TODO: Both values are smaller than N^(1/4), would have to use a bigint + * for a instead but any a biger than about 120 are already so rare that + * it is possible to ignore them and still get enough pseudoprimes. + * But it is still a restriction of the set of available pseudoprimes + * which makes this implementation less secure if used stand-alone. + */ +#define LTM_FROBENIUS_UNDERWOOD_A 177 +#else +#define LTM_FROBENIUS_UNDERWOOD_A 32764 +#endif +mp_err mp_prime_frobenius_underwood(const mp_int *N, mp_bool *result) +{ + mp_int T1z, T2z, Np1z, sz, tz; + + int a, ap2, length, i, j; + mp_err err; + + *result = MP_NO; + + if ((err = mp_init_multi(&T1z, &T2z, &Np1z, &sz, &tz, NULL)) != MP_OKAY) { + return err; + } + + for (a = 0; a < LTM_FROBENIUS_UNDERWOOD_A; a++) { + /* TODO: That's ugly! No, really, it is! */ + if ((a==2) || (a==4) || (a==7) || (a==8) || (a==10) || + (a==14) || (a==18) || (a==23) || (a==26) || (a==28)) { + continue; + } + /* (32764^2 - 4) < 2^31, no bigint for >MP_8BIT needed) */ + mp_set_u32(&T1z, (uint32_t)a); + + if ((err = mp_sqr(&T1z, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + + if ((err = mp_sub_d(&T1z, 4uL, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + + if ((err = mp_kronecker(&T1z, N, &j)) != MP_OKAY) goto LBL_FU_ERR; + + if (j == -1) { + break; + } + + if (j == 0) { + /* composite */ + goto LBL_FU_ERR; + } + } + /* Tell it a composite and set return value accordingly */ + if (a >= LTM_FROBENIUS_UNDERWOOD_A) { + err = MP_ITER; + goto LBL_FU_ERR; + } + /* Composite if N and (a+4)*(2*a+5) are not coprime */ + mp_set_u32(&T1z, (uint32_t)((a+4)*((2*a)+5))); + + if ((err = mp_gcd(N, &T1z, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + + if (!((T1z.used == 1) && (T1z.dp[0] == 1u))) goto LBL_FU_ERR; + + ap2 = a + 2; + if ((err = mp_add_d(N, 1uL, &Np1z)) != MP_OKAY) goto LBL_FU_ERR; + + mp_set(&sz, 1uL); + mp_set(&tz, 2uL); + length = mp_count_bits(&Np1z); + + for (i = length - 2; i >= 0; i--) { + /* + * temp = (sz*(a*sz+2*tz))%N; + * tz = ((tz-sz)*(tz+sz))%N; + * sz = temp; + */ + if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR; + + /* a = 0 at about 50% of the cases (non-square and odd input) */ + if (a != 0) { + if ((err = mp_mul_d(&sz, (mp_digit)a, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_add(&T1z, &T2z, &T2z)) != MP_OKAY) goto LBL_FU_ERR; + } + + if ((err = mp_mul(&T2z, &sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_sub(&tz, &sz, &T2z)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_add(&sz, &tz, &sz)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_mul(&sz, &T2z, &tz)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_mod(&tz, N, &tz)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_mod(&T1z, N, &sz)) != MP_OKAY) goto LBL_FU_ERR; + if (s_mp_get_bit(&Np1z, (unsigned int)i) == MP_YES) { + /* + * temp = (a+2) * sz + tz + * tz = 2 * tz - sz + * sz = temp + */ + if (a == 0) { + if ((err = mp_mul_2(&sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + } else { + if ((err = mp_mul_d(&sz, (mp_digit)ap2, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + } + if ((err = mp_add(&T1z, &tz, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR; + if ((err = mp_sub(&T2z, &sz, &tz)) != MP_OKAY) goto LBL_FU_ERR; + mp_exch(&sz, &T1z); + } + } + + mp_set_u32(&T1z, (uint32_t)((2 * a) + 5)); + if ((err = mp_mod(&T1z, N, &T1z)) != MP_OKAY) goto LBL_FU_ERR; + if (MP_IS_ZERO(&sz) && (mp_cmp(&tz, &T1z) == MP_EQ)) { + *result = MP_YES; + } + +LBL_FU_ERR: + mp_clear_multi(&tz, &sz, &Np1z, &T2z, &T1z, NULL); + return err; +} + +#endif +#endif + +/* End: bn_mp_prime_frobenius_underwood.c */ + +/* Start: bn_mp_prime_is_prime.c */ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_IS_PRIME_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* portable integer log of two with small footprint */ +static unsigned int s_floor_ilog2(int value) +{ + unsigned int r = 0; + while ((value >>= 1) != 0) { + r++; + } + return r; +} + + +mp_err mp_prime_is_prime(const mp_int *a, int t, mp_bool *result) +{ + mp_int b; + int ix, p_max = 0, size_a, len; + mp_bool res; + mp_err err; + unsigned int fips_rand, mask; + + /* default to no */ + *result = MP_NO; + + /* Some shortcuts */ + /* N > 3 */ + if (a->used == 1) { + if ((a->dp[0] == 0u) || (a->dp[0] == 1u)) { + *result = MP_NO; + return MP_OKAY; + } + if (a->dp[0] == 2u) { + *result = MP_YES; + return MP_OKAY; + } + } + + /* N must be odd */ + if (MP_IS_EVEN(a)) { + return MP_OKAY; + } + /* N is not a perfect square: floor(sqrt(N))^2 != N */ + if ((err = mp_is_square(a, &res)) != MP_OKAY) { + return err; + } + if (res != MP_NO) { + return MP_OKAY; + } + + /* is the input equal to one of the primes in the table? */ + for (ix = 0; ix < PRIVATE_MP_PRIME_TAB_SIZE; ix++) { + if (mp_cmp_d(a, s_mp_prime_tab[ix]) == MP_EQ) { + *result = MP_YES; + return MP_OKAY; + } + } +#ifdef MP_8BIT + /* The search in the loop above was exhaustive in this case */ + if ((a->used == 1) && (PRIVATE_MP_PRIME_TAB_SIZE >= 31)) { + return MP_OKAY; + } +#endif + + /* first perform trial division */ + if ((err = s_mp_prime_is_divisible(a, &res)) != MP_OKAY) { + return err; + } + + /* return if it was trivially divisible */ + if (res == MP_YES) { + return MP_OKAY; + } + + /* + Run the Miller-Rabin test with base 2 for the BPSW test. + */ + if ((err = mp_init_set(&b, 2uL)) != MP_OKAY) { + return err; + } + + if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { + goto LBL_B; + } + if (res == MP_NO) { + goto LBL_B; + } + /* + Rumours have it that Mathematica does a second M-R test with base 3. + Other rumours have it that their strong L-S test is slightly different. + It does not hurt, though, beside a bit of extra runtime. + */ + b.dp[0]++; + if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { + goto LBL_B; + } + if (res == MP_NO) { + goto LBL_B; + } + + /* + * Both, the Frobenius-Underwood test and the the Lucas-Selfridge test are quite + * slow so if speed is an issue, define LTM_USE_ONLY_MR to use M-R tests with + * bases 2, 3 and t random bases. + */ +#ifndef LTM_USE_ONLY_MR + if (t >= 0) { + /* + * Use a Frobenius-Underwood test instead of the Lucas-Selfridge test for + * MP_8BIT (It is unknown if the Lucas-Selfridge test works with 16-bit + * integers but the necesssary analysis is on the todo-list). + */ +#if defined (MP_8BIT) || defined (LTM_USE_FROBENIUS_TEST) + err = mp_prime_frobenius_underwood(a, &res); + if ((err != MP_OKAY) && (err != MP_ITER)) { + goto LBL_B; + } + if (res == MP_NO) { + goto LBL_B; + } +#else + if ((err = mp_prime_strong_lucas_selfridge(a, &res)) != MP_OKAY) { + goto LBL_B; + } + if (res == MP_NO) { + goto LBL_B; + } +#endif + } +#endif + + /* run at least one Miller-Rabin test with a random base */ + if (t == 0) { + t = 1; + } + + /* + Only recommended if the input range is known to be < 3317044064679887385961981 + + It uses the bases necessary for a deterministic M-R test if the input is + smaller than 3317044064679887385961981 + The caller has to check the size. + TODO: can be made a bit finer grained but comparing is not free. + */ + if (t < 0) { + /* + Sorenson, Jonathan; Webster, Jonathan (2015). + "Strong Pseudoprimes to Twelve Prime Bases". + */ + /* 0x437ae92817f9fc85b7e5 = 318665857834031151167461 */ + if ((err = mp_read_radix(&b, "437ae92817f9fc85b7e5", 16)) != MP_OKAY) { + goto LBL_B; + } + + if (mp_cmp(a, &b) == MP_LT) { + p_max = 12; + } else { + /* 0x2be6951adc5b22410a5fd = 3317044064679887385961981 */ + if ((err = mp_read_radix(&b, "2be6951adc5b22410a5fd", 16)) != MP_OKAY) { + goto LBL_B; + } + + if (mp_cmp(a, &b) == MP_LT) { + p_max = 13; + } else { + err = MP_VAL; + goto LBL_B; + } + } + + /* we did bases 2 and 3 already, skip them */ + for (ix = 2; ix < p_max; ix++) { + mp_set(&b, s_mp_prime_tab[ix]); + if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { + goto LBL_B; + } + if (res == MP_NO) { + goto LBL_B; + } + } + } + /* + Do "t" M-R tests with random bases between 3 and "a". + See Fips 186.4 p. 126ff + */ + else if (t > 0) { + /* + * The mp_digit's have a defined bit-size but the size of the + * array a.dp is a simple 'int' and this library can not assume full + * compliance to the current C-standard (ISO/IEC 9899:2011) because + * it gets used for small embeded processors, too. Some of those MCUs + * have compilers that one cannot call standard compliant by any means. + * Hence the ugly type-fiddling in the following code. + */ + size_a = mp_count_bits(a); + mask = (1u << s_floor_ilog2(size_a)) - 1u; + /* + Assuming the General Rieman hypothesis (never thought to write that in a + comment) the upper bound can be lowered to 2*(log a)^2. + E. Bach, "Explicit bounds for primality testing and related problems," + Math. Comp. 55 (1990), 355-380. + + size_a = (size_a/10) * 7; + len = 2 * (size_a * size_a); + + E.g.: a number of size 2^2048 would be reduced to the upper limit + + floor(2048/10)*7 = 1428 + 2 * 1428^2 = 4078368 + + (would have been ~4030331.9962 with floats and natural log instead) + That number is smaller than 2^28, the default bit-size of mp_digit. + */ + + /* + How many tests, you might ask? Dana Jacobsen of Math::Prime::Util fame + does exactly 1. In words: one. Look at the end of _GMP_is_prime() in + Math-Prime-Util-GMP-0.50/primality.c if you do not believe it. + + The function mp_rand() goes to some length to use a cryptographically + good PRNG. That also means that the chance to always get the same base + in the loop is non-zero, although very low. + If the BPSW test and/or the addtional Frobenious test have been + performed instead of just the Miller-Rabin test with the bases 2 and 3, + a single extra test should suffice, so such a very unlikely event + will not do much harm. + + To preemptivly answer the dangling question: no, a witness does not + need to be prime. + */ + for (ix = 0; ix < t; ix++) { + /* mp_rand() guarantees the first digit to be non-zero */ + if ((err = mp_rand(&b, 1)) != MP_OKAY) { + goto LBL_B; + } + /* + * Reduce digit before casting because mp_digit might be bigger than + * an unsigned int and "mask" on the other side is most probably not. + */ + fips_rand = (unsigned int)(b.dp[0] & (mp_digit) mask); +#ifdef MP_8BIT + /* + * One 8-bit digit is too small, so concatenate two if the size of + * unsigned int allows for it. + */ + if ((MP_SIZEOF_BITS(unsigned int)/2) >= MP_SIZEOF_BITS(mp_digit)) { + if ((err = mp_rand(&b, 1)) != MP_OKAY) { + goto LBL_B; + } + fips_rand <<= MP_SIZEOF_BITS(mp_digit); + fips_rand |= (unsigned int) b.dp[0]; + fips_rand &= mask; + } +#endif + if (fips_rand > (unsigned int)(INT_MAX - MP_DIGIT_BIT)) { + len = INT_MAX / MP_DIGIT_BIT; + } else { + len = (((int)fips_rand + MP_DIGIT_BIT) / MP_DIGIT_BIT); + } + /* Unlikely. */ + if (len < 0) { + ix--; + continue; + } + /* + * As mentioned above, one 8-bit digit is too small and + * although it can only happen in the unlikely case that + * an "unsigned int" is smaller than 16 bit a simple test + * is cheap and the correction even cheaper. + */ +#ifdef MP_8BIT + /* All "a" < 2^8 have been caught before */ + if (len == 1) { + len++; + } +#endif + if ((err = mp_rand(&b, len)) != MP_OKAY) { + goto LBL_B; + } + /* + * That number might got too big and the witness has to be + * smaller than "a" + */ + len = mp_count_bits(&b); + if (len >= size_a) { + len = (len - size_a) + 1; + if ((err = mp_div_2d(&b, len, &b, NULL)) != MP_OKAY) { + goto LBL_B; + } + } + /* Although the chance for b <= 3 is miniscule, try again. */ + if (mp_cmp_d(&b, 3uL) != MP_GT) { + ix--; + continue; + } + if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { + goto LBL_B; + } + if (res == MP_NO) { + goto LBL_B; + } + } + } + + /* passed the test */ + *result = MP_YES; +LBL_B: + mp_clear(&b); + return err; +} + +#endif + +/* End: bn_mp_prime_is_prime.c */ + +/* Start: bn_mp_prime_miller_rabin.c */ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_MILLER_RABIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Miller-Rabin test of "a" to the base of "b" as described in + * HAC pp. 139 Algorithm 4.24 + * + * Sets result to 0 if definitely composite or 1 if probably prime. + * Randomly the chance of error is no more than 1/4 and often + * very much lower. + */ +mp_err mp_prime_miller_rabin(const mp_int *a, const mp_int *b, mp_bool *result) +{ + mp_int n1, y, r; + mp_err err; + int s, j; + + /* default */ + *result = MP_NO; + + /* ensure b > 1 */ + if (mp_cmp_d(b, 1uL) != MP_GT) { + return MP_VAL; + } + + /* get n1 = a - 1 */ + if ((err = mp_init_copy(&n1, a)) != MP_OKAY) { + return err; + } + if ((err = mp_sub_d(&n1, 1uL, &n1)) != MP_OKAY) { + goto LBL_N1; + } + + /* set 2**s * r = n1 */ + if ((err = mp_init_copy(&r, &n1)) != MP_OKAY) { + goto LBL_N1; + } + + /* count the number of least significant bits + * which are zero + */ + s = mp_cnt_lsb(&r); + + /* now divide n - 1 by 2**s */ + if ((err = mp_div_2d(&r, s, &r, NULL)) != MP_OKAY) { + goto LBL_R; + } + + /* compute y = b**r mod a */ + if ((err = mp_init(&y)) != MP_OKAY) { + goto LBL_R; + } + if ((err = mp_exptmod(b, &r, a, &y)) != MP_OKAY) { + goto LBL_Y; + } + + /* if y != 1 and y != n1 do */ + if ((mp_cmp_d(&y, 1uL) != MP_EQ) && (mp_cmp(&y, &n1) != MP_EQ)) { + j = 1; + /* while j <= s-1 and y != n1 */ + while ((j <= (s - 1)) && (mp_cmp(&y, &n1) != MP_EQ)) { + if ((err = mp_sqrmod(&y, a, &y)) != MP_OKAY) { + goto LBL_Y; + } + + /* if y == 1 then composite */ + if (mp_cmp_d(&y, 1uL) == MP_EQ) { + goto LBL_Y; + } + + ++j; + } + + /* if y != n1 then composite */ + if (mp_cmp(&y, &n1) != MP_EQ) { + goto LBL_Y; + } + } + + /* probably prime now */ + *result = MP_YES; +LBL_Y: + mp_clear(&y); +LBL_R: + mp_clear(&r); +LBL_N1: + mp_clear(&n1); + return err; +} +#endif + +/* End: bn_mp_prime_miller_rabin.c */ + +/* Start: bn_mp_prime_next_prime.c */ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_NEXT_PRIME_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* finds the next prime after the number "a" using "t" trials + * of Miller-Rabin. + * + * bbs_style = 1 means the prime must be congruent to 3 mod 4 + */ +mp_err mp_prime_next_prime(mp_int *a, int t, int bbs_style) +{ + int x, y; + mp_ord cmp; + mp_err err; + mp_bool res = MP_NO; + mp_digit res_tab[PRIVATE_MP_PRIME_TAB_SIZE], step, kstep; + mp_int b; + + /* force positive */ + a->sign = MP_ZPOS; + + /* simple algo if a is less than the largest prime in the table */ + if (mp_cmp_d(a, s_mp_prime_tab[PRIVATE_MP_PRIME_TAB_SIZE-1]) == MP_LT) { + /* find which prime it is bigger than "a" */ + for (x = 0; x < PRIVATE_MP_PRIME_TAB_SIZE; x++) { + cmp = mp_cmp_d(a, s_mp_prime_tab[x]); + if (cmp == MP_EQ) { + continue; + } + if (cmp != MP_GT) { + if ((bbs_style == 1) && ((s_mp_prime_tab[x] & 3u) != 3u)) { + /* try again until we get a prime congruent to 3 mod 4 */ + continue; + } else { + mp_set(a, s_mp_prime_tab[x]); + return MP_OKAY; + } + } + } + /* fall through to the sieve */ + } + + /* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */ + if (bbs_style == 1) { + kstep = 4; + } else { + kstep = 2; + } + + /* at this point we will use a combination of a sieve and Miller-Rabin */ + + if (bbs_style == 1) { + /* if a mod 4 != 3 subtract the correct value to make it so */ + if ((a->dp[0] & 3u) != 3u) { + if ((err = mp_sub_d(a, (a->dp[0] & 3u) + 1u, a)) != MP_OKAY) { + return err; + } + } + } else { + if (MP_IS_EVEN(a)) { + /* force odd */ + if ((err = mp_sub_d(a, 1uL, a)) != MP_OKAY) { + return err; + } + } + } + + /* generate the restable */ + for (x = 1; x < PRIVATE_MP_PRIME_TAB_SIZE; x++) { + if ((err = mp_mod_d(a, s_mp_prime_tab[x], res_tab + x)) != MP_OKAY) { + return err; + } + } + + /* init temp used for Miller-Rabin Testing */ + if ((err = mp_init(&b)) != MP_OKAY) { + return err; + } + + for (;;) { + /* skip to the next non-trivially divisible candidate */ + step = 0; + do { + /* y == 1 if any residue was zero [e.g. cannot be prime] */ + y = 0; + + /* increase step to next candidate */ + step += kstep; + + /* compute the new residue without using division */ + for (x = 1; x < PRIVATE_MP_PRIME_TAB_SIZE; x++) { + /* add the step to each residue */ + res_tab[x] += kstep; + + /* subtract the modulus [instead of using division] */ + if (res_tab[x] >= s_mp_prime_tab[x]) { + res_tab[x] -= s_mp_prime_tab[x]; + } + + /* set flag if zero */ + if (res_tab[x] == 0u) { + y = 1; + } + } + } while ((y == 1) && (step < (((mp_digit)1 << MP_DIGIT_BIT) - kstep))); + + /* add the step */ + if ((err = mp_add_d(a, step, a)) != MP_OKAY) { + goto LBL_ERR; + } + + /* if didn't pass sieve and step == MP_MAX then skip test */ + if ((y == 1) && (step >= (((mp_digit)1 << MP_DIGIT_BIT) - kstep))) { + continue; + } + + if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { + goto LBL_ERR; + } + if (res == MP_YES) { + break; + } + } + + err = MP_OKAY; +LBL_ERR: + mp_clear(&b); + return err; +} + +#endif + +/* End: bn_mp_prime_next_prime.c */ + +/* Start: bn_mp_prime_rabin_miller_trials.c */ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +static const struct { + int k, t; +} sizes[] = { + { 80, -1 }, /* Use deterministic algorithm for size <= 80 bits */ + { 81, 37 }, /* max. error = 2^(-96)*/ + { 96, 32 }, /* max. error = 2^(-96)*/ + { 128, 40 }, /* max. error = 2^(-112)*/ + { 160, 35 }, /* max. error = 2^(-112)*/ + { 256, 27 }, /* max. error = 2^(-128)*/ + { 384, 16 }, /* max. error = 2^(-128)*/ + { 512, 18 }, /* max. error = 2^(-160)*/ + { 768, 11 }, /* max. error = 2^(-160)*/ + { 896, 10 }, /* max. error = 2^(-160)*/ + { 1024, 12 }, /* max. error = 2^(-192)*/ + { 1536, 8 }, /* max. error = 2^(-192)*/ + { 2048, 6 }, /* max. error = 2^(-192)*/ + { 3072, 4 }, /* max. error = 2^(-192)*/ + { 4096, 5 }, /* max. error = 2^(-256)*/ + { 5120, 4 }, /* max. error = 2^(-256)*/ + { 6144, 4 }, /* max. error = 2^(-256)*/ + { 8192, 3 }, /* max. error = 2^(-256)*/ + { 9216, 3 }, /* max. error = 2^(-256)*/ + { 10240, 2 } /* For bigger keysizes use always at least 2 Rounds */ +}; + +/* returns # of RM trials required for a given bit size */ +int mp_prime_rabin_miller_trials(int size) +{ + int x; + + for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) { + if (sizes[x].k == size) { + return sizes[x].t; + } else if (sizes[x].k > size) { + return (x == 0) ? sizes[0].t : sizes[x - 1].t; + } + } + return sizes[x-1].t; +} + + +#endif + +/* End: bn_mp_prime_rabin_miller_trials.c */ + +/* Start: bn_mp_prime_rand.c */ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_RAND_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* makes a truly random prime of a given size (bits), + * + * Flags are as follows: + * + * MP_PRIME_BBS - make prime congruent to 3 mod 4 + * MP_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies MP_PRIME_BBS) + * MP_PRIME_2MSB_ON - make the 2nd highest bit one + * + * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can + * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself + * so it can be NULL + * + */ + +/* This is possibly the mother of all prime generation functions, muahahahahaha! */ +mp_err s_mp_prime_random_ex(mp_int *a, int t, int size, int flags, private_mp_prime_callback cb, void *dat) +{ + unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb; + int bsize, maskOR_msb_offset; + mp_bool res; + mp_err err; + + /* sanity check the input */ + if ((size <= 1) || (t <= 0)) { + return MP_VAL; + } + + /* MP_PRIME_SAFE implies MP_PRIME_BBS */ + if ((flags & MP_PRIME_SAFE) != 0) { + flags |= MP_PRIME_BBS; + } + + /* calc the byte size */ + bsize = (size>>3) + ((size&7)?1:0); + + /* we need a buffer of bsize bytes */ + tmp = (unsigned char *) MP_MALLOC((size_t)bsize); + if (tmp == NULL) { + return MP_MEM; + } + + /* calc the maskAND value for the MSbyte*/ + maskAND = ((size&7) == 0) ? 0xFFu : (unsigned char)(0xFFu >> (8 - (size & 7))); + + /* calc the maskOR_msb */ + maskOR_msb = 0; + maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0; + if ((flags & MP_PRIME_2MSB_ON) != 0) { + maskOR_msb |= (unsigned char)(0x80 >> ((9 - size) & 7)); + } + + /* get the maskOR_lsb */ + maskOR_lsb = 1u; + if ((flags & MP_PRIME_BBS) != 0) { + maskOR_lsb |= 3u; + } + + do { + /* read the bytes */ + if (cb(tmp, bsize, dat) != bsize) { + err = MP_VAL; + goto error; + } + + /* work over the MSbyte */ + tmp[0] &= maskAND; + tmp[0] |= (unsigned char)(1 << ((size - 1) & 7)); + + /* mix in the maskORs */ + tmp[maskOR_msb_offset] |= maskOR_msb; + tmp[bsize-1] |= maskOR_lsb; + + /* read it in */ + /* TODO: casting only for now until all lengths have been changed to the type "size_t"*/ + if ((err = mp_from_ubin(a, tmp, (size_t)bsize)) != MP_OKAY) { + goto error; + } + + /* is it prime? */ + if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { + goto error; + } + if (res == MP_NO) { + continue; + } + + if ((flags & MP_PRIME_SAFE) != 0) { + /* see if (a-1)/2 is prime */ + if ((err = mp_sub_d(a, 1uL, a)) != MP_OKAY) { + goto error; + } + if ((err = mp_div_2(a, a)) != MP_OKAY) { + goto error; + } + + /* is it prime? */ + if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { + goto error; + } + } + } while (res == MP_NO); + + if ((flags & MP_PRIME_SAFE) != 0) { + /* restore a to the original value */ + if ((err = mp_mul_2(a, a)) != MP_OKAY) { + goto error; + } + if ((err = mp_add_d(a, 1uL, a)) != MP_OKAY) { + goto error; + } + } + + err = MP_OKAY; +error: + MP_FREE_BUFFER(tmp, (size_t)bsize); + return err; +} + +static int s_mp_rand_cb(unsigned char *dst, int len, void *dat) +{ + (void)dat; + if (len <= 0) { + return len; + } + if (s_mp_rand_source(dst, (size_t)len) != MP_OKAY) { + return 0; + } + return len; +} + +mp_err mp_prime_rand(mp_int *a, int t, int size, int flags) +{ + return s_mp_prime_random_ex(a, t, size, flags, s_mp_rand_cb, NULL); +} + +#endif + +/* End: bn_mp_prime_rand.c */ + +/* Start: bn_mp_prime_strong_lucas_selfridge.c */ +#include "tommath_private.h" +#ifdef BN_MP_PRIME_STRONG_LUCAS_SELFRIDGE_C + +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* + * See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details + */ +#ifndef LTM_USE_ONLY_MR + +/* + * 8-bit is just too small. You can try the Frobenius test + * but that frobenius test can fail, too, for the same reason. + */ +#ifndef MP_8BIT + +/* + * multiply bigint a with int d and put the result in c + * Like mp_mul_d() but with a signed long as the small input + */ +static mp_err s_mp_mul_si(const mp_int *a, int32_t d, mp_int *c) +{ + mp_int t; + mp_err err; + + if ((err = mp_init(&t)) != MP_OKAY) { + return err; + } + + /* + * mp_digit might be smaller than a long, which excludes + * the use of mp_mul_d() here. + */ + mp_set_i32(&t, d); + err = mp_mul(a, &t, c); + mp_clear(&t); + return err; +} +/* + Strong Lucas-Selfridge test. + returns MP_YES if it is a strong L-S prime, MP_NO if it is composite + + Code ported from Thomas Ray Nicely's implementation of the BPSW test + at http://www.trnicely.net/misc/bpsw.html + + Freeware copyright (C) 2016 Thomas R. Nicely <http://www.trnicely.net>. + Released into the public domain by the author, who disclaims any legal + liability arising from its use + + The multi-line comments are made by Thomas R. Nicely and are copied verbatim. + Additional comments marked "CZ" (without the quotes) are by the code-portist. + + (If that name sounds familiar, he is the guy who found the fdiv bug in the + Pentium (P5x, I think) Intel processor) +*/ +mp_err mp_prime_strong_lucas_selfridge(const mp_int *a, mp_bool *result) +{ + /* CZ TODO: choose better variable names! */ + mp_int Dz, gcd, Np1, Uz, Vz, U2mz, V2mz, Qmz, Q2mz, Qkdz, T1z, T2z, T3z, T4z, Q2kdz; + /* CZ TODO: Some of them need the full 32 bit, hence the (temporary) exclusion of MP_8BIT */ + int32_t D, Ds, J, sign, P, Q, r, s, u, Nbits; + mp_err err; + mp_bool oddness; + + *result = MP_NO; + /* + Find the first element D in the sequence {5, -7, 9, -11, 13, ...} + such that Jacobi(D,N) = -1 (Selfridge's algorithm). Theory + indicates that, if N is not a perfect square, D will "nearly + always" be "small." Just in case, an overflow trap for D is + included. + */ + + if ((err = mp_init_multi(&Dz, &gcd, &Np1, &Uz, &Vz, &U2mz, &V2mz, &Qmz, &Q2mz, &Qkdz, &T1z, &T2z, &T3z, &T4z, &Q2kdz, + NULL)) != MP_OKAY) { + return err; + } + + D = 5; + sign = 1; + + for (;;) { + Ds = sign * D; + sign = -sign; + mp_set_u32(&Dz, (uint32_t)D); + if ((err = mp_gcd(a, &Dz, &gcd)) != MP_OKAY) goto LBL_LS_ERR; + + /* if 1 < GCD < N then N is composite with factor "D", and + Jacobi(D,N) is technically undefined (but often returned + as zero). */ + if ((mp_cmp_d(&gcd, 1uL) == MP_GT) && (mp_cmp(&gcd, a) == MP_LT)) { + goto LBL_LS_ERR; + } + if (Ds < 0) { + Dz.sign = MP_NEG; + } + if ((err = mp_kronecker(&Dz, a, &J)) != MP_OKAY) goto LBL_LS_ERR; + + if (J == -1) { + break; + } + D += 2; + + if (D > (INT_MAX - 2)) { + err = MP_VAL; + goto LBL_LS_ERR; + } + } + + + + P = 1; /* Selfridge's choice */ + Q = (1 - Ds) / 4; /* Required so D = P*P - 4*Q */ + + /* NOTE: The conditions (a) N does not divide Q, and + (b) D is square-free or not a perfect square, are included by + some authors; e.g., "Prime numbers and computer methods for + factorization," Hans Riesel (2nd ed., 1994, Birkhauser, Boston), + p. 130. For this particular application of Lucas sequences, + these conditions were found to be immaterial. */ + + /* Now calculate N - Jacobi(D,N) = N + 1 (even), and calculate the + odd positive integer d and positive integer s for which + N + 1 = 2^s*d (similar to the step for N - 1 in Miller's test). + The strong Lucas-Selfridge test then returns N as a strong + Lucas probable prime (slprp) if any of the following + conditions is met: U_d=0, V_d=0, V_2d=0, V_4d=0, V_8d=0, + V_16d=0, ..., etc., ending with V_{2^(s-1)*d}=V_{(N+1)/2}=0 + (all equalities mod N). Thus d is the highest index of U that + must be computed (since V_2m is independent of U), compared + to U_{N+1} for the standard Lucas-Selfridge test; and no + index of V beyond (N+1)/2 is required, just as in the + standard Lucas-Selfridge test. However, the quantity Q^d must + be computed for use (if necessary) in the latter stages of + the test. The result is that the strong Lucas-Selfridge test + has a running time only slightly greater (order of 10 %) than + that of the standard Lucas-Selfridge test, while producing + only (roughly) 30 % as many pseudoprimes (and every strong + Lucas pseudoprime is also a standard Lucas pseudoprime). Thus + the evidence indicates that the strong Lucas-Selfridge test is + more effective than the standard Lucas-Selfridge test, and a + Baillie-PSW test based on the strong Lucas-Selfridge test + should be more reliable. */ + + if ((err = mp_add_d(a, 1uL, &Np1)) != MP_OKAY) goto LBL_LS_ERR; + s = mp_cnt_lsb(&Np1); + + /* CZ + * This should round towards zero because + * Thomas R. Nicely used GMP's mpz_tdiv_q_2exp() + * and mp_div_2d() is equivalent. Additionally: + * dividing an even number by two does not produce + * any leftovers. + */ + if ((err = mp_div_2d(&Np1, s, &Dz, NULL)) != MP_OKAY) goto LBL_LS_ERR; + /* We must now compute U_d and V_d. Since d is odd, the accumulated + values U and V are initialized to U_1 and V_1 (if the target + index were even, U and V would be initialized instead to U_0=0 + and V_0=2). The values of U_2m and V_2m are also initialized to + U_1 and V_1; the FOR loop calculates in succession U_2 and V_2, + U_4 and V_4, U_8 and V_8, etc. If the corresponding bits + (1, 2, 3, ...) of t are on (the zero bit having been accounted + for in the initialization of U and V), these values are then + combined with the previous totals for U and V, using the + composition formulas for addition of indices. */ + + mp_set(&Uz, 1uL); /* U=U_1 */ + mp_set(&Vz, (mp_digit)P); /* V=V_1 */ + mp_set(&U2mz, 1uL); /* U_1 */ + mp_set(&V2mz, (mp_digit)P); /* V_1 */ + + mp_set_i32(&Qmz, Q); + if ((err = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) goto LBL_LS_ERR; + /* Initializes calculation of Q^d */ + mp_set_i32(&Qkdz, Q); + + Nbits = mp_count_bits(&Dz); + + for (u = 1; u < Nbits; u++) { /* zero bit off, already accounted for */ + /* Formulas for doubling of indices (carried out mod N). Note that + * the indices denoted as "2m" are actually powers of 2, specifically + * 2^(ul-1) beginning each loop and 2^ul ending each loop. + * + * U_2m = U_m*V_m + * V_2m = V_m*V_m - 2*Q^m + */ + + if ((err = mp_mul(&U2mz, &V2mz, &U2mz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&U2mz, a, &U2mz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_sqr(&V2mz, &V2mz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_sub(&V2mz, &Q2mz, &V2mz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&V2mz, a, &V2mz)) != MP_OKAY) goto LBL_LS_ERR; + + /* Must calculate powers of Q for use in V_2m, also for Q^d later */ + if ((err = mp_sqr(&Qmz, &Qmz)) != MP_OKAY) goto LBL_LS_ERR; + + /* prevents overflow */ /* CZ still necessary without a fixed prealloc'd mem.? */ + if ((err = mp_mod(&Qmz, a, &Qmz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) goto LBL_LS_ERR; + + if (s_mp_get_bit(&Dz, (unsigned int)u) == MP_YES) { + /* Formulas for addition of indices (carried out mod N); + * + * U_(m+n) = (U_m*V_n + U_n*V_m)/2 + * V_(m+n) = (V_m*V_n + D*U_m*U_n)/2 + * + * Be careful with division by 2 (mod N)! + */ + if ((err = mp_mul(&U2mz, &Vz, &T1z)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mul(&Uz, &V2mz, &T2z)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mul(&V2mz, &Vz, &T3z)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mul(&U2mz, &Uz, &T4z)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = s_mp_mul_si(&T4z, Ds, &T4z)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_add(&T1z, &T2z, &Uz)) != MP_OKAY) goto LBL_LS_ERR; + if (MP_IS_ODD(&Uz)) { + if ((err = mp_add(&Uz, a, &Uz)) != MP_OKAY) goto LBL_LS_ERR; + } + /* CZ + * This should round towards negative infinity because + * Thomas R. Nicely used GMP's mpz_fdiv_q_2exp(). + * But mp_div_2() does not do so, it is truncating instead. + */ + oddness = MP_IS_ODD(&Uz) ? MP_YES : MP_NO; + if ((err = mp_div_2(&Uz, &Uz)) != MP_OKAY) goto LBL_LS_ERR; + if ((Uz.sign == MP_NEG) && (oddness != MP_NO)) { + if ((err = mp_sub_d(&Uz, 1uL, &Uz)) != MP_OKAY) goto LBL_LS_ERR; + } + if ((err = mp_add(&T3z, &T4z, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + if (MP_IS_ODD(&Vz)) { + if ((err = mp_add(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + } + oddness = MP_IS_ODD(&Vz) ? MP_YES : MP_NO; + if ((err = mp_div_2(&Vz, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + if ((Vz.sign == MP_NEG) && (oddness != MP_NO)) { + if ((err = mp_sub_d(&Vz, 1uL, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + } + if ((err = mp_mod(&Uz, a, &Uz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + + /* Calculating Q^d for later use */ + if ((err = mp_mul(&Qkdz, &Qmz, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR; + } + } + + /* If U_d or V_d is congruent to 0 mod N, then N is a prime or a + strong Lucas pseudoprime. */ + if (MP_IS_ZERO(&Uz) || MP_IS_ZERO(&Vz)) { + *result = MP_YES; + goto LBL_LS_ERR; + } + + /* NOTE: Ribenboim ("The new book of prime number records," 3rd ed., + 1995/6) omits the condition V0 on p.142, but includes it on + p. 130. The condition is NECESSARY; otherwise the test will + return false negatives---e.g., the primes 29 and 2000029 will be + returned as composite. */ + + /* Otherwise, we must compute V_2d, V_4d, V_8d, ..., V_{2^(s-1)*d} + by repeated use of the formula V_2m = V_m*V_m - 2*Q^m. If any of + these are congruent to 0 mod N, then N is a prime or a strong + Lucas pseudoprime. */ + + /* Initialize 2*Q^(d*2^r) for V_2m */ + if ((err = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) goto LBL_LS_ERR; + + for (r = 1; r < s; r++) { + if ((err = mp_sqr(&Vz, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_sub(&Vz, &Q2kdz, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR; + if (MP_IS_ZERO(&Vz)) { + *result = MP_YES; + goto LBL_LS_ERR; + } + /* Calculate Q^{d*2^r} for next r (final iteration irrelevant). */ + if (r < (s - 1)) { + if ((err = mp_sqr(&Qkdz, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR; + if ((err = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) goto LBL_LS_ERR; + } + } +LBL_LS_ERR: + mp_clear_multi(&Q2kdz, &T4z, &T3z, &T2z, &T1z, &Qkdz, &Q2mz, &Qmz, &V2mz, &U2mz, &Vz, &Uz, &Np1, &gcd, &Dz, NULL); + return err; +} +#endif +#endif +#endif + +/* End: bn_mp_prime_strong_lucas_selfridge.c */ + +/* Start: bn_mp_radix_size.c */ +#include "tommath_private.h" +#ifdef BN_MP_RADIX_SIZE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* returns size of ASCII representation */ +mp_err mp_radix_size(const mp_int *a, int radix, int *size) +{ + mp_err err; + int digs; + mp_int t; + mp_digit d; + + *size = 0; + + /* make sure the radix is in range */ + if ((radix < 2) || (radix > 64)) { + return MP_VAL; + } + + if (MP_IS_ZERO(a)) { + *size = 2; + return MP_OKAY; + } + + /* special case for binary */ + if (radix == 2) { + *size = (mp_count_bits(a) + ((a->sign == MP_NEG) ? 1 : 0) + 1); + return MP_OKAY; + } + + /* digs is the digit count */ + digs = 0; + + /* if it's negative add one for the sign */ + if (a->sign == MP_NEG) { + ++digs; + } + + /* init a copy of the input */ + if ((err = mp_init_copy(&t, a)) != MP_OKAY) { + return err; + } + + /* force temp to positive */ + t.sign = MP_ZPOS; + + /* fetch out all of the digits */ + while (!MP_IS_ZERO(&t)) { + if ((err = mp_div_d(&t, (mp_digit)radix, &t, &d)) != MP_OKAY) { + goto LBL_ERR; + } + ++digs; + } + + /* return digs + 1, the 1 is for the NULL byte that would be required. */ + *size = digs + 1; + err = MP_OKAY; + +LBL_ERR: + mp_clear(&t); + return err; +} + +#endif + +/* End: bn_mp_radix_size.c */ + +/* Start: bn_mp_radix_smap.c */ +#include "tommath_private.h" +#ifdef BN_MP_RADIX_SMAP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* chars used in radix conversions */ +const char *const mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; +const uint8_t mp_s_rmap_reverse[] = { + 0xff, 0xff, 0xff, 0x3e, 0xff, 0xff, 0xff, 0x3f, /* ()*+,-./ */ + 0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, /* 01234567 */ + 0x08, 0x09, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, /* 89:;<=>? */ + 0xff, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, /* @ABCDEFG */ + 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, /* HIJKLMNO */ + 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x20, /* PQRSTUVW */ + 0x21, 0x22, 0x23, 0xff, 0xff, 0xff, 0xff, 0xff, /* XYZ[\]^_ */ + 0xff, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, /* `abcdefg */ + 0x2b, 0x2c, 0x2d, 0x2e, 0x2f, 0x30, 0x31, 0x32, /* hijklmno */ + 0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x3a, /* pqrstuvw */ + 0x3b, 0x3c, 0x3d, 0xff, 0xff, 0xff, 0xff, 0xff, /* xyz{|}~. */ +}; +const size_t mp_s_rmap_reverse_sz = sizeof(mp_s_rmap_reverse); +#endif + +/* End: bn_mp_radix_smap.c */ + +/* Start: bn_mp_rand.c */ +#include "tommath_private.h" +#ifdef BN_MP_RAND_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +mp_err(*s_mp_rand_source)(void *out, size_t size) = s_mp_rand_platform; + +void mp_rand_source(mp_err(*source)(void *out, size_t size)) +{ + s_mp_rand_source = (source == NULL) ? s_mp_rand_platform : source; +} + +mp_err mp_rand(mp_int *a, int digits) +{ + int i; + mp_err err; + + mp_zero(a); + + if (digits <= 0) { + return MP_OKAY; + } + + if ((err = mp_grow(a, digits)) != MP_OKAY) { + return err; + } + + if ((err = s_mp_rand_source(a->dp, (size_t)digits * sizeof(mp_digit))) != MP_OKAY) { + return err; + } + + /* TODO: We ensure that the highest digit is nonzero. Should this be removed? */ + while ((a->dp[digits - 1] & MP_MASK) == 0u) { + if ((err = s_mp_rand_source(a->dp + digits - 1, sizeof(mp_digit))) != MP_OKAY) { + return err; + } + } + + a->used = digits; + for (i = 0; i < digits; ++i) { + a->dp[i] &= MP_MASK; + } + + return MP_OKAY; +} +#endif + +/* End: bn_mp_rand.c */ + +/* Start: bn_mp_read_radix.c */ +#include "tommath_private.h" +#ifdef BN_MP_READ_RADIX_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#define MP_TOUPPER(c) ((((c) >= 'a') && ((c) <= 'z')) ? (((c) + 'A') - 'a') : (c)) + +/* read a string [ASCII] in a given radix */ +mp_err mp_read_radix(mp_int *a, const char *str, int radix) +{ + mp_err err; + int y; + mp_sign neg; + unsigned pos; + char ch; + + /* zero the digit bignum */ + mp_zero(a); + + /* make sure the radix is ok */ + if ((radix < 2) || (radix > 64)) { + return MP_VAL; + } + + /* if the leading digit is a + * minus set the sign to negative. + */ + if (*str == '-') { + ++str; + neg = MP_NEG; + } else { + neg = MP_ZPOS; + } + + /* set the integer to the default of zero */ + mp_zero(a); + + /* process each digit of the string */ + while (*str != '\0') { + /* if the radix <= 36 the conversion is case insensitive + * this allows numbers like 1AB and 1ab to represent the same value + * [e.g. in hex] + */ + ch = (radix <= 36) ? (char)MP_TOUPPER((int)*str) : *str; + pos = (unsigned)(ch - '('); + if (mp_s_rmap_reverse_sz < pos) { + break; + } + y = (int)mp_s_rmap_reverse[pos]; + + /* if the char was found in the map + * and is less than the given radix add it + * to the number, otherwise exit the loop. + */ + if ((y == 0xff) || (y >= radix)) { + break; + } + if ((err = mp_mul_d(a, (mp_digit)radix, a)) != MP_OKAY) { + return err; + } + if ((err = mp_add_d(a, (mp_digit)y, a)) != MP_OKAY) { + return err; + } + ++str; + } + + /* if an illegal character was found, fail. */ + if (!((*str == '\0') || (*str == '\r') || (*str == '\n'))) { + mp_zero(a); + return MP_VAL; + } + + /* set the sign only if a != 0 */ + if (!MP_IS_ZERO(a)) { + a->sign = neg; + } + return MP_OKAY; +} +#endif + +/* End: bn_mp_read_radix.c */ + +/* Start: bn_mp_reduce.c */ +#include "tommath_private.h" +#ifdef BN_MP_REDUCE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* reduces x mod m, assumes 0 < x < m**2, mu is + * precomputed via mp_reduce_setup. + * From HAC pp.604 Algorithm 14.42 + */ +mp_err mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu) +{ + mp_int q; + mp_err err; + int um = m->used; + + /* q = x */ + if ((err = mp_init_copy(&q, x)) != MP_OKAY) { + return err; + } + + /* q1 = x / b**(k-1) */ + mp_rshd(&q, um - 1); + + /* according to HAC this optimization is ok */ + if ((mp_digit)um > ((mp_digit)1 << (MP_DIGIT_BIT - 1))) { + if ((err = mp_mul(&q, mu, &q)) != MP_OKAY) { + goto CLEANUP; + } + } else if (MP_HAS(S_MP_MUL_HIGH_DIGS)) { + if ((err = s_mp_mul_high_digs(&q, mu, &q, um)) != MP_OKAY) { + goto CLEANUP; + } + } else if (MP_HAS(S_MP_MUL_HIGH_DIGS_FAST)) { + if ((err = s_mp_mul_high_digs_fast(&q, mu, &q, um)) != MP_OKAY) { + goto CLEANUP; + } + } else { + err = MP_VAL; + goto CLEANUP; + } + + /* q3 = q2 / b**(k+1) */ + mp_rshd(&q, um + 1); + + /* x = x mod b**(k+1), quick (no division) */ + if ((err = mp_mod_2d(x, MP_DIGIT_BIT * (um + 1), x)) != MP_OKAY) { + goto CLEANUP; + } + + /* q = q * m mod b**(k+1), quick (no division) */ + if ((err = s_mp_mul_digs(&q, m, &q, um + 1)) != MP_OKAY) { + goto CLEANUP; + } + + /* x = x - q */ + if ((err = mp_sub(x, &q, x)) != MP_OKAY) { + goto CLEANUP; + } + + /* If x < 0, add b**(k+1) to it */ + if (mp_cmp_d(x, 0uL) == MP_LT) { + mp_set(&q, 1uL); + if ((err = mp_lshd(&q, um + 1)) != MP_OKAY) { + goto CLEANUP; + } + if ((err = mp_add(x, &q, x)) != MP_OKAY) { + goto CLEANUP; + } + } + + /* Back off if it's too big */ + while (mp_cmp(x, m) != MP_LT) { + if ((err = s_mp_sub(x, m, x)) != MP_OKAY) { + goto CLEANUP; + } + } + +CLEANUP: + mp_clear(&q); + + return err; +} +#endif + +/* End: bn_mp_reduce.c */ + +/* Start: bn_mp_reduce_2k.c */ +#include "tommath_private.h" +#ifdef BN_MP_REDUCE_2K_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* reduces a modulo n where n is of the form 2**p - d */ +mp_err mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d) +{ + mp_int q; + mp_err err; + int p; + + if ((err = mp_init(&q)) != MP_OKAY) { + return err; + } + + p = mp_count_bits(n); +top: + /* q = a/2**p, a = a mod 2**p */ + if ((err = mp_div_2d(a, p, &q, a)) != MP_OKAY) { + goto LBL_ERR; + } + + if (d != 1u) { + /* q = q * d */ + if ((err = mp_mul_d(&q, d, &q)) != MP_OKAY) { + goto LBL_ERR; + } + } + + /* a = a + q */ + if ((err = s_mp_add(a, &q, a)) != MP_OKAY) { + goto LBL_ERR; + } + + if (mp_cmp_mag(a, n) != MP_LT) { + if ((err = s_mp_sub(a, n, a)) != MP_OKAY) { + goto LBL_ERR; + } + goto top; + } + +LBL_ERR: + mp_clear(&q); + return err; +} + +#endif + +/* End: bn_mp_reduce_2k.c */ + +/* Start: bn_mp_reduce_2k_l.c */ +#include "tommath_private.h" +#ifdef BN_MP_REDUCE_2K_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* reduces a modulo n where n is of the form 2**p - d + This differs from reduce_2k since "d" can be larger + than a single digit. +*/ +mp_err mp_reduce_2k_l(mp_int *a, const mp_int *n, const mp_int *d) +{ + mp_int q; + mp_err err; + int p; + + if ((err = mp_init(&q)) != MP_OKAY) { + return err; + } + + p = mp_count_bits(n); +top: + /* q = a/2**p, a = a mod 2**p */ + if ((err = mp_div_2d(a, p, &q, a)) != MP_OKAY) { + goto LBL_ERR; + } + + /* q = q * d */ + if ((err = mp_mul(&q, d, &q)) != MP_OKAY) { + goto LBL_ERR; + } + + /* a = a + q */ + if ((err = s_mp_add(a, &q, a)) != MP_OKAY) { + goto LBL_ERR; + } + + if (mp_cmp_mag(a, n) != MP_LT) { + if ((err = s_mp_sub(a, n, a)) != MP_OKAY) { + goto LBL_ERR; + } + goto top; + } + +LBL_ERR: + mp_clear(&q); + return err; +} + +#endif + +/* End: bn_mp_reduce_2k_l.c */ + +/* Start: bn_mp_reduce_2k_setup.c */ +#include "tommath_private.h" +#ifdef BN_MP_REDUCE_2K_SETUP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* determines the setup value */ +mp_err mp_reduce_2k_setup(const mp_int *a, mp_digit *d) +{ + mp_err err; + mp_int tmp; + int p; + + if ((err = mp_init(&tmp)) != MP_OKAY) { + return err; + } + + p = mp_count_bits(a); + if ((err = mp_2expt(&tmp, p)) != MP_OKAY) { + mp_clear(&tmp); + return err; + } + + if ((err = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) { + mp_clear(&tmp); + return err; + } + + *d = tmp.dp[0]; + mp_clear(&tmp); + return MP_OKAY; +} +#endif + +/* End: bn_mp_reduce_2k_setup.c */ + +/* Start: bn_mp_reduce_2k_setup_l.c */ +#include "tommath_private.h" +#ifdef BN_MP_REDUCE_2K_SETUP_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* determines the setup value */ +mp_err mp_reduce_2k_setup_l(const mp_int *a, mp_int *d) +{ + mp_err err; + mp_int tmp; + + if ((err = mp_init(&tmp)) != MP_OKAY) { + return err; + } + + if ((err = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) { + goto LBL_ERR; + } + + if ((err = s_mp_sub(&tmp, a, d)) != MP_OKAY) { + goto LBL_ERR; + } + +LBL_ERR: + mp_clear(&tmp); + return err; +} +#endif + +/* End: bn_mp_reduce_2k_setup_l.c */ + +/* Start: bn_mp_reduce_is_2k.c */ +#include "tommath_private.h" +#ifdef BN_MP_REDUCE_IS_2K_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* determines if mp_reduce_2k can be used */ +mp_bool mp_reduce_is_2k(const mp_int *a) +{ + int ix, iy, iw; + mp_digit iz; + + if (a->used == 0) { + return MP_NO; + } else if (a->used == 1) { + return MP_YES; + } else if (a->used > 1) { + iy = mp_count_bits(a); + iz = 1; + iw = 1; + + /* Test every bit from the second digit up, must be 1 */ + for (ix = MP_DIGIT_BIT; ix < iy; ix++) { + if ((a->dp[iw] & iz) == 0u) { + return MP_NO; + } + iz <<= 1; + if (iz > MP_DIGIT_MAX) { + ++iw; + iz = 1; + } + } + return MP_YES; + } else { + return MP_YES; + } +} + +#endif + +/* End: bn_mp_reduce_is_2k.c */ + +/* Start: bn_mp_reduce_is_2k_l.c */ +#include "tommath_private.h" +#ifdef BN_MP_REDUCE_IS_2K_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* determines if reduce_2k_l can be used */ +mp_bool mp_reduce_is_2k_l(const mp_int *a) +{ + int ix, iy; + + if (a->used == 0) { + return MP_NO; + } else if (a->used == 1) { + return MP_YES; + } else if (a->used > 1) { + /* if more than half of the digits are -1 we're sold */ + for (iy = ix = 0; ix < a->used; ix++) { + if (a->dp[ix] == MP_DIGIT_MAX) { + ++iy; + } + } + return (iy >= (a->used/2)) ? MP_YES : MP_NO; + } else { + return MP_NO; + } +} + +#endif + +/* End: bn_mp_reduce_is_2k_l.c */ + +/* Start: bn_mp_reduce_setup.c */ +#include "tommath_private.h" +#ifdef BN_MP_REDUCE_SETUP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* pre-calculate the value required for Barrett reduction + * For a given modulus "b" it calulates the value required in "a" + */ +mp_err mp_reduce_setup(mp_int *a, const mp_int *b) +{ + mp_err err; + if ((err = mp_2expt(a, b->used * 2 * MP_DIGIT_BIT)) != MP_OKAY) { + return err; + } + return mp_div(a, b, a, NULL); +} +#endif + +/* End: bn_mp_reduce_setup.c */ + +/* Start: bn_mp_root_u32.c */ +#include "tommath_private.h" +#ifdef BN_MP_ROOT_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* 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. + */ +mp_err mp_root_u32(const mp_int *a, uint32_t b, mp_int *c) +{ + mp_int t1, t2, t3, a_; + mp_ord cmp; + int ilog2; + mp_err err; + + /* input must be positive if b is even */ + if (((b & 1u) == 0u) && (a->sign == MP_NEG)) { + return MP_VAL; + } + + if ((err = mp_init_multi(&t1, &t2, &t3, NULL)) != MP_OKAY) { + return err; + } + + /* if a is negative fudge the sign but keep track */ + a_ = *a; + a_.sign = MP_ZPOS; + + /* Compute seed: 2^(log_2(n)/b + 2)*/ + ilog2 = mp_count_bits(a); + + /* + If "b" is larger than INT_MAX it is also larger than + log_2(n) because the bit-length of the "n" is measured + with an int and hence the root is always < 2 (two). + */ + if (b > (uint32_t)(INT_MAX/2)) { + mp_set(c, 1uL); + c->sign = a->sign; + err = MP_OKAY; + goto LBL_ERR; + } + + /* "b" is smaller than INT_MAX, we can cast safely */ + if (ilog2 < (int)b) { + mp_set(c, 1uL); + c->sign = a->sign; + err = MP_OKAY; + goto LBL_ERR; + } + ilog2 = ilog2 / ((int)b); + if (ilog2 == 0) { + mp_set(c, 1uL); + c->sign = a->sign; + err = MP_OKAY; + goto LBL_ERR; + } + /* Start value must be larger than root */ + ilog2 += 2; + if ((err = mp_2expt(&t2,ilog2)) != MP_OKAY) goto LBL_ERR; + do { + /* t1 = t2 */ + if ((err = mp_copy(&t2, &t1)) != MP_OKAY) goto LBL_ERR; + + /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */ + + /* t3 = t1**(b-1) */ + if ((err = mp_expt_u32(&t1, b - 1u, &t3)) != MP_OKAY) goto LBL_ERR; + + /* numerator */ + /* t2 = t1**b */ + if ((err = mp_mul(&t3, &t1, &t2)) != MP_OKAY) goto LBL_ERR; + + /* t2 = t1**b - a */ + if ((err = mp_sub(&t2, &a_, &t2)) != MP_OKAY) goto LBL_ERR; + + /* denominator */ + /* t3 = t1**(b-1) * b */ + if ((err = mp_mul_d(&t3, b, &t3)) != MP_OKAY) goto LBL_ERR; + + /* t3 = (t1**b - a)/(b * t1**(b-1)) */ + if ((err = mp_div(&t2, &t3, &t3, NULL)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&t1, &t3, &t2)) != MP_OKAY) goto LBL_ERR; + + /* + Number of rounds is at most log_2(root). If it is more it + got stuck, so break out of the loop and do the rest manually. + */ + if (ilog2-- == 0) { + break; + } + } while (mp_cmp(&t1, &t2) != MP_EQ); + + /* result can be off by a few so check */ + /* Loop beneath can overshoot by one if found root is smaller than actual root */ + for (;;) { + if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR; + cmp = mp_cmp(&t2, &a_); + if (cmp == MP_EQ) { + err = MP_OKAY; + goto LBL_ERR; + } + if (cmp == MP_LT) { + if ((err = mp_add_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR; + } else { + break; + } + } + /* correct overshoot from above or from recurrence */ + for (;;) { + if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR; + if (mp_cmp(&t2, &a_) == MP_GT) { + if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR; + } else { + break; + } + } + + /* set the result */ + mp_exch(&t1, c); + + /* set the sign of the result */ + c->sign = a->sign; + + err = MP_OKAY; + +LBL_ERR: + mp_clear_multi(&t1, &t2, &t3, NULL); + return err; +} + +#endif + +/* End: bn_mp_root_u32.c */ + +/* Start: bn_mp_rshd.c */ +#include "tommath_private.h" +#ifdef BN_MP_RSHD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* shift right a certain amount of digits */ +void mp_rshd(mp_int *a, int b) +{ + int x; + mp_digit *bottom, *top; + + /* if b <= 0 then ignore it */ + if (b <= 0) { + return; + } + + /* if b > used then simply zero it and return */ + if (a->used <= b) { + mp_zero(a); + return; + } + + /* shift the digits down */ + + /* bottom */ + bottom = a->dp; + + /* top [offset into digits] */ + top = a->dp + b; + + /* this is implemented as a sliding window where + * the window is b-digits long and digits from + * the top of the window are copied to the bottom + * + * e.g. + + b-2 | b-1 | b0 | b1 | b2 | ... | bb | ----> + /\ | ----> + \-------------------/ ----> + */ + for (x = 0; x < (a->used - b); x++) { + *bottom++ = *top++; + } + + /* zero the top digits */ + MP_ZERO_DIGITS(bottom, a->used - x); + + /* remove excess digits */ + a->used -= b; +} +#endif + +/* End: bn_mp_rshd.c */ + +/* Start: bn_mp_sbin_size.c */ +#include "tommath_private.h" +#ifdef BN_MP_SBIN_SIZE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* get the size for an signed equivalent */ +size_t mp_sbin_size(const mp_int *a) +{ + return 1u + mp_ubin_size(a); +} +#endif + +/* End: bn_mp_sbin_size.c */ + +/* Start: bn_mp_set.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* set to a digit */ +void mp_set(mp_int *a, mp_digit b) +{ + a->dp[0] = b & MP_MASK; + a->sign = MP_ZPOS; + a->used = (a->dp[0] != 0u) ? 1 : 0; + MP_ZERO_DIGITS(a->dp + a->used, a->alloc - a->used); +} +#endif + +/* End: bn_mp_set.c */ + +/* Start: bn_mp_set_double.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_DOUBLE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#if defined(__STDC_IEC_559__) || defined(__GCC_IEC_559) +mp_err mp_set_double(mp_int *a, double b) +{ + uint64_t frac; + int exp; + mp_err err; + union { + double dbl; + uint64_t bits; + } cast; + cast.dbl = b; + + exp = (int)((unsigned)(cast.bits >> 52) & 0x7FFu); + frac = (cast.bits & ((1uLL << 52) - 1uLL)) | (1uLL << 52); + + if (exp == 0x7FF) { /* +-inf, NaN */ + return MP_VAL; + } + exp -= 1023 + 52; + + mp_set_u64(a, frac); + + err = (exp < 0) ? mp_div_2d(a, -exp, a, NULL) : mp_mul_2d(a, exp, a); + if (err != MP_OKAY) { + return err; + } + + if (((cast.bits >> 63) != 0uLL) && !MP_IS_ZERO(a)) { + a->sign = MP_NEG; + } + + return MP_OKAY; +} +#else +/* pragma message() not supported by several compilers (in mostly older but still used versions) */ +# ifdef _MSC_VER +# pragma message("mp_set_double implementation is only available on platforms with IEEE754 floating point format") +# else +# warning "mp_set_double implementation is only available on platforms with IEEE754 floating point format" +# endif +#endif +#endif + +/* End: bn_mp_set_double.c */ + +/* Start: bn_mp_set_i32.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_I32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_SIGNED(mp_set_i32, mp_set_u32, int32_t, uint32_t) +#endif + +/* End: bn_mp_set_i32.c */ + +/* Start: bn_mp_set_i64.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_I64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_SIGNED(mp_set_i64, mp_set_u64, int64_t, uint64_t) +#endif + +/* End: bn_mp_set_i64.c */ + +/* Start: bn_mp_set_l.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_SIGNED(mp_set_l, mp_set_ul, long, unsigned long) +#endif + +/* End: bn_mp_set_l.c */ + +/* Start: bn_mp_set_ll.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_LL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_SIGNED(mp_set_ll, mp_set_ull, long long, unsigned long long) +#endif + +/* End: bn_mp_set_ll.c */ + +/* Start: bn_mp_set_u32.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_U32_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_UNSIGNED(mp_set_u32, uint32_t) +#endif + +/* End: bn_mp_set_u32.c */ + +/* Start: bn_mp_set_u64.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_U64_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_UNSIGNED(mp_set_u64, uint64_t) +#endif + +/* End: bn_mp_set_u64.c */ + +/* Start: bn_mp_set_ul.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_UL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_UNSIGNED(mp_set_ul, unsigned long) +#endif + +/* End: bn_mp_set_ul.c */ + +/* Start: bn_mp_set_ull.c */ +#include "tommath_private.h" +#ifdef BN_MP_SET_ULL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +MP_SET_UNSIGNED(mp_set_ull, unsigned long long) +#endif + +/* End: bn_mp_set_ull.c */ + +/* Start: bn_mp_shrink.c */ +#include "tommath_private.h" +#ifdef BN_MP_SHRINK_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* shrink a bignum */ +mp_err mp_shrink(mp_int *a) +{ + mp_digit *tmp; + int alloc = MP_MAX(MP_MIN_PREC, a->used); + if (a->alloc != alloc) { + if ((tmp = (mp_digit *) MP_REALLOC(a->dp, + (size_t)a->alloc * sizeof(mp_digit), + (size_t)alloc * sizeof(mp_digit))) == NULL) { + return MP_MEM; + } + a->dp = tmp; + a->alloc = alloc; + } + return MP_OKAY; +} +#endif + +/* End: bn_mp_shrink.c */ + +/* Start: bn_mp_signed_rsh.c */ +#include "tommath_private.h" +#ifdef BN_MP_SIGNED_RSH_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* shift right by a certain bit count with sign extension */ +mp_err mp_signed_rsh(const mp_int *a, int b, mp_int *c) +{ + mp_err res; + if (a->sign == MP_ZPOS) { + return mp_div_2d(a, b, c, NULL); + } + + res = mp_add_d(a, 1uL, c); + if (res != MP_OKAY) { + return res; + } + + res = mp_div_2d(c, b, c, NULL); + return (res == MP_OKAY) ? mp_sub_d(c, 1uL, c) : res; +} +#endif + +/* End: bn_mp_signed_rsh.c */ + +/* Start: bn_mp_sqr.c */ +#include "tommath_private.h" +#ifdef BN_MP_SQR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* computes b = a*a */ +mp_err mp_sqr(const mp_int *a, mp_int *b) +{ + mp_err err; + if (MP_HAS(S_MP_TOOM_SQR) && /* use Toom-Cook? */ + (a->used >= MP_TOOM_SQR_CUTOFF)) { + err = s_mp_toom_sqr(a, b); + } else if (MP_HAS(S_MP_KARATSUBA_SQR) && /* Karatsuba? */ + (a->used >= MP_KARATSUBA_SQR_CUTOFF)) { + err = s_mp_karatsuba_sqr(a, b); + } else if (MP_HAS(S_MP_SQR_FAST) && /* can we use the fast comba multiplier? */ + (((a->used * 2) + 1) < MP_WARRAY) && + (a->used < (MP_MAXFAST / 2))) { + err = s_mp_sqr_fast(a, b); + } else if (MP_HAS(S_MP_SQR)) { + err = s_mp_sqr(a, b); + } else { + err = MP_VAL; + } + b->sign = MP_ZPOS; + return err; +} +#endif + +/* End: bn_mp_sqr.c */ + +/* Start: bn_mp_sqrmod.c */ +#include "tommath_private.h" +#ifdef BN_MP_SQRMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* c = a * a (mod b) */ +mp_err mp_sqrmod(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_err err; + mp_int t; + + if ((err = mp_init(&t)) != MP_OKAY) { + return err; + } + + if ((err = mp_sqr(a, &t)) != MP_OKAY) { + goto LBL_ERR; + } + err = mp_mod(&t, b, c); + +LBL_ERR: + mp_clear(&t); + return err; +} +#endif + +/* End: bn_mp_sqrmod.c */ + +/* Start: bn_mp_sqrt.c */ +#include "tommath_private.h" +#ifdef BN_MP_SQRT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* this function is less generic than mp_n_root, simpler and faster */ +mp_err mp_sqrt(const mp_int *arg, mp_int *ret) +{ + mp_err err; + mp_int t1, t2; + + /* must be positive */ + if (arg->sign == MP_NEG) { + return MP_VAL; + } + + /* easy out */ + if (MP_IS_ZERO(arg)) { + mp_zero(ret); + return MP_OKAY; + } + + if ((err = mp_init_copy(&t1, arg)) != MP_OKAY) { + return err; + } + + if ((err = mp_init(&t2)) != MP_OKAY) { + goto E2; + } + + /* First approx. (not very bad for large arg) */ + mp_rshd(&t1, t1.used/2); + + /* t1 > 0 */ + if ((err = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) { + goto E1; + } + if ((err = mp_add(&t1, &t2, &t1)) != MP_OKAY) { + goto E1; + } + if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) { + goto E1; + } + /* And now t1 > sqrt(arg) */ + do { + if ((err = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) { + goto E1; + } + if ((err = mp_add(&t1, &t2, &t1)) != MP_OKAY) { + goto E1; + } + if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) { + goto E1; + } + /* t1 >= sqrt(arg) >= t2 at this point */ + } while (mp_cmp_mag(&t1, &t2) == MP_GT); + + mp_exch(&t1, ret); + +E1: + mp_clear(&t2); +E2: + mp_clear(&t1); + return err; +} + +#endif + +/* End: bn_mp_sqrt.c */ + +/* Start: bn_mp_sqrtmod_prime.c */ +#include "tommath_private.h" +#ifdef BN_MP_SQRTMOD_PRIME_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Tonelli-Shanks algorithm + * https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm + * https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html + * + */ + +mp_err mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret) +{ + mp_err err; + int legendre; + mp_int t1, C, Q, S, Z, M, T, R, two; + mp_digit i; + + /* first handle the simple cases */ + if (mp_cmp_d(n, 0uL) == MP_EQ) { + mp_zero(ret); + return MP_OKAY; + } + if (mp_cmp_d(prime, 2uL) == MP_EQ) return MP_VAL; /* prime must be odd */ + if ((err = mp_kronecker(n, prime, &legendre)) != MP_OKAY) return err; + if (legendre == -1) return MP_VAL; /* quadratic non-residue mod prime */ + + if ((err = mp_init_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL)) != MP_OKAY) { + return err; + } + + /* SPECIAL CASE: if prime mod 4 == 3 + * compute directly: err = n^(prime+1)/4 mod prime + * Handbook of Applied Cryptography algorithm 3.36 + */ + if ((err = mp_mod_d(prime, 4uL, &i)) != MP_OKAY) goto cleanup; + if (i == 3u) { + if ((err = mp_add_d(prime, 1uL, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_exptmod(n, &t1, prime, ret)) != MP_OKAY) goto cleanup; + err = MP_OKAY; + goto cleanup; + } + + /* NOW: Tonelli-Shanks algorithm */ + + /* factor out powers of 2 from prime-1, defining Q and S as: prime-1 = Q*2^S */ + if ((err = mp_copy(prime, &Q)) != MP_OKAY) goto cleanup; + if ((err = mp_sub_d(&Q, 1uL, &Q)) != MP_OKAY) goto cleanup; + /* Q = prime - 1 */ + mp_zero(&S); + /* S = 0 */ + while (MP_IS_EVEN(&Q)) { + if ((err = mp_div_2(&Q, &Q)) != MP_OKAY) goto cleanup; + /* Q = Q / 2 */ + if ((err = mp_add_d(&S, 1uL, &S)) != MP_OKAY) goto cleanup; + /* S = S + 1 */ + } + + /* find a Z such that the Legendre symbol (Z|prime) == -1 */ + mp_set_u32(&Z, 2u); + /* Z = 2 */ + for (;;) { + if ((err = mp_kronecker(&Z, prime, &legendre)) != MP_OKAY) goto cleanup; + if (legendre == -1) break; + if ((err = mp_add_d(&Z, 1uL, &Z)) != MP_OKAY) goto cleanup; + /* Z = Z + 1 */ + } + + if ((err = mp_exptmod(&Z, &Q, prime, &C)) != MP_OKAY) goto cleanup; + /* C = Z ^ Q mod prime */ + if ((err = mp_add_d(&Q, 1uL, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup; + /* t1 = (Q + 1) / 2 */ + if ((err = mp_exptmod(n, &t1, prime, &R)) != MP_OKAY) goto cleanup; + /* R = n ^ ((Q + 1) / 2) mod prime */ + if ((err = mp_exptmod(n, &Q, prime, &T)) != MP_OKAY) goto cleanup; + /* T = n ^ Q mod prime */ + if ((err = mp_copy(&S, &M)) != MP_OKAY) goto cleanup; + /* M = S */ + mp_set_u32(&two, 2u); + + for (;;) { + if ((err = mp_copy(&T, &t1)) != MP_OKAY) goto cleanup; + i = 0; + for (;;) { + if (mp_cmp_d(&t1, 1uL) == MP_EQ) break; + if ((err = mp_exptmod(&t1, &two, prime, &t1)) != MP_OKAY) goto cleanup; + i++; + } + if (i == 0u) { + if ((err = mp_copy(&R, ret)) != MP_OKAY) goto cleanup; + err = MP_OKAY; + goto cleanup; + } + if ((err = mp_sub_d(&M, i, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto cleanup; + if ((err = mp_exptmod(&two, &t1, prime, &t1)) != MP_OKAY) goto cleanup; + /* t1 = 2 ^ (M - i - 1) */ + if ((err = mp_exptmod(&C, &t1, prime, &t1)) != MP_OKAY) goto cleanup; + /* t1 = C ^ (2 ^ (M - i - 1)) mod prime */ + if ((err = mp_sqrmod(&t1, prime, &C)) != MP_OKAY) goto cleanup; + /* C = (t1 * t1) mod prime */ + if ((err = mp_mulmod(&R, &t1, prime, &R)) != MP_OKAY) goto cleanup; + /* R = (R * t1) mod prime */ + if ((err = mp_mulmod(&T, &C, prime, &T)) != MP_OKAY) goto cleanup; + /* T = (T * C) mod prime */ + mp_set(&M, i); + /* M = i */ + } + +cleanup: + mp_clear_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL); + return err; +} + +#endif + +/* End: bn_mp_sqrtmod_prime.c */ + +/* Start: bn_mp_sub.c */ +#include "tommath_private.h" +#ifdef BN_MP_SUB_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* high level subtraction (handles signs) */ +mp_err mp_sub(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_sign sa = a->sign, sb = b->sign; + mp_err err; + + if (sa != sb) { + /* subtract a negative from a positive, OR */ + /* subtract a positive from a negative. */ + /* In either case, ADD their magnitudes, */ + /* and use the sign of the first number. */ + c->sign = sa; + err = s_mp_add(a, b, c); + } else { + /* subtract a positive from a positive, OR */ + /* subtract a negative from a negative. */ + /* First, take the difference between their */ + /* magnitudes, then... */ + if (mp_cmp_mag(a, b) != MP_LT) { + /* Copy the sign from the first */ + c->sign = sa; + /* The first has a larger or equal magnitude */ + err = s_mp_sub(a, b, c); + } else { + /* The result has the *opposite* sign from */ + /* the first number. */ + c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS; + /* The second has a larger magnitude */ + err = s_mp_sub(b, a, c); + } + } + return err; +} + +#endif + +/* End: bn_mp_sub.c */ + +/* Start: bn_mp_sub_d.c */ +#include "tommath_private.h" +#ifdef BN_MP_SUB_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* single digit subtraction */ +mp_err mp_sub_d(const mp_int *a, mp_digit b, mp_int *c) +{ + mp_digit *tmpa, *tmpc; + mp_err err; + int ix, oldused; + + /* grow c as required */ + if (c->alloc < (a->used + 1)) { + if ((err = mp_grow(c, a->used + 1)) != MP_OKAY) { + return err; + } + } + + /* if a is negative just do an unsigned + * addition [with fudged signs] + */ + if (a->sign == MP_NEG) { + mp_int a_ = *a; + a_.sign = MP_ZPOS; + err = mp_add_d(&a_, b, c); + c->sign = MP_NEG; + + /* clamp */ + mp_clamp(c); + + return err; + } + + /* setup regs */ + oldused = c->used; + tmpa = a->dp; + tmpc = c->dp; + + /* if a <= b simply fix the single digit */ + if (((a->used == 1) && (a->dp[0] <= b)) || (a->used == 0)) { + if (a->used == 1) { + *tmpc++ = b - *tmpa; + } else { + *tmpc++ = b; + } + ix = 1; + + /* negative/1digit */ + c->sign = MP_NEG; + c->used = 1; + } else { + mp_digit mu = b; + + /* positive/size */ + c->sign = MP_ZPOS; + c->used = a->used; + + /* subtract digits, mu is carry */ + for (ix = 0; ix < a->used; ix++) { + *tmpc = *tmpa++ - mu; + mu = *tmpc >> (MP_SIZEOF_BITS(mp_digit) - 1u); + *tmpc++ &= MP_MASK; + } + } + + /* zero excess digits */ + MP_ZERO_DIGITS(tmpc, oldused - ix); + + mp_clamp(c); + return MP_OKAY; +} + +#endif + +/* End: bn_mp_sub_d.c */ + +/* Start: bn_mp_submod.c */ +#include "tommath_private.h" +#ifdef BN_MP_SUBMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* d = a - b (mod c) */ +mp_err mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d) +{ + mp_err err; + mp_int t; + + if ((err = mp_init(&t)) != MP_OKAY) { + return err; + } + + if ((err = mp_sub(a, b, &t)) != MP_OKAY) { + goto LBL_ERR; + } + err = mp_mod(&t, c, d); + +LBL_ERR: + mp_clear(&t); + return err; +} +#endif + +/* End: bn_mp_submod.c */ + +/* Start: bn_mp_to_radix.c */ +#include "tommath_private.h" +#ifdef BN_MP_TO_RADIX_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* stores a bignum as a ASCII string in a given radix (2..64) + * + * Stores upto "size - 1" chars and always a NULL byte, puts the number of characters + * written, including the '\0', in "written". + */ +mp_err mp_to_radix(const mp_int *a, char *str, size_t maxlen, size_t *written, int radix) +{ + size_t digs; + mp_err err; + mp_int t; + mp_digit d; + char *_s = str; + + /* check range of radix and size*/ + if (maxlen < 2u) { + return MP_BUF; + } + if ((radix < 2) || (radix > 64)) { + return MP_VAL; + } + + /* quick out if its zero */ + if (MP_IS_ZERO(a)) { + *str++ = '0'; + *str = '\0'; + if (written != NULL) { + *written = 2u; + } + return MP_OKAY; + } + + if ((err = mp_init_copy(&t, a)) != MP_OKAY) { + return err; + } + + /* if it is negative output a - */ + if (t.sign == MP_NEG) { + /* we have to reverse our digits later... but not the - sign!! */ + ++_s; + + /* store the flag and mark the number as positive */ + *str++ = '-'; + t.sign = MP_ZPOS; + + /* subtract a char */ + --maxlen; + } + digs = 0u; + while (!MP_IS_ZERO(&t)) { + if (--maxlen < 1u) { + /* no more room */ + err = MP_BUF; + goto LBL_ERR; + } + if ((err = mp_div_d(&t, (mp_digit)radix, &t, &d)) != MP_OKAY) { + goto LBL_ERR; + } + *str++ = mp_s_rmap[d]; + ++digs; + } + /* reverse the digits of the string. In this case _s points + * to the first digit [exluding the sign] of the number + */ + s_mp_reverse((unsigned char *)_s, digs); + + /* append a NULL so the string is properly terminated */ + *str = '\0'; + digs++; + + if (written != NULL) { + *written = (a->sign == MP_NEG) ? (digs + 1u): digs; + } + +LBL_ERR: + mp_clear(&t); + return err; +} + +#endif + +/* End: bn_mp_to_radix.c */ + +/* Start: bn_mp_to_sbin.c */ +#include "tommath_private.h" +#ifdef BN_MP_TO_SBIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* store in signed [big endian] format */ +mp_err mp_to_sbin(const mp_int *a, unsigned char *buf, size_t maxlen, size_t *written) +{ + mp_err err; + if (maxlen == 0u) { + return MP_BUF; + } + if ((err = mp_to_ubin(a, buf + 1, maxlen - 1u, written)) != MP_OKAY) { + return err; + } + if (written != NULL) { + (*written)++; + } + buf[0] = (a->sign == MP_ZPOS) ? (unsigned char)0 : (unsigned char)1; + return MP_OKAY; +} +#endif + +/* End: bn_mp_to_sbin.c */ + +/* Start: bn_mp_to_ubin.c */ +#include "tommath_private.h" +#ifdef BN_MP_TO_UBIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* store in unsigned [big endian] format */ +mp_err mp_to_ubin(const mp_int *a, unsigned char *buf, size_t maxlen, size_t *written) +{ + size_t x, count; + mp_err err; + mp_int t; + + count = mp_ubin_size(a); + if (count > maxlen) { + return MP_BUF; + } + + if ((err = mp_init_copy(&t, a)) != MP_OKAY) { + return err; + } + + for (x = count; x --> 0u;) { +#ifndef MP_8BIT + buf[x] = (unsigned char)(t.dp[0] & 255u); +#else + buf[x] = (unsigned char)(t.dp[0] | ((t.dp[1] & 1u) << 7)); +#endif + if ((err = mp_div_2d(&t, 8, &t, NULL)) != MP_OKAY) { + goto LBL_ERR; + } + } + + if (written != NULL) { + *written = count; + } + +LBL_ERR: + mp_clear(&t); + return err; +} +#endif + +/* End: bn_mp_to_ubin.c */ + +/* Start: bn_mp_ubin_size.c */ +#include "tommath_private.h" +#ifdef BN_MP_UBIN_SIZE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* get the size for an unsigned equivalent */ +size_t mp_ubin_size(const mp_int *a) +{ + size_t size = (size_t)mp_count_bits(a); + return (size / 8u) + (((size & 7u) != 0u) ? 1u : 0u); +} +#endif + +/* End: bn_mp_ubin_size.c */ + +/* Start: bn_mp_unpack.c */ +#include "tommath_private.h" +#ifdef BN_MP_UNPACK_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* based on gmp's mpz_import. + * see http://gmplib.org/manual/Integer-Import-and-Export.html + */ +mp_err mp_unpack(mp_int *rop, size_t count, mp_order order, size_t size, + mp_endian endian, size_t nails, const void *op) +{ + mp_err err; + size_t odd_nails, nail_bytes, i, j; + unsigned char odd_nail_mask; + + mp_zero(rop); + + if (endian == MP_NATIVE_ENDIAN) { + MP_GET_ENDIANNESS(endian); + } + + odd_nails = (nails % 8u); + odd_nail_mask = 0xff; + for (i = 0; i < odd_nails; ++i) { + odd_nail_mask ^= (unsigned char)(1u << (7u - i)); + } + nail_bytes = nails / 8u; + + for (i = 0; i < count; ++i) { + for (j = 0; j < (size - nail_bytes); ++j) { + unsigned char byte = *((const unsigned char *)op + + (((order == MP_MSB_FIRST) ? i : ((count - 1u) - i)) * size) + + ((endian == MP_BIG_ENDIAN) ? (j + nail_bytes) : (((size - 1u) - j) - nail_bytes))); + + if ((err = mp_mul_2d(rop, (j == 0u) ? (int)(8u - odd_nails) : 8, rop)) != MP_OKAY) { + return err; + } + + rop->dp[0] |= (j == 0u) ? (mp_digit)(byte & odd_nail_mask) : (mp_digit)byte; + rop->used += 1; + } + } + + mp_clamp(rop); + + return MP_OKAY; +} + +#endif + +/* End: bn_mp_unpack.c */ + +/* Start: bn_mp_xor.c */ +#include "tommath_private.h" +#ifdef BN_MP_XOR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* two complement xor */ +mp_err mp_xor(const mp_int *a, const mp_int *b, mp_int *c) +{ + int used = MP_MAX(a->used, b->used) + 1, i; + mp_err err; + mp_digit ac = 1, bc = 1, cc = 1; + mp_sign csign = (a->sign != b->sign) ? MP_NEG : MP_ZPOS; + + if (c->alloc < used) { + if ((err = mp_grow(c, used)) != MP_OKAY) { + return err; + } + } + + for (i = 0; i < used; i++) { + mp_digit x, y; + + /* convert to two complement if negative */ + if (a->sign == MP_NEG) { + ac += (i >= a->used) ? MP_MASK : (~a->dp[i] & MP_MASK); + x = ac & MP_MASK; + ac >>= MP_DIGIT_BIT; + } else { + x = (i >= a->used) ? 0uL : a->dp[i]; + } + + /* convert to two complement if negative */ + if (b->sign == MP_NEG) { + bc += (i >= b->used) ? MP_MASK : (~b->dp[i] & MP_MASK); + y = bc & MP_MASK; + bc >>= MP_DIGIT_BIT; + } else { + y = (i >= b->used) ? 0uL : b->dp[i]; + } + + c->dp[i] = x ^ y; + + /* convert to to sign-magnitude if negative */ + if (csign == MP_NEG) { + cc += ~c->dp[i] & MP_MASK; + c->dp[i] = cc & MP_MASK; + cc >>= MP_DIGIT_BIT; + } + } + + c->used = used; + c->sign = csign; + mp_clamp(c); + return MP_OKAY; +} +#endif + +/* End: bn_mp_xor.c */ + +/* Start: bn_mp_zero.c */ +#include "tommath_private.h" +#ifdef BN_MP_ZERO_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* set to zero */ +void mp_zero(mp_int *a) +{ + a->sign = MP_ZPOS; + a->used = 0; + MP_ZERO_DIGITS(a->dp, a->alloc); +} +#endif + +/* End: bn_mp_zero.c */ + +/* Start: bn_prime_tab.c */ +#include "tommath_private.h" +#ifdef BN_PRIME_TAB_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +const mp_digit ltm_prime_tab[] = { + 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, + 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035, + 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059, + 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, +#ifndef MP_8BIT + 0x0083, + 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD, + 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF, + 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107, + 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137, + + 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167, + 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199, + 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9, + 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7, + 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239, + 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265, + 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293, + 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF, + + 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301, + 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B, + 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371, + 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD, + 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5, + 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419, + 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449, + 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B, + + 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7, + 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503, + 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529, + 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F, + 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3, + 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7, + 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623, + 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653 +#endif +}; + +#if defined(__GNUC__) && __GNUC__ >= 4 +#pragma GCC diagnostic push +#pragma GCC diagnostic ignored "-Wdeprecated-declarations" +const mp_digit *s_mp_prime_tab = ltm_prime_tab; +#pragma GCC diagnostic pop +#elif defined(_MSC_VER) && _MSC_VER >= 1500 +#pragma warning(push) +#pragma warning(disable: 4996) +const mp_digit *s_mp_prime_tab = ltm_prime_tab; +#pragma warning(pop) +#else +const mp_digit *s_mp_prime_tab = ltm_prime_tab; +#endif + +#endif + +/* End: bn_prime_tab.c */ + +/* Start: bn_s_mp_add.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_ADD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* low level addition, based on HAC pp.594, Algorithm 14.7 */ +mp_err s_mp_add(const mp_int *a, const mp_int *b, mp_int *c) +{ + const mp_int *x; + mp_err err; + int olduse, min, max; + + /* find sizes, we let |a| <= |b| which means we have to sort + * them. "x" will point to the input with the most digits + */ + if (a->used > b->used) { + min = b->used; + max = a->used; + x = a; + } else { + min = a->used; + max = b->used; + x = b; + } + + /* init result */ + if (c->alloc < (max + 1)) { + if ((err = mp_grow(c, max + 1)) != MP_OKAY) { + return err; + } + } + + /* get old used digit count and set new one */ + olduse = c->used; + c->used = max + 1; + + { + mp_digit u, *tmpa, *tmpb, *tmpc; + int i; + + /* alias for digit pointers */ + + /* first input */ + tmpa = a->dp; + + /* second input */ + tmpb = b->dp; + + /* destination */ + tmpc = c->dp; + + /* zero the carry */ + u = 0; + for (i = 0; i < min; i++) { + /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */ + *tmpc = *tmpa++ + *tmpb++ + u; + + /* U = carry bit of T[i] */ + u = *tmpc >> (mp_digit)MP_DIGIT_BIT; + + /* take away carry bit from T[i] */ + *tmpc++ &= MP_MASK; + } + + /* now copy higher words if any, that is in A+B + * if A or B has more digits add those in + */ + if (min != max) { + for (; i < max; i++) { + /* T[i] = X[i] + U */ + *tmpc = x->dp[i] + u; + + /* U = carry bit of T[i] */ + u = *tmpc >> (mp_digit)MP_DIGIT_BIT; + + /* take away carry bit from T[i] */ + *tmpc++ &= MP_MASK; + } + } + + /* add carry */ + *tmpc++ = u; + + /* clear digits above oldused */ + MP_ZERO_DIGITS(tmpc, olduse - c->used); + } + + mp_clamp(c); + return MP_OKAY; +} +#endif + +/* End: bn_s_mp_add.c */ + +/* Start: bn_s_mp_balance_mul.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_BALANCE_MUL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* single-digit multiplication with the smaller number as the single-digit */ +mp_err s_mp_balance_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + int count, len_a, len_b, nblocks, i, j, bsize; + mp_int a0, tmp, A, B, r; + mp_err err; + + len_a = a->used; + len_b = b->used; + + nblocks = MP_MAX(a->used, b->used) / MP_MIN(a->used, b->used); + bsize = MP_MIN(a->used, b->used) ; + + if ((err = mp_init_size(&a0, bsize + 2)) != MP_OKAY) { + return err; + } + if ((err = mp_init_multi(&tmp, &r, NULL)) != MP_OKAY) { + mp_clear(&a0); + return err; + } + + /* Make sure that A is the larger one*/ + if (len_a < len_b) { + B = *a; + A = *b; + } else { + A = *a; + B = *b; + } + + for (i = 0, j=0; i < nblocks; i++) { + /* Cut a slice off of a */ + a0.used = 0; + for (count = 0; count < bsize; count++) { + a0.dp[count] = A.dp[ j++ ]; + a0.used++; + } + mp_clamp(&a0); + /* Multiply with b */ + if ((err = mp_mul(&a0, &B, &tmp)) != MP_OKAY) { + goto LBL_ERR; + } + /* Shift tmp to the correct position */ + if ((err = mp_lshd(&tmp, bsize * i)) != MP_OKAY) { + goto LBL_ERR; + } + /* Add to output. No carry needed */ + if ((err = mp_add(&r, &tmp, &r)) != MP_OKAY) { + goto LBL_ERR; + } + } + /* The left-overs; there are always left-overs */ + if (j < A.used) { + a0.used = 0; + for (count = 0; j < A.used; count++) { + a0.dp[count] = A.dp[ j++ ]; + a0.used++; + } + mp_clamp(&a0); + if ((err = mp_mul(&a0, &B, &tmp)) != MP_OKAY) { + goto LBL_ERR; + } + if ((err = mp_lshd(&tmp, bsize * i)) != MP_OKAY) { + goto LBL_ERR; + } + if ((err = mp_add(&r, &tmp, &r)) != MP_OKAY) { + goto LBL_ERR; + } + } + + mp_exch(&r,c); +LBL_ERR: + mp_clear_multi(&a0, &tmp, &r,NULL); + return err; +} +#endif + +/* End: bn_s_mp_balance_mul.c */ + +/* Start: bn_s_mp_exptmod.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_EXPTMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +#ifdef MP_LOW_MEM +# define TAB_SIZE 32 +# define MAX_WINSIZE 5 +#else +# define TAB_SIZE 256 +# define MAX_WINSIZE 0 +#endif + +mp_err s_mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode) +{ + mp_int M[TAB_SIZE], res, mu; + mp_digit buf; + mp_err err; + int bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; + mp_err(*redux)(mp_int *x, const mp_int *m, const mp_int *mu); + + /* 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; + } + + winsize = MAX_WINSIZE ? MP_MIN(MAX_WINSIZE, winsize) : winsize; + + /* init M array */ + /* init first cell */ + if ((err = mp_init(&M[1])) != MP_OKAY) { + return err; + } + + /* now init the second half of the array */ + for (x = 1<<(winsize-1); x < (1 << winsize); x++) { + if ((err = mp_init(&M[x])) != MP_OKAY) { + for (y = 1<<(winsize-1); y < x; y++) { + mp_clear(&M[y]); + } + mp_clear(&M[1]); + return err; + } + } + + /* create mu, used for Barrett reduction */ + if ((err = mp_init(&mu)) != MP_OKAY) goto LBL_M; + + if (redmode == 0) { + if ((err = mp_reduce_setup(&mu, P)) != MP_OKAY) goto LBL_MU; + redux = mp_reduce; + } else { + if ((err = mp_reduce_2k_setup_l(P, &mu)) != MP_OKAY) goto LBL_MU; + redux = mp_reduce_2k_l; + } + + /* create M table + * + * The M table contains powers of the base, + * e.g. M[x] = G**x mod P + * + * The first half of the table is not + * computed though accept for M[0] and M[1] + */ + if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) goto LBL_MU; + + /* compute the value at M[1<<(winsize-1)] by squaring + * M[1] (winsize-1) times + */ + if ((err = mp_copy(&M[1], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_MU; + + for (x = 0; x < (winsize - 1); x++) { + /* square it */ + if ((err = mp_sqr(&M[(size_t)1 << (winsize - 1)], + &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_MU; + + /* reduce modulo P */ + if ((err = redux(&M[(size_t)1 << (winsize - 1)], P, &mu)) != MP_OKAY) goto LBL_MU; + } + + /* create upper table, that is M[x] = M[x-1] * M[1] (mod P) + * for x = (2**(winsize - 1) + 1) to (2**winsize - 1) + */ + for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { + if ((err = mp_mul(&M[x - 1], &M[1], &M[x])) != MP_OKAY) goto LBL_MU; + if ((err = redux(&M[x], P, &mu)) != MP_OKAY) goto LBL_MU; + } + + /* setup result */ + if ((err = mp_init(&res)) != MP_OKAY) goto LBL_MU; + mp_set(&res, 1uL); + + /* set initial mode and bit cnt */ + mode = 0; + bitcnt = 1; + buf = 0; + digidx = X->used - 1; + bitcpy = 0; + bitbuf = 0; + + for (;;) { + /* grab next digit as required */ + if (--bitcnt == 0) { + /* if digidx == -1 we are out of digits */ + if (digidx == -1) { + break; + } + /* read next digit and reset the bitcnt */ + buf = X->dp[digidx--]; + bitcnt = (int)MP_DIGIT_BIT; + } + + /* grab the next msb from the exponent */ + y = (buf >> (mp_digit)(MP_DIGIT_BIT - 1)) & 1uL; + buf <<= (mp_digit)1; + + /* if the bit is zero and mode == 0 then we ignore it + * These represent the leading zero bits before the first 1 bit + * in the exponent. Technically this opt is not required but it + * does lower the # of trivial squaring/reductions used + */ + if ((mode == 0) && (y == 0)) { + continue; + } + + /* if the bit is zero and mode == 1 then we square */ + if ((mode == 1) && (y == 0)) { + if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES; + continue; + } + + /* else we add it to the window */ + bitbuf |= (y << (winsize - ++bitcpy)); + mode = 2; + + if (bitcpy == winsize) { + /* ok window is filled so square as required and multiply */ + /* square first */ + for (x = 0; x < winsize; x++) { + if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES; + } + + /* then multiply */ + if ((err = mp_mul(&res, &M[bitbuf], &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES; + + /* empty window and reset */ + bitcpy = 0; + bitbuf = 0; + mode = 1; + } + } + + /* if bits remain then square/multiply */ + if ((mode == 2) && (bitcpy > 0)) { + /* square then multiply if the bit is set */ + for (x = 0; x < bitcpy; x++) { + if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES; + + bitbuf <<= 1; + if ((bitbuf & (1 << winsize)) != 0) { + /* then multiply */ + if ((err = mp_mul(&res, &M[1], &res)) != MP_OKAY) goto LBL_RES; + if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES; + } + } + } + + mp_exch(&res, Y); + err = MP_OKAY; +LBL_RES: + mp_clear(&res); +LBL_MU: + mp_clear(&mu); +LBL_M: + mp_clear(&M[1]); + for (x = 1<<(winsize-1); x < (1 << winsize); x++) { + mp_clear(&M[x]); + } + return err; +} +#endif + +/* End: bn_s_mp_exptmod.c */ + +/* Start: bn_s_mp_exptmod_fast.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_EXPTMOD_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* 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 +# define MAX_WINSIZE 5 +#else +# define TAB_SIZE 256 +# define MAX_WINSIZE 0 +#endif + +mp_err s_mp_exptmod_fast(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode) +{ + mp_int M[TAB_SIZE], res; + mp_digit buf, mp; + int bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; + mp_err err; + + /* 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. + */ + mp_err(*redux)(mp_int *x, const mp_int *n, mp_digit rho); + + /* 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; + } + + winsize = MAX_WINSIZE ? MP_MIN(MAX_WINSIZE, winsize) : winsize; + + /* init M array */ + /* init first cell */ + if ((err = mp_init_size(&M[1], P->alloc)) != 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_size(&M[x], P->alloc)) != 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) { + if (MP_HAS(MP_MONTGOMERY_SETUP)) { + /* now setup montgomery */ + if ((err = mp_montgomery_setup(P, &mp)) != MP_OKAY) goto LBL_M; + } else { + err = MP_VAL; + goto LBL_M; + } + + /* automatically pick the comba one if available (saves quite a few calls/ifs) */ + if (MP_HAS(S_MP_MONTGOMERY_REDUCE_FAST) && + (((P->used * 2) + 1) < MP_WARRAY) && + (P->used < MP_MAXFAST)) { + redux = s_mp_montgomery_reduce_fast; + } else if (MP_HAS(MP_MONTGOMERY_REDUCE)) { + /* use slower baseline Montgomery method */ + redux = mp_montgomery_reduce; + } else { + err = MP_VAL; + goto LBL_M; + } + } else if (redmode == 1) { + if (MP_HAS(MP_DR_SETUP) && MP_HAS(MP_DR_REDUCE)) { + /* 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; + } + } else if (MP_HAS(MP_REDUCE_2K_SETUP) && MP_HAS(MP_REDUCE_2K)) { + /* 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; + } + + /* setup result */ + if ((err = mp_init_size(&res, P->alloc)) != 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) { + if (MP_HAS(MP_MONTGOMERY_CALC_NORMALIZATION)) { + /* now we need R mod m */ + if ((err = mp_montgomery_calc_normalization(&res, P)) != MP_OKAY) goto LBL_RES; + + /* now set M[1] to G * R mod m */ + if ((err = mp_mulmod(G, &res, P, &M[1])) != MP_OKAY) goto LBL_RES; + } else { + err = MP_VAL; + goto LBL_RES; + } + } else { + mp_set(&res, 1uL); + 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[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_RES; + + for (x = 0; x < (winsize - 1); x++) { + if ((err = mp_sqr(&M[(size_t)1 << (winsize - 1)], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_RES; + if ((err = redux(&M[(size_t)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)MP_DIGIT_BIT; + } + + /* grab the next msb from the exponent */ + y = (mp_digit)(buf >> (MP_DIGIT_BIT - 1)) & 1uL; + 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 + +/* End: bn_s_mp_exptmod_fast.c */ + +/* Start: bn_s_mp_get_bit.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_GET_BIT_C + +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Get bit at position b and return MP_YES if the bit is 1, MP_NO if it is 0 */ +mp_bool s_mp_get_bit(const mp_int *a, unsigned int b) +{ + mp_digit bit; + int limb = (int)(b / MP_DIGIT_BIT); + + if (limb >= a->used) { + return MP_NO; + } + + bit = (mp_digit)1 << (b % MP_DIGIT_BIT); + return ((a->dp[limb] & bit) != 0u) ? MP_YES : MP_NO; +} + +#endif + +/* End: bn_s_mp_get_bit.c */ + +/* Start: bn_s_mp_invmod_fast.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_INVMOD_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* 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 + */ +mp_err s_mp_invmod_fast(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_int x, y, u, v, B, D; + mp_sign neg; + mp_err err; + + /* 2. [modified] b must be odd */ + if (MP_IS_EVEN(b)) { + return MP_VAL; + } + + /* init all our temps */ + if ((err = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) { + return err; + } + + /* x == modulus, y == value to invert */ + if ((err = mp_copy(b, &x)) != MP_OKAY) goto LBL_ERR; + + /* we need y = |a| */ + if ((err = mp_mod(a, b, &y)) != MP_OKAY) goto LBL_ERR; + + /* if one of x,y is zero return an error! */ + if (MP_IS_ZERO(&x) || MP_IS_ZERO(&y)) { + err = MP_VAL; + goto LBL_ERR; + } + + /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ + if ((err = mp_copy(&x, &u)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&y, &v)) != MP_OKAY) goto LBL_ERR; + mp_set(&D, 1uL); + +top: + /* 4. while u is even do */ + while (MP_IS_EVEN(&u)) { + /* 4.1 u = u/2 */ + if ((err = mp_div_2(&u, &u)) != MP_OKAY) goto LBL_ERR; + + /* 4.2 if B is odd then */ + if (MP_IS_ODD(&B)) { + if ((err = mp_sub(&B, &x, &B)) != MP_OKAY) goto LBL_ERR; + } + /* B = B/2 */ + if ((err = mp_div_2(&B, &B)) != MP_OKAY) goto LBL_ERR; + } + + /* 5. while v is even do */ + while (MP_IS_EVEN(&v)) { + /* 5.1 v = v/2 */ + if ((err = mp_div_2(&v, &v)) != MP_OKAY) goto LBL_ERR; + + /* 5.2 if D is odd then */ + if (MP_IS_ODD(&D)) { + /* D = (D-x)/2 */ + if ((err = mp_sub(&D, &x, &D)) != MP_OKAY) goto LBL_ERR; + } + /* D = D/2 */ + if ((err = 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 ((err = mp_sub(&u, &v, &u)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&B, &D, &B)) != MP_OKAY) goto LBL_ERR; + } else { + /* v - v - u, D = D - B */ + if ((err = mp_sub(&v, &u, &v)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&D, &B, &D)) != MP_OKAY) goto LBL_ERR; + } + + /* if not zero goto step 4 */ + if (!MP_IS_ZERO(&u)) { + goto top; + } + + /* now a = C, b = D, gcd == g*v */ + + /* if v != 1 then there is no inverse */ + if (mp_cmp_d(&v, 1uL) != MP_EQ) { + err = MP_VAL; + goto LBL_ERR; + } + + /* b is now the inverse */ + neg = a->sign; + while (D.sign == MP_NEG) { + if ((err = mp_add(&D, b, &D)) != MP_OKAY) goto LBL_ERR; + } + + /* too big */ + while (mp_cmp_mag(&D, b) != MP_LT) { + if ((err = mp_sub(&D, b, &D)) != MP_OKAY) goto LBL_ERR; + } + + mp_exch(&D, c); + c->sign = neg; + err = MP_OKAY; + +LBL_ERR: + mp_clear_multi(&x, &y, &u, &v, &B, &D, NULL); + return err; +} +#endif + +/* End: bn_s_mp_invmod_fast.c */ + +/* Start: bn_s_mp_invmod_slow.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_INVMOD_SLOW_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* hac 14.61, pp608 */ +mp_err s_mp_invmod_slow(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_int x, y, u, v, A, B, C, D; + mp_err err; + + /* b cannot be negative */ + if ((b->sign == MP_NEG) || MP_IS_ZERO(b)) { + return MP_VAL; + } + + /* init temps */ + if ((err = mp_init_multi(&x, &y, &u, &v, + &A, &B, &C, &D, NULL)) != MP_OKAY) { + return err; + } + + /* x = a, y = b */ + if ((err = mp_mod(a, b, &x)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(b, &y)) != MP_OKAY) goto LBL_ERR; + + /* 2. [modified] if x,y are both even then return an error! */ + if (MP_IS_EVEN(&x) && MP_IS_EVEN(&y)) { + err = MP_VAL; + goto LBL_ERR; + } + + /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ + if ((err = mp_copy(&x, &u)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_copy(&y, &v)) != MP_OKAY) goto LBL_ERR; + mp_set(&A, 1uL); + mp_set(&D, 1uL); + +top: + /* 4. while u is even do */ + while (MP_IS_EVEN(&u)) { + /* 4.1 u = u/2 */ + if ((err = mp_div_2(&u, &u)) != MP_OKAY) goto LBL_ERR; + + /* 4.2 if A or B is odd then */ + if (MP_IS_ODD(&A) || MP_IS_ODD(&B)) { + /* A = (A+y)/2, B = (B-x)/2 */ + if ((err = mp_add(&A, &y, &A)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_sub(&B, &x, &B)) != MP_OKAY) goto LBL_ERR; + } + /* A = A/2, B = B/2 */ + if ((err = mp_div_2(&A, &A)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_div_2(&B, &B)) != MP_OKAY) goto LBL_ERR; + } + + /* 5. while v is even do */ + while (MP_IS_EVEN(&v)) { + /* 5.1 v = v/2 */ + if ((err = mp_div_2(&v, &v)) != MP_OKAY) goto LBL_ERR; + + /* 5.2 if C or D is odd then */ + if (MP_IS_ODD(&C) || MP_IS_ODD(&D)) { + /* C = (C+y)/2, D = (D-x)/2 */ + if ((err = mp_add(&C, &y, &C)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_sub(&D, &x, &D)) != MP_OKAY) goto LBL_ERR; + } + /* C = C/2, D = D/2 */ + if ((err = mp_div_2(&C, &C)) != MP_OKAY) goto LBL_ERR; + if ((err = 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 ((err = mp_sub(&u, &v, &u)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&A, &C, &A)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&B, &D, &B)) != MP_OKAY) goto LBL_ERR; + } else { + /* v - v - u, C = C - A, D = D - B */ + if ((err = mp_sub(&v, &u, &v)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&C, &A, &C)) != MP_OKAY) goto LBL_ERR; + + if ((err = mp_sub(&D, &B, &D)) != MP_OKAY) goto LBL_ERR; + } + + /* if not zero goto step 4 */ + if (!MP_IS_ZERO(&u)) { + goto top; + } + + /* now a = C, b = D, gcd == g*v */ + + /* if v != 1 then there is no inverse */ + if (mp_cmp_d(&v, 1uL) != MP_EQ) { + err = MP_VAL; + goto LBL_ERR; + } + + /* if its too low */ + while (mp_cmp_d(&C, 0uL) == MP_LT) { + if ((err = mp_add(&C, b, &C)) != MP_OKAY) goto LBL_ERR; + } + + /* too big */ + while (mp_cmp_mag(&C, b) != MP_LT) { + if ((err = mp_sub(&C, b, &C)) != MP_OKAY) goto LBL_ERR; + } + + /* C is now the inverse */ + mp_exch(&C, c); + err = MP_OKAY; +LBL_ERR: + mp_clear_multi(&x, &y, &u, &v, &A, &B, &C, &D, NULL); + return err; +} +#endif + +/* End: bn_s_mp_invmod_slow.c */ + +/* Start: bn_s_mp_karatsuba_mul.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_KARATSUBA_MUL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* c = |a| * |b| using Karatsuba Multiplication using + * three half size multiplications + * + * Let B represent the radix [e.g. 2**MP_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. + */ +mp_err s_mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_int x0, x1, y0, y1, t1, x0y0, x1y1; + int B; + mp_err err = MP_MEM; /* default the return code to an error */ + + /* min # of digits */ + B = MP_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 LBL_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; + + { + int x; + 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); +LBL_ERR: + return err; +} +#endif + +/* End: bn_s_mp_karatsuba_mul.c */ + +/* Start: bn_s_mp_karatsuba_sqr.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_KARATSUBA_SQR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Karatsuba squaring, computes b = a*a using three + * half size squarings + * + * See comments of karatsuba_mul for details. It + * is essentially the same algorithm but merely + * tuned to perform recursive squarings. + */ +mp_err s_mp_karatsuba_sqr(const mp_int *a, mp_int *b) +{ + mp_int x0, x1, t1, t2, x0x0, x1x1; + int B; + mp_err err = MP_MEM; + + /* min # of digits */ + B = a->used; + + /* now divide in two */ + B = B >> 1; + + /* init copy all the temps */ + if (mp_init_size(&x0, B) != MP_OKAY) + goto LBL_ERR; + if (mp_init_size(&x1, a->used - B) != MP_OKAY) + goto X0; + + /* init temps */ + if (mp_init_size(&t1, a->used * 2) != MP_OKAY) + goto X1; + if (mp_init_size(&t2, a->used * 2) != MP_OKAY) + goto T1; + if (mp_init_size(&x0x0, B * 2) != MP_OKAY) + goto T2; + if (mp_init_size(&x1x1, (a->used - B) * 2) != MP_OKAY) + goto X0X0; + + { + int x; + mp_digit *dst, *src; + + src = a->dp; + + /* now shift the digits */ + dst = x0.dp; + for (x = 0; x < B; x++) { + *dst++ = *src++; + } + + dst = x1.dp; + for (x = B; x < a->used; x++) { + *dst++ = *src++; + } + } + + x0.used = B; + x1.used = a->used - B; + + mp_clamp(&x0); + + /* now calc the products x0*x0 and x1*x1 */ + if (mp_sqr(&x0, &x0x0) != MP_OKAY) + goto X1X1; /* x0x0 = x0*x0 */ + if (mp_sqr(&x1, &x1x1) != MP_OKAY) + goto X1X1; /* x1x1 = x1*x1 */ + + /* now calc (x1+x0)**2 */ + if (s_mp_add(&x1, &x0, &t1) != MP_OKAY) + goto X1X1; /* t1 = x1 - x0 */ + if (mp_sqr(&t1, &t1) != MP_OKAY) + goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */ + + /* add x0y0 */ + if (s_mp_add(&x0x0, &x1x1, &t2) != MP_OKAY) + goto X1X1; /* t2 = x0x0 + x1x1 */ + if (s_mp_sub(&t1, &t2, &t1) != MP_OKAY) + goto X1X1; /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */ + + /* shift by B */ + if (mp_lshd(&t1, B) != MP_OKAY) + goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */ + if (mp_lshd(&x1x1, B * 2) != MP_OKAY) + goto X1X1; /* x1x1 = x1x1 << 2*B */ + + if (mp_add(&x0x0, &t1, &t1) != MP_OKAY) + goto X1X1; /* t1 = x0x0 + t1 */ + if (mp_add(&t1, &x1x1, b) != MP_OKAY) + goto X1X1; /* t1 = x0x0 + t1 + x1x1 */ + + err = MP_OKAY; + +X1X1: + mp_clear(&x1x1); +X0X0: + mp_clear(&x0x0); +T2: + mp_clear(&t2); +T1: + mp_clear(&t1); +X1: + mp_clear(&x1); +X0: + mp_clear(&x0); +LBL_ERR: + return err; +} +#endif + +/* End: bn_s_mp_karatsuba_sqr.c */ + +/* Start: bn_s_mp_montgomery_reduce_fast.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_MONTGOMERY_REDUCE_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* 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. +*/ +mp_err s_mp_montgomery_reduce_fast(mp_int *x, const mp_int *n, mp_digit rho) +{ + int ix, olduse; + mp_err err; + mp_word W[MP_WARRAY]; + + if (x->used > MP_WARRAY) { + return MP_VAL; + } + + /* get old used count */ + olduse = x->used; + + /* grow a as required */ + if (x->alloc < (n->used + 1)) { + if ((err = mp_grow(x, n->used + 1)) != MP_OKAY) { + return err; + } + } + + /* first we have to get the digits of the input into + * an array of double precision words W[...] + */ + { + mp_word *_W; + 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] */ + if (ix < ((n->used * 2) + 1)) { + MP_ZERO_BUFFER(_W, sizeof(mp_word) * (size_t)(((n->used * 2) + 1) - ix)); + } + } + + /* 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) + */ + mp_digit mu; + mu = ((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 + */ + { + int iy; + mp_digit *tmpn; + 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)MP_DIGIT_BIT; + } + + /* now we have to propagate the carries and + * shift the words downward [all those least + * significant digits we zeroed]. + */ + { + mp_digit *tmpx; + 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)MP_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++ = *_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 + */ + MP_ZERO_DIGITS(tmpx, olduse - ix); + } + + /* 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 + +/* End: bn_s_mp_montgomery_reduce_fast.c */ + +/* Start: bn_s_mp_mul_digs.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_MUL_DIGS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* multiplies |a| * |b| and only computes upto digs digits of result + * HAC pp. 595, Algorithm 14.12 Modified so you can control how + * many digits of output are created. + */ +mp_err s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs) +{ + mp_int t; + mp_err err; + int pa, pb, ix, iy; + mp_digit u; + mp_word r; + mp_digit tmpx, *tmpt, *tmpy; + + /* can we use the fast multiplier? */ + if ((digs < MP_WARRAY) && + (MP_MIN(a->used, b->used) < MP_MAXFAST)) { + return s_mp_mul_digs_fast(a, b, c, digs); + } + + if ((err = mp_init_size(&t, digs)) != MP_OKAY) { + return err; + } + t.used = digs; + + /* compute the digits of the product directly */ + pa = a->used; + for (ix = 0; ix < pa; ix++) { + /* set the carry to zero */ + u = 0; + + /* limit ourselves to making digs digits of output */ + pb = MP_MIN(b->used, digs - ix); + + /* setup some aliases */ + /* copy of the digit from a used within the nested loop */ + tmpx = a->dp[ix]; + + /* an alias for the destination shifted ix places */ + tmpt = t.dp + ix; + + /* an alias for the digits of b */ + tmpy = b->dp; + + /* compute the columns of the output and propagate the carry */ + for (iy = 0; iy < pb; iy++) { + /* compute the column as a mp_word */ + r = (mp_word)*tmpt + + ((mp_word)tmpx * (mp_word)*tmpy++) + + (mp_word)u; + + /* the new column is the lower part of the result */ + *tmpt++ = (mp_digit)(r & (mp_word)MP_MASK); + + /* get the carry word from the result */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + } + /* set carry if it is placed below digs */ + if ((ix + iy) < digs) { + *tmpt = u; + } + } + + mp_clamp(&t); + mp_exch(&t, c); + + mp_clear(&t); + return MP_OKAY; +} +#endif + +/* End: bn_s_mp_mul_digs.c */ + +/* Start: bn_s_mp_mul_digs_fast.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_MUL_DIGS_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* 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. + * + */ +mp_err s_mp_mul_digs_fast(const mp_int *a, const mp_int *b, mp_int *c, int digs) +{ + int olduse, pa, ix, iz; + mp_err err; + mp_digit W[MP_WARRAY]; + mp_word _W; + + /* grow the destination as required */ + if (c->alloc < digs) { + if ((err = mp_grow(c, digs)) != MP_OKAY) { + return err; + } + } + + /* number of output digits to produce */ + pa = MP_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 = MP_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 = MP_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)MP_DIGIT_BIT; + } + + /* setup dest */ + olduse = c->used; + c->used = pa; + + { + mp_digit *tmpc; + tmpc = c->dp; + for (ix = 0; 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] */ + MP_ZERO_DIGITS(tmpc, olduse - ix); + } + mp_clamp(c); + return MP_OKAY; +} +#endif + +/* End: bn_s_mp_mul_digs_fast.c */ + +/* Start: bn_s_mp_mul_high_digs.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_MUL_HIGH_DIGS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* multiplies |a| * |b| and does not compute the lower digs digits + * [meant to get the higher part of the product] + */ +mp_err s_mp_mul_high_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs) +{ + mp_int t; + int pa, pb, ix, iy; + mp_err err; + mp_digit u; + mp_word r; + mp_digit tmpx, *tmpt, *tmpy; + + /* can we use the fast multiplier? */ + if (MP_HAS(S_MP_MUL_HIGH_DIGS_FAST) + && ((a->used + b->used + 1) < MP_WARRAY) + && (MP_MIN(a->used, b->used) < MP_MAXFAST)) { + return s_mp_mul_high_digs_fast(a, b, c, digs); + } + + if ((err = mp_init_size(&t, a->used + b->used + 1)) != MP_OKAY) { + return err; + } + t.used = a->used + b->used + 1; + + pa = a->used; + pb = b->used; + for (ix = 0; ix < pa; ix++) { + /* clear the carry */ + u = 0; + + /* left hand side of A[ix] * B[iy] */ + tmpx = a->dp[ix]; + + /* alias to the address of where the digits will be stored */ + tmpt = &(t.dp[digs]); + + /* alias for where to read the right hand side from */ + tmpy = b->dp + (digs - ix); + + for (iy = digs - ix; iy < pb; iy++) { + /* calculate the double precision result */ + r = (mp_word)*tmpt + + ((mp_word)tmpx * (mp_word)*tmpy++) + + (mp_word)u; + + /* get the lower part */ + *tmpt++ = (mp_digit)(r & (mp_word)MP_MASK); + + /* carry the carry */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + } + *tmpt = u; + } + mp_clamp(&t); + mp_exch(&t, c); + mp_clear(&t); + return MP_OKAY; +} +#endif + +/* End: bn_s_mp_mul_high_digs.c */ + +/* Start: bn_s_mp_mul_high_digs_fast.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_MUL_HIGH_DIGS_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* 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. + */ +mp_err s_mp_mul_high_digs_fast(const mp_int *a, const mp_int *b, mp_int *c, int digs) +{ + int olduse, pa, ix, iz; + mp_err err; + mp_digit W[MP_WARRAY]; + mp_word _W; + + /* grow the destination as required */ + pa = a->used + b->used; + if (c->alloc < pa) { + if ((err = mp_grow(c, pa)) != MP_OKAY) { + return err; + } + } + + /* 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 = MP_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 = MP_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)MP_DIGIT_BIT; + } + + /* setup dest */ + olduse = c->used; + c->used = pa; + + { + 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] */ + MP_ZERO_DIGITS(tmpc, olduse - ix); + } + mp_clamp(c); + return MP_OKAY; +} +#endif + +/* End: bn_s_mp_mul_high_digs_fast.c */ + +/* Start: bn_s_mp_prime_is_divisible.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_PRIME_IS_DIVISIBLE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* determines if an integers is divisible by one + * of the first PRIME_SIZE primes or not + * + * sets result to 0 if not, 1 if yes + */ +mp_err s_mp_prime_is_divisible(const mp_int *a, mp_bool *result) +{ + int ix; + mp_err err; + mp_digit res; + + /* default to not */ + *result = MP_NO; + + for (ix = 0; ix < PRIVATE_MP_PRIME_TAB_SIZE; ix++) { + /* what is a mod LBL_prime_tab[ix] */ + if ((err = mp_mod_d(a, s_mp_prime_tab[ix], &res)) != MP_OKAY) { + return err; + } + + /* is the residue zero? */ + if (res == 0u) { + *result = MP_YES; + return MP_OKAY; + } + } + + return MP_OKAY; +} +#endif + +/* End: bn_s_mp_prime_is_divisible.c */ + +/* Start: bn_s_mp_rand_jenkins.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_RAND_JENKINS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* Bob Jenkins' http://burtleburtle.net/bob/rand/smallprng.html */ +/* Chosen for speed and a good "mix" */ +typedef struct { + uint64_t a; + uint64_t b; + uint64_t c; + uint64_t d; +} ranctx; + +static ranctx jenkins_x; + +#define rot(x,k) (((x)<<(k))|((x)>>(64-(k)))) +static uint64_t s_rand_jenkins_val(void) +{ + uint64_t e = jenkins_x.a - rot(jenkins_x.b, 7); + jenkins_x.a = jenkins_x.b ^ rot(jenkins_x.c, 13); + jenkins_x.b = jenkins_x.c + rot(jenkins_x.d, 37); + jenkins_x.c = jenkins_x.d + e; + jenkins_x.d = e + jenkins_x.a; + return jenkins_x.d; +} + +void s_mp_rand_jenkins_init(uint64_t seed) +{ + uint64_t i; + jenkins_x.a = 0xf1ea5eedULL; + jenkins_x.b = jenkins_x.c = jenkins_x.d = seed; + for (i = 0uLL; i < 20uLL; ++i) { + (void)s_rand_jenkins_val(); + } +} + +mp_err s_mp_rand_jenkins(void *p, size_t n) +{ + char *q = (char *)p; + while (n > 0u) { + int i; + uint64_t x = s_rand_jenkins_val(); + for (i = 0; (i < 8) && (n > 0u); ++i, --n) { + *q++ = (char)(x & 0xFFuLL); + x >>= 8; + } + } + return MP_OKAY; +} + +#endif + +/* End: bn_s_mp_rand_jenkins.c */ + +/* Start: bn_s_mp_rand_platform.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_RAND_PLATFORM_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* First the OS-specific special cases + * - *BSD + * - Windows + */ +#if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__) +#define BN_S_READ_ARC4RANDOM_C +static mp_err s_read_arc4random(void *p, size_t n) +{ + arc4random_buf(p, n); + return MP_OKAY; +} +#endif + +#if defined(_WIN32) || defined(_WIN32_WCE) +#define BN_S_READ_WINCSP_C + +#ifndef _WIN32_WINNT +#define _WIN32_WINNT 0x0400 +#endif +#ifdef _WIN32_WCE +#define UNDER_CE +#define ARM +#endif + +#define WIN32_LEAN_AND_MEAN +#include <windows.h> +#include <wincrypt.h> + +static mp_err s_read_wincsp(void *p, size_t n) +{ + static HCRYPTPROV hProv = 0; + if (hProv == 0) { + HCRYPTPROV h = 0; + if (!CryptAcquireContext(&h, NULL, MS_DEF_PROV, PROV_RSA_FULL, + (CRYPT_VERIFYCONTEXT | CRYPT_MACHINE_KEYSET)) && + !CryptAcquireContext(&h, NULL, MS_DEF_PROV, PROV_RSA_FULL, + CRYPT_VERIFYCONTEXT | CRYPT_MACHINE_KEYSET | CRYPT_NEWKEYSET)) { + return MP_ERR; + } + hProv = h; + } + return CryptGenRandom(hProv, (DWORD)n, (BYTE *)p) == TRUE ? MP_OKAY : MP_ERR; +} +#endif /* WIN32 */ + +#if !defined(BN_S_READ_WINCSP_C) && defined(__linux__) && defined(__GLIBC_PREREQ) +#if __GLIBC_PREREQ(2, 25) +#define BN_S_READ_GETRANDOM_C +#include <sys/random.h> +#include <errno.h> + +static mp_err s_read_getrandom(void *p, size_t n) +{ + char *q = (char *)p; + while (n > 0u) { + ssize_t ret = getrandom(q, n, 0); + if (ret < 0) { + if (errno == EINTR) { + continue; + } + return MP_ERR; + } + q += ret; + n -= (size_t)ret; + } + return MP_OKAY; +} +#endif +#endif + +/* We assume all platforms besides windows provide "/dev/urandom". + * In case yours doesn't, define MP_NO_DEV_URANDOM at compile-time. + */ +#if !defined(BN_S_READ_WINCSP_C) && !defined(MP_NO_DEV_URANDOM) +#define BN_S_READ_URANDOM_C +#ifndef MP_DEV_URANDOM +#define MP_DEV_URANDOM "/dev/urandom" +#endif +#include <fcntl.h> +#include <errno.h> +#include <unistd.h> + +static mp_err s_read_urandom(void *p, size_t n) +{ + int fd; + char *q = (char *)p; + + do { + fd = open(MP_DEV_URANDOM, O_RDONLY); + } while ((fd == -1) && (errno == EINTR)); + if (fd == -1) return MP_ERR; + + while (n > 0u) { + ssize_t ret = read(fd, p, n); + if (ret < 0) { + if (errno == EINTR) { + continue; + } + close(fd); + return MP_ERR; + } + q += ret; + n -= (size_t)ret; + } + + close(fd); + return MP_OKAY; +} +#endif + +#if defined(MP_PRNG_ENABLE_LTM_RNG) +#define BN_S_READ_LTM_RNG +unsigned long (*ltm_rng)(unsigned char *out, unsigned long outlen, void (*callback)(void)); +void (*ltm_rng_callback)(void); + +static mp_err s_read_ltm_rng(void *p, size_t n) +{ + unsigned long res; + if (ltm_rng == NULL) return MP_ERR; + res = ltm_rng(p, n, ltm_rng_callback); + if (res != n) return MP_ERR; + return MP_OKAY; +} +#endif + +mp_err s_read_arc4random(void *p, size_t n); +mp_err s_read_wincsp(void *p, size_t n); +mp_err s_read_getrandom(void *p, size_t n); +mp_err s_read_urandom(void *p, size_t n); +mp_err s_read_ltm_rng(void *p, size_t n); + +mp_err s_mp_rand_platform(void *p, size_t n) +{ + mp_err err = MP_ERR; + if ((err != MP_OKAY) && MP_HAS(S_READ_ARC4RANDOM)) err = s_read_arc4random(p, n); + if ((err != MP_OKAY) && MP_HAS(S_READ_WINCSP)) err = s_read_wincsp(p, n); + if ((err != MP_OKAY) && MP_HAS(S_READ_GETRANDOM)) err = s_read_getrandom(p, n); + if ((err != MP_OKAY) && MP_HAS(S_READ_URANDOM)) err = s_read_urandom(p, n); + if ((err != MP_OKAY) && MP_HAS(S_READ_LTM_RNG)) err = s_read_ltm_rng(p, n); + return err; +} + +#endif + +/* End: bn_s_mp_rand_platform.c */ + +/* Start: bn_s_mp_reverse.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_REVERSE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* reverse an array, used for radix code */ +void s_mp_reverse(unsigned char *s, size_t len) +{ + size_t ix, iy; + unsigned char t; + + ix = 0u; + iy = len - 1u; + while (ix < iy) { + t = s[ix]; + s[ix] = s[iy]; + s[iy] = t; + ++ix; + --iy; + } +} +#endif + +/* End: bn_s_mp_reverse.c */ + +/* Start: bn_s_mp_sqr.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_SQR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */ +mp_err s_mp_sqr(const mp_int *a, mp_int *b) +{ + mp_int t; + int ix, iy, pa; + mp_err err; + mp_word r; + mp_digit u, tmpx, *tmpt; + + pa = a->used; + if ((err = mp_init_size(&t, (2 * pa) + 1)) != MP_OKAY) { + return err; + } + + /* default used is maximum possible size */ + t.used = (2 * pa) + 1; + + for (ix = 0; ix < pa; ix++) { + /* first calculate the digit at 2*ix */ + /* calculate double precision result */ + r = (mp_word)t.dp[2*ix] + + ((mp_word)a->dp[ix] * (mp_word)a->dp[ix]); + + /* store lower part in result */ + t.dp[ix+ix] = (mp_digit)(r & (mp_word)MP_MASK); + + /* get the carry */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + + /* left hand side of A[ix] * A[iy] */ + tmpx = a->dp[ix]; + + /* alias for where to store the results */ + tmpt = t.dp + ((2 * ix) + 1); + + for (iy = ix + 1; iy < pa; iy++) { + /* first calculate the product */ + r = (mp_word)tmpx * (mp_word)a->dp[iy]; + + /* now calculate the double precision result, note we use + * addition instead of *2 since it's easier to optimize + */ + r = (mp_word)*tmpt + r + r + (mp_word)u; + + /* store lower part */ + *tmpt++ = (mp_digit)(r & (mp_word)MP_MASK); + + /* get carry */ + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + } + /* propagate upwards */ + while (u != 0uL) { + r = (mp_word)*tmpt + (mp_word)u; + *tmpt++ = (mp_digit)(r & (mp_word)MP_MASK); + u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT); + } + } + + mp_clamp(&t); + mp_exch(&t, b); + mp_clear(&t); + return MP_OKAY; +} +#endif + +/* End: bn_s_mp_sqr.c */ + +/* Start: bn_s_mp_sqr_fast.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_SQR_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* 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. +*/ + +mp_err s_mp_sqr_fast(const mp_int *a, mp_int *b) +{ + int olduse, pa, ix, iz; + mp_digit W[MP_WARRAY], *tmpx; + mp_word W1; + mp_err err; + + /* grow the destination as required */ + pa = a->used + a->used; + if (b->alloc < pa) { + if ((err = mp_grow(b, pa)) != MP_OKAY) { + return err; + } + } + + /* 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 = MP_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 = MP_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 = MP_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 (((unsigned)ix & 1u) == 0u) { + _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)MP_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] */ + MP_ZERO_DIGITS(tmpb, olduse - ix); + } + mp_clamp(b); + return MP_OKAY; +} +#endif + +/* End: bn_s_mp_sqr_fast.c */ + +/* Start: bn_s_mp_sub.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_SUB_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */ +mp_err s_mp_sub(const mp_int *a, const mp_int *b, mp_int *c) +{ + int olduse, min, max; + mp_err err; + + /* find sizes */ + min = b->used; + max = a->used; + + /* init result */ + if (c->alloc < max) { + if ((err = mp_grow(c, max)) != MP_OKAY) { + return err; + } + } + olduse = c->used; + c->used = max; + + { + mp_digit u, *tmpa, *tmpb, *tmpc; + int i; + + /* alias for digit pointers */ + tmpa = a->dp; + tmpb = b->dp; + tmpc = c->dp; + + /* set carry to zero */ + u = 0; + for (i = 0; i < min; i++) { + /* T[i] = A[i] - B[i] - U */ + *tmpc = (*tmpa++ - *tmpb++) - u; + + /* U = carry bit of T[i] + * Note this saves performing an AND operation since + * if a carry does occur it will propagate all the way to the + * MSB. As a result a single shift is enough to get the carry + */ + u = *tmpc >> (MP_SIZEOF_BITS(mp_digit) - 1u); + + /* Clear carry from T[i] */ + *tmpc++ &= MP_MASK; + } + + /* now copy higher words if any, e.g. if A has more digits than B */ + for (; i < max; i++) { + /* T[i] = A[i] - U */ + *tmpc = *tmpa++ - u; + + /* U = carry bit of T[i] */ + u = *tmpc >> (MP_SIZEOF_BITS(mp_digit) - 1u); + + /* Clear carry from T[i] */ + *tmpc++ &= MP_MASK; + } + + /* clear digits above used (since we may not have grown result above) */ + MP_ZERO_DIGITS(tmpc, olduse - c->used); + } + + mp_clamp(c); + return MP_OKAY; +} + +#endif + +/* End: bn_s_mp_sub.c */ + +/* Start: bn_s_mp_toom_mul.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_TOOM_MUL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* multiplication using the Toom-Cook 3-way algorithm + * + * Much more complicated than Karatsuba but has a lower + * asymptotic running time of O(N**1.464). This algorithm is + * only particularly useful on VERY large inputs + * (we're talking 1000s of digits here...). +*/ + +/* + This file contains code from J. Arndt's book "Matters Computational" + and the accompanying FXT-library with permission of the author. +*/ + +/* + Setup from + + Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae." + 18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007. + + The interpolation from above needed one temporary variable more + than the interpolation here: + + Bodrato, Marco, and Alberto Zanoni. "What about Toom-Cook matrices optimality." + Centro Vito Volterra Universita di Roma Tor Vergata (2006) +*/ + +mp_err s_mp_toom_mul(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_int S1, S2, T1, a0, a1, a2, b0, b1, b2; + int B, count; + mp_err err; + + /* init temps */ + if ((err = mp_init_multi(&S1, &S2, &T1, NULL)) != MP_OKAY) { + return err; + } + + /* B */ + B = MP_MIN(a->used, b->used) / 3; + + /** a = a2 * x^2 + a1 * x + a0; */ + if ((err = mp_init_size(&a0, B)) != MP_OKAY) goto LBL_ERRa0; + + for (count = 0; count < B; count++) { + a0.dp[count] = a->dp[count]; + a0.used++; + } + mp_clamp(&a0); + if ((err = mp_init_size(&a1, B)) != MP_OKAY) goto LBL_ERRa1; + for (; count < (2 * B); count++) { + a1.dp[count - B] = a->dp[count]; + a1.used++; + } + mp_clamp(&a1); + if ((err = mp_init_size(&a2, B + (a->used - (3 * B)))) != MP_OKAY) goto LBL_ERRa2; + for (; count < a->used; count++) { + a2.dp[count - (2 * B)] = a->dp[count]; + a2.used++; + } + mp_clamp(&a2); + + /** b = b2 * x^2 + b1 * x + b0; */ + if ((err = mp_init_size(&b0, B)) != MP_OKAY) goto LBL_ERRb0; + for (count = 0; count < B; count++) { + b0.dp[count] = b->dp[count]; + b0.used++; + } + mp_clamp(&b0); + if ((err = mp_init_size(&b1, B)) != MP_OKAY) goto LBL_ERRb1; + for (; count < (2 * B); count++) { + b1.dp[count - B] = b->dp[count]; + b1.used++; + } + mp_clamp(&b1); + if ((err = mp_init_size(&b2, B + (b->used - (3 * B)))) != MP_OKAY) goto LBL_ERRb2; + for (; count < b->used; count++) { + b2.dp[count - (2 * B)] = b->dp[count]; + b2.used++; + } + mp_clamp(&b2); + + /** \\ S1 = (a2+a1+a0) * (b2+b1+b0); */ + /** T1 = a2 + a1; */ + if ((err = mp_add(&a2, &a1, &T1)) != MP_OKAY) goto LBL_ERR; + + /** S2 = T1 + a0; */ + if ((err = mp_add(&T1, &a0, &S2)) != MP_OKAY) goto LBL_ERR; + + /** c = b2 + b1; */ + if ((err = mp_add(&b2, &b1, c)) != MP_OKAY) goto LBL_ERR; + + /** S1 = c + b0; */ + if ((err = mp_add(c, &b0, &S1)) != MP_OKAY) goto LBL_ERR; + + /** S1 = S1 * S2; */ + if ((err = mp_mul(&S1, &S2, &S1)) != MP_OKAY) goto LBL_ERR; + + /** \\S2 = (4*a2+2*a1+a0) * (4*b2+2*b1+b0); */ + /** T1 = T1 + a2; */ + if ((err = mp_add(&T1, &a2, &T1)) != MP_OKAY) goto LBL_ERR; + + /** T1 = T1 << 1; */ + if ((err = mp_mul_2(&T1, &T1)) != MP_OKAY) goto LBL_ERR; + + /** T1 = T1 + a0; */ + if ((err = mp_add(&T1, &a0, &T1)) != MP_OKAY) goto LBL_ERR; + + /** c = c + b2; */ + if ((err = mp_add(c, &b2, c)) != MP_OKAY) goto LBL_ERR; + + /** c = c << 1; */ + if ((err = mp_mul_2(c, c)) != MP_OKAY) goto LBL_ERR; + + /** c = c + b0; */ + if ((err = mp_add(c, &b0, c)) != MP_OKAY) goto LBL_ERR; + + /** S2 = T1 * c; */ + if ((err = mp_mul(&T1, c, &S2)) != MP_OKAY) goto LBL_ERR; + + /** \\S3 = (a2-a1+a0) * (b2-b1+b0); */ + /** a1 = a2 - a1; */ + if ((err = mp_sub(&a2, &a1, &a1)) != MP_OKAY) goto LBL_ERR; + + /** a1 = a1 + a0; */ + if ((err = mp_add(&a1, &a0, &a1)) != MP_OKAY) goto LBL_ERR; + + /** b1 = b2 - b1; */ + if ((err = mp_sub(&b2, &b1, &b1)) != MP_OKAY) goto LBL_ERR; + + /** b1 = b1 + b0; */ + if ((err = mp_add(&b1, &b0, &b1)) != MP_OKAY) goto LBL_ERR; + + /** a1 = a1 * b1; */ + if ((err = mp_mul(&a1, &b1, &a1)) != MP_OKAY) goto LBL_ERR; + + /** b1 = a2 * b2; */ + if ((err = mp_mul(&a2, &b2, &b1)) != MP_OKAY) goto LBL_ERR; + + /** \\S2 = (S2 - S3)/3; */ + /** S2 = S2 - a1; */ + if ((err = mp_sub(&S2, &a1, &S2)) != MP_OKAY) goto LBL_ERR; + + /** S2 = S2 / 3; \\ this is an exact division */ + if ((err = mp_div_3(&S2, &S2, NULL)) != MP_OKAY) goto LBL_ERR; + + /** a1 = S1 - a1; */ + if ((err = mp_sub(&S1, &a1, &a1)) != MP_OKAY) goto LBL_ERR; + + /** a1 = a1 >> 1; */ + if ((err = mp_div_2(&a1, &a1)) != MP_OKAY) goto LBL_ERR; + + /** a0 = a0 * b0; */ + if ((err = mp_mul(&a0, &b0, &a0)) != MP_OKAY) goto LBL_ERR; + + /** S1 = S1 - a0; */ + if ((err = mp_sub(&S1, &a0, &S1)) != MP_OKAY) goto LBL_ERR; + + /** S2 = S2 - S1; */ + if ((err = mp_sub(&S2, &S1, &S2)) != MP_OKAY) goto LBL_ERR; + + /** S2 = S2 >> 1; */ + if ((err = mp_div_2(&S2, &S2)) != MP_OKAY) goto LBL_ERR; + + /** S1 = S1 - a1; */ + if ((err = mp_sub(&S1, &a1, &S1)) != MP_OKAY) goto LBL_ERR; + + /** S1 = S1 - b1; */ + if ((err = mp_sub(&S1, &b1, &S1)) != MP_OKAY) goto LBL_ERR; + + /** T1 = b1 << 1; */ + if ((err = mp_mul_2(&b1, &T1)) != MP_OKAY) goto LBL_ERR; + + /** S2 = S2 - T1; */ + if ((err = mp_sub(&S2, &T1, &S2)) != MP_OKAY) goto LBL_ERR; + + /** a1 = a1 - S2; */ + if ((err = mp_sub(&a1, &S2, &a1)) != MP_OKAY) goto LBL_ERR; + + + /** P = b1*x^4+ S2*x^3+ S1*x^2+ a1*x + a0; */ + if ((err = mp_lshd(&b1, 4 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(&S2, 3 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&b1, &S2, &b1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(&S1, 2 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&b1, &S1, &b1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(&a1, 1 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&b1, &a1, &b1)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&b1, &a0, c)) != MP_OKAY) goto LBL_ERR; + + /** a * b - P */ + + +LBL_ERR: + mp_clear(&b2); +LBL_ERRb2: + mp_clear(&b1); +LBL_ERRb1: + mp_clear(&b0); +LBL_ERRb0: + mp_clear(&a2); +LBL_ERRa2: + mp_clear(&a1); +LBL_ERRa1: + mp_clear(&a0); +LBL_ERRa0: + mp_clear_multi(&S1, &S2, &T1, NULL); + return err; +} + +#endif + +/* End: bn_s_mp_toom_mul.c */ + +/* Start: bn_s_mp_toom_sqr.c */ +#include "tommath_private.h" +#ifdef BN_S_MP_TOOM_SQR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis */ +/* SPDX-License-Identifier: Unlicense */ + +/* squaring using Toom-Cook 3-way algorithm */ + +/* + This file contains code from J. Arndt's book "Matters Computational" + and the accompanying FXT-library with permission of the author. +*/ + +/* squaring using Toom-Cook 3-way algorithm */ +/* + Setup and interpolation from algorithm SQR_3 in + + Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae." + 18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007. + +*/ +mp_err s_mp_toom_sqr(const mp_int *a, mp_int *b) +{ + mp_int S0, a0, a1, a2; + mp_digit *tmpa, *tmpc; + int B, count; + mp_err err; + + + /* init temps */ + if ((err = mp_init(&S0)) != MP_OKAY) { + return err; + } + + /* B */ + B = a->used / 3; + + /** a = a2 * x^2 + a1 * x + a0; */ + if ((err = mp_init_size(&a0, B)) != MP_OKAY) goto LBL_ERRa0; + + a0.used = B; + if ((err = mp_init_size(&a1, B)) != MP_OKAY) goto LBL_ERRa1; + a1.used = B; + if ((err = mp_init_size(&a2, B + (a->used - (3 * B)))) != MP_OKAY) goto LBL_ERRa2; + + tmpa = a->dp; + tmpc = a0.dp; + for (count = 0; count < B; count++) { + *tmpc++ = *tmpa++; + } + tmpc = a1.dp; + for (; count < (2 * B); count++) { + *tmpc++ = *tmpa++; + } + tmpc = a2.dp; + for (; count < a->used; count++) { + *tmpc++ = *tmpa++; + a2.used++; + } + mp_clamp(&a0); + mp_clamp(&a1); + mp_clamp(&a2); + + /** S0 = a0^2; */ + if ((err = mp_sqr(&a0, &S0)) != MP_OKAY) goto LBL_ERR; + + /** \\S1 = (a2 + a1 + a0)^2 */ + /** \\S2 = (a2 - a1 + a0)^2 */ + /** \\S1 = a0 + a2; */ + /** a0 = a0 + a2; */ + if ((err = mp_add(&a0, &a2, &a0)) != MP_OKAY) goto LBL_ERR; + /** \\S2 = S1 - a1; */ + /** b = a0 - a1; */ + if ((err = mp_sub(&a0, &a1, b)) != MP_OKAY) goto LBL_ERR; + /** \\S1 = S1 + a1; */ + /** a0 = a0 + a1; */ + if ((err = mp_add(&a0, &a1, &a0)) != MP_OKAY) goto LBL_ERR; + /** \\S1 = S1^2; */ + /** a0 = a0^2; */ + if ((err = mp_sqr(&a0, &a0)) != MP_OKAY) goto LBL_ERR; + /** \\S2 = S2^2; */ + /** b = b^2; */ + if ((err = mp_sqr(b, b)) != MP_OKAY) goto LBL_ERR; + + /** \\ S3 = 2 * a1 * a2 */ + /** \\S3 = a1 * a2; */ + /** a1 = a1 * a2; */ + if ((err = mp_mul(&a1, &a2, &a1)) != MP_OKAY) goto LBL_ERR; + /** \\S3 = S3 << 1; */ + /** a1 = a1 << 1; */ + if ((err = mp_mul_2(&a1, &a1)) != MP_OKAY) goto LBL_ERR; + + /** \\S4 = a2^2; */ + /** a2 = a2^2; */ + if ((err = mp_sqr(&a2, &a2)) != MP_OKAY) goto LBL_ERR; + + /** \\ tmp = (S1 + S2)/2 */ + /** \\tmp = S1 + S2; */ + /** b = a0 + b; */ + if ((err = mp_add(&a0, b, b)) != MP_OKAY) goto LBL_ERR; + /** \\tmp = tmp >> 1; */ + /** b = b >> 1; */ + if ((err = mp_div_2(b, b)) != MP_OKAY) goto LBL_ERR; + + /** \\ S1 = S1 - tmp - S3 */ + /** \\S1 = S1 - tmp; */ + /** a0 = a0 - b; */ + if ((err = mp_sub(&a0, b, &a0)) != MP_OKAY) goto LBL_ERR; + /** \\S1 = S1 - S3; */ + /** a0 = a0 - a1; */ + if ((err = mp_sub(&a0, &a1, &a0)) != MP_OKAY) goto LBL_ERR; + + /** \\S2 = tmp - S4 -S0 */ + /** \\S2 = tmp - S4; */ + /** b = b - a2; */ + if ((err = mp_sub(b, &a2, b)) != MP_OKAY) goto LBL_ERR; + /** \\S2 = S2 - S0; */ + /** b = b - S0; */ + if ((err = mp_sub(b, &S0, b)) != MP_OKAY) goto LBL_ERR; + + + /** \\P = S4*x^4 + S3*x^3 + S2*x^2 + S1*x + S0; */ + /** P = a2*x^4 + a1*x^3 + b*x^2 + a0*x + S0; */ + + if ((err = mp_lshd(&a2, 4 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(&a1, 3 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(b, 2 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_lshd(&a0, 1 * B)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&a2, &a1, &a2)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(&a2, b, b)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(b, &a0, b)) != MP_OKAY) goto LBL_ERR; + if ((err = mp_add(b, &S0, b)) != MP_OKAY) goto LBL_ERR; + /** a^2 - P */ + + +LBL_ERR: + mp_clear(&a2); +LBL_ERRa2: + mp_clear(&a1); +LBL_ERRa1: + mp_clear(&a0); +LBL_ERRa0: + mp_clear(&S0); + + return err; +} + +#endif + +/* End: bn_s_mp_toom_sqr.c */ + + +/* EOF */ |