/* * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved. * * Licensed under the OpenSSL license (the "License"). You may not use * this file except in compliance with the License. You can obtain a copy * in the file LICENSE in the source distribution or at * https://www.openssl.org/source/license.html */ #include #include #include "internal/cryptlib.h" #include "bn_lcl.h" #include /* This stuff appears to be completely unused, so is deprecated */ #if OPENSSL_API_COMPAT < 0x00908000L /*- * For a 32 bit machine * 2 - 4 == 128 * 3 - 8 == 256 * 4 - 16 == 512 * 5 - 32 == 1024 * 6 - 64 == 2048 * 7 - 128 == 4096 * 8 - 256 == 8192 */ static int bn_limit_bits = 0; static int bn_limit_num = 8; /* (1<= 0) { if (mult > (int)(sizeof(int) * 8) - 1) mult = sizeof(int) * 8 - 1; bn_limit_bits = mult; bn_limit_num = 1 << mult; } if (high >= 0) { if (high > (int)(sizeof(int) * 8) - 1) high = sizeof(int) * 8 - 1; bn_limit_bits_high = high; bn_limit_num_high = 1 << high; } if (low >= 0) { if (low > (int)(sizeof(int) * 8) - 1) low = sizeof(int) * 8 - 1; bn_limit_bits_low = low; bn_limit_num_low = 1 << low; } if (mont >= 0) { if (mont > (int)(sizeof(int) * 8) - 1) mont = sizeof(int) * 8 - 1; bn_limit_bits_mont = mont; bn_limit_num_mont = 1 << mont; } } int BN_get_params(int which) { if (which == 0) return (bn_limit_bits); else if (which == 1) return (bn_limit_bits_high); else if (which == 2) return (bn_limit_bits_low); else if (which == 3) return (bn_limit_bits_mont); else return (0); } #endif const BIGNUM *BN_value_one(void) { static const BN_ULONG data_one = 1L; static const BIGNUM const_one = { (BN_ULONG *)&data_one, 1, 1, 0, BN_FLG_STATIC_DATA }; return (&const_one); } int BN_num_bits_word(BN_ULONG l) { static const unsigned char bits[256] = { 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, }; #if defined(SIXTY_FOUR_BIT_LONG) if (l & 0xffffffff00000000L) { if (l & 0xffff000000000000L) { if (l & 0xff00000000000000L) { return (bits[(int)(l >> 56)] + 56); } else return (bits[(int)(l >> 48)] + 48); } else { if (l & 0x0000ff0000000000L) { return (bits[(int)(l >> 40)] + 40); } else return (bits[(int)(l >> 32)] + 32); } } else #else # ifdef SIXTY_FOUR_BIT if (l & 0xffffffff00000000LL) { if (l & 0xffff000000000000LL) { if (l & 0xff00000000000000LL) { return (bits[(int)(l >> 56)] + 56); } else return (bits[(int)(l >> 48)] + 48); } else { if (l & 0x0000ff0000000000LL) { return (bits[(int)(l >> 40)] + 40); } else return (bits[(int)(l >> 32)] + 32); } } else # endif #endif { #if defined(THIRTY_TWO_BIT) || defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG) if (l & 0xffff0000L) { if (l & 0xff000000L) return (bits[(int)(l >> 24L)] + 24); else return (bits[(int)(l >> 16L)] + 16); } else #endif { #if defined(THIRTY_TWO_BIT) || defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG) if (l & 0xff00L) return (bits[(int)(l >> 8)] + 8); else #endif return (bits[(int)(l)]); } } } int BN_num_bits(const BIGNUM *a) { int i = a->top - 1; bn_check_top(a); if (BN_is_zero(a)) return 0; return ((i * BN_BITS2) + BN_num_bits_word(a->d[i])); } static void bn_free_d(BIGNUM *a) { if (BN_get_flags(a, BN_FLG_SECURE)) OPENSSL_secure_free(a->d); else OPENSSL_free(a->d); } void BN_clear_free(BIGNUM *a) { int i; if (a == NULL) return; bn_check_top(a); if (a->d != NULL) { OPENSSL_cleanse(a->d, a->dmax * sizeof(a->d[0])); if (!BN_get_flags(a, BN_FLG_STATIC_DATA)) bn_free_d(a); } i = BN_get_flags(a, BN_FLG_MALLOCED); OPENSSL_cleanse(a, sizeof(*a)); if (i) OPENSSL_free(a); } void BN_free(BIGNUM *a) { if (a == NULL) return; bn_check_top(a); if (!BN_get_flags(a, BN_FLG_STATIC_DATA)) bn_free_d(a); if (a->flags & BN_FLG_MALLOCED) OPENSSL_free(a); else { #if OPENSSL_API_COMPAT < 0x00908000L a->flags |= BN_FLG_FREE; #endif a->d = NULL; } } void bn_init(BIGNUM *a) { static BIGNUM nilbn; *a = nilbn; bn_check_top(a); } BIGNUM *BN_new(void) { BIGNUM *ret; if ((ret = OPENSSL_zalloc(sizeof(*ret))) == NULL) { BNerr(BN_F_BN_NEW, ERR_R_MALLOC_FAILURE); return (NULL); } ret->flags = BN_FLG_MALLOCED; bn_check_top(ret); return (ret); } BIGNUM *BN_secure_new(void) { BIGNUM *ret = BN_new(); if (ret != NULL) ret->flags |= BN_FLG_SECURE; return (ret); } /* This is used by bn_expand2() */ /* The caller MUST check that words > b->dmax before calling this */ static BN_ULONG *bn_expand_internal(const BIGNUM *b, int words) { BN_ULONG *a = NULL; bn_check_top(b); if (words > (INT_MAX / (4 * BN_BITS2))) { BNerr(BN_F_BN_EXPAND_INTERNAL, BN_R_BIGNUM_TOO_LONG); return NULL; } if (BN_get_flags(b, BN_FLG_STATIC_DATA)) { BNerr(BN_F_BN_EXPAND_INTERNAL, BN_R_EXPAND_ON_STATIC_BIGNUM_DATA); return (NULL); } if (BN_get_flags(b, BN_FLG_SECURE)) a = OPENSSL_secure_zalloc(words * sizeof(*a)); else a = OPENSSL_zalloc(words * sizeof(*a)); if (a == NULL) { BNerr(BN_F_BN_EXPAND_INTERNAL, ERR_R_MALLOC_FAILURE); return (NULL); } assert(b->top <= words); if (b->top > 0) memcpy(a, b->d, sizeof(*a) * b->top); return a; } /* * This is an internal function that should not be used in applications. It * ensures that 'b' has enough room for a 'words' word number and initialises * any unused part of b->d with leading zeros. It is mostly used by the * various BIGNUM routines. If there is an error, NULL is returned. If not, * 'b' is returned. */ BIGNUM *bn_expand2(BIGNUM *b, int words) { bn_check_top(b); if (words > b->dmax) { BN_ULONG *a = bn_expand_internal(b, words); if (!a) return NULL; if (b->d) { OPENSSL_cleanse(b->d, b->dmax * sizeof(b->d[0])); bn_free_d(b); } b->d = a; b->dmax = words; } bn_check_top(b); return b; } BIGNUM *BN_dup(const BIGNUM *a) { BIGNUM *t; if (a == NULL) return NULL; bn_check_top(a); t = BN_get_flags(a, BN_FLG_SECURE) ? BN_secure_new() : BN_new(); if (t == NULL) return NULL; if (!BN_copy(t, a)) { BN_free(t); return NULL; } bn_check_top(t); return t; } BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b) { bn_check_top(b); if (a == b) return a; if (bn_wexpand(a, b->top) == NULL) return NULL; if (b->top > 0) memcpy(a->d, b->d, sizeof(b->d[0]) * b->top); if (BN_get_flags(b, BN_FLG_CONSTTIME) != 0) BN_set_flags(a, BN_FLG_CONSTTIME); a->top = b->top; a->neg = b->neg; bn_check_top(a); return a; } void BN_swap(BIGNUM *a, BIGNUM *b) { int flags_old_a, flags_old_b; BN_ULONG *tmp_d; int tmp_top, tmp_dmax, tmp_neg; bn_check_top(a); bn_check_top(b); flags_old_a = a->flags; flags_old_b = b->flags; tmp_d = a->d; tmp_top = a->top; tmp_dmax = a->dmax; tmp_neg = a->neg; a->d = b->d; a->top = b->top; a->dmax = b->dmax; a->neg = b->neg; b->d = tmp_d; b->top = tmp_top; b->dmax = tmp_dmax; b->neg = tmp_neg; a->flags = (flags_old_a & BN_FLG_MALLOCED) | (flags_old_b & BN_FLG_STATIC_DATA); b->flags = (flags_old_b & BN_FLG_MALLOCED) | (flags_old_a & BN_FLG_STATIC_DATA); bn_check_top(a); bn_check_top(b); } void BN_clear(BIGNUM *a) { bn_check_top(a); if (a->d != NULL) OPENSSL_cleanse(a->d, sizeof(*a->d) * a->dmax); a->top = 0; a->neg = 0; } BN_ULONG BN_get_word(const BIGNUM *a) { if (a->top > 1) return BN_MASK2; else if (a->top == 1) return a->d[0]; /* a->top == 0 */ return 0; } int BN_set_word(BIGNUM *a, BN_ULONG w) { bn_check_top(a); if (bn_expand(a, (int)sizeof(BN_ULONG) * 8) == NULL) return (0); a->neg = 0; a->d[0] = w; a->top = (w ? 1 : 0); bn_check_top(a); return 1; } BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret) { unsigned int i, m; unsigned int n; BN_ULONG l; BIGNUM *bn = NULL; if (ret == NULL) ret = bn = BN_new(); if (ret == NULL) return (NULL); bn_check_top(ret); /* Skip leading zero's. */ for ( ; len > 0 && *s == 0; s++, len--) continue; n = len; if (n == 0) { ret->top = 0; return (ret); } i = ((n - 1) / BN_BYTES) + 1; m = ((n - 1) % (BN_BYTES)); if (bn_wexpand(ret, (int)i) == NULL) { BN_free(bn); return NULL; } ret->top = i; ret->neg = 0; l = 0; while (n--) { l = (l << 8L) | *(s++); if (m-- == 0) { ret->d[--i] = l; l = 0; m = BN_BYTES - 1; } } /* * need to call this due to clear byte at top if avoiding having the top * bit set (-ve number) */ bn_correct_top(ret); return (ret); } /* ignore negative */ static int bn2binpad(const BIGNUM *a, unsigned char *to, int tolen) { int i; BN_ULONG l; bn_check_top(a); i = BN_num_bytes(a); if (tolen == -1) tolen = i; else if (tolen < i) return -1; /* Add leading zeroes if necessary */ if (tolen > i) { memset(to, 0, tolen - i); to += tolen - i; } while (i--) { l = a->d[i / BN_BYTES]; *(to++) = (unsigned char)(l >> (8 * (i % BN_BYTES))) & 0xff; } return tolen; } int BN_bn2binpad(const BIGNUM *a, unsigned char *to, int tolen) { if (tolen < 0) return -1; return bn2binpad(a, to, tolen); } int BN_bn2bin(const BIGNUM *a, unsigned char *to) { return bn2binpad(a, to, -1); } BIGNUM *BN_lebin2bn(const unsigned char *s, int len, BIGNUM *ret) { unsigned int i, m; unsigned int n; BN_ULONG l; BIGNUM *bn = NULL; if (ret == NULL) ret = bn = BN_new(); if (ret == NULL) return (NULL); bn_check_top(ret); s += len; /* Skip trailing zeroes. */ for ( ; len > 0 && s[-1] == 0; s--, len--) continue; n = len; if (n == 0) { ret->top = 0; return ret; } i = ((n - 1) / BN_BYTES) + 1; m = ((n - 1) % (BN_BYTES)); if (bn_wexpand(ret, (int)i) == NULL) { BN_free(bn); return NULL; } ret->top = i; ret->neg = 0; l = 0; while (n--) { s--; l = (l << 8L) | *s; if (m-- == 0) { ret->d[--i] = l; l = 0; m = BN_BYTES - 1; } } /* * need to call this due to clear byte at top if avoiding having the top * bit set (-ve number) */ bn_correct_top(ret); return ret; } int BN_bn2lebinpad(const BIGNUM *a, unsigned char *to, int tolen) { int i; BN_ULONG l; bn_check_top(a); i = BN_num_bytes(a); if (tolen < i) return -1; /* Add trailing zeroes if necessary */ if (tolen > i) memset(to + i, 0, tolen - i); to += i; while (i--) { l = a->d[i / BN_BYTES]; to--; *to = (unsigned char)(l >> (8 * (i % BN_BYTES))) & 0xff; } return tolen; } int BN_ucmp(const BIGNUM *a, const BIGNUM *b) { int i; BN_ULONG t1, t2, *ap, *bp; bn_check_top(a); bn_check_top(b); i = a->top - b->top; if (i != 0) return (i); ap = a->d; bp = b->d; for (i = a->top - 1; i >= 0; i--) { t1 = ap[i]; t2 = bp[i]; if (t1 != t2) return ((t1 > t2) ? 1 : -1); } return (0); } int BN_cmp(const BIGNUM *a, const BIGNUM *b) { int i; int gt, lt; BN_ULONG t1, t2; if ((a == NULL) || (b == NULL)) { if (a != NULL) return (-1); else if (b != NULL) return 1; else return (0); } bn_check_top(a); bn_check_top(b); if (a->neg != b->neg) { if (a->neg) return (-1); else return 1; } if (a->neg == 0) { gt = 1; lt = -1; } else { gt = -1; lt = 1; } if (a->top > b->top) return (gt); if (a->top < b->top) return (lt); for (i = a->top - 1; i >= 0; i--) { t1 = a->d[i]; t2 = b->d[i]; if (t1 > t2) return (gt); if (t1 < t2) return (lt); } return (0); } int BN_set_bit(BIGNUM *a, int n) { int i, j, k; if (n < 0) return 0; i = n / BN_BITS2; j = n % BN_BITS2; if (a->top <= i) { if (bn_wexpand(a, i + 1) == NULL) return (0); for (k = a->top; k < i + 1; k++) a->d[k] = 0; a->top = i + 1; } a->d[i] |= (((BN_ULONG)1) << j); bn_check_top(a); return 1; } int BN_clear_bit(BIGNUM *a, int n) { int i, j; bn_check_top(a); if (n < 0) return 0; i = n / BN_BITS2; j = n % BN_BITS2; if (a->top <= i) return (0); a->d[i] &= (~(((BN_ULONG)1) << j)); bn_correct_top(a); return 1; } int BN_is_bit_set(const BIGNUM *a, int n) { int i, j; bn_check_top(a); if (n < 0) return 0; i = n / BN_BITS2; j = n % BN_BITS2; if (a->top <= i) return 0; return (int)(((a->d[i]) >> j) & ((BN_ULONG)1)); } int BN_mask_bits(BIGNUM *a, int n) { int b, w; bn_check_top(a); if (n < 0) return 0; w = n / BN_BITS2; b = n % BN_BITS2; if (w >= a->top) return 0; if (b == 0) a->top = w; else { a->top = w + 1; a->d[w] &= ~(BN_MASK2 << b); } bn_correct_top(a); return 1; } void BN_set_negative(BIGNUM *a, int b) { if (b && !BN_is_zero(a)) a->neg = 1; else a->neg = 0; } int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n) { int i; BN_ULONG aa, bb; aa = a[n - 1]; bb = b[n - 1]; if (aa != bb) return ((aa > bb) ? 1 : -1); for (i = n - 2; i >= 0; i--) { aa = a[i]; bb = b[i]; if (aa != bb) return ((aa > bb) ? 1 : -1); } return (0); } /* * Here follows a specialised variants of bn_cmp_words(). It has the * capability of performing the operation on arrays of different sizes. The * sizes of those arrays is expressed through cl, which is the common length * ( basically, min(len(a),len(b)) ), and dl, which is the delta between the * two lengths, calculated as len(a)-len(b). All lengths are the number of * BN_ULONGs... */ int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl) { int n, i; n = cl - 1; if (dl < 0) { for (i = dl; i < 0; i++) { if (b[n - i] != 0) return -1; /* a < b */ } } if (dl > 0) { for (i = dl; i > 0; i--) { if (a[n + i] != 0) return 1; /* a > b */ } } return bn_cmp_words(a, b, cl); } /* * Constant-time conditional swap of a and b. * a and b are swapped if condition is not 0. The code assumes that at most one bit of condition is set. * nwords is the number of words to swap. The code assumes that at least nwords are allocated in both a and b, * and that no more than nwords are used by either a or b. * a and b cannot be the same number */ void BN_consttime_swap(BN_ULONG condition, BIGNUM *a, BIGNUM *b, int nwords) { BN_ULONG t; int i; bn_wcheck_size(a, nwords); bn_wcheck_size(b, nwords); assert(a != b); assert((condition & (condition - 1)) == 0); assert(sizeof(BN_ULONG) >= sizeof(int)); condition = ((condition - 1) >> (BN_BITS2 - 1)) - 1; t = (a->top ^ b->top) & condition; a->top ^= t; b->top ^= t; #define BN_CONSTTIME_SWAP(ind) \ do { \ t = (a->d[ind] ^ b->d[ind]) & condition; \ a->d[ind] ^= t; \ b->d[ind] ^= t; \ } while (0) switch (nwords) { default: for (i = 10; i < nwords; i++) BN_CONSTTIME_SWAP(i); /* Fallthrough */ case 10: BN_CONSTTIME_SWAP(9); /* Fallthrough */ case 9: BN_CONSTTIME_SWAP(8); /* Fallthrough */ case 8: BN_CONSTTIME_SWAP(7); /* Fallthrough */ case 7: BN_CONSTTIME_SWAP(6); /* Fallthrough */ case 6: BN_CONSTTIME_SWAP(5); /* Fallthrough */ case 5: BN_CONSTTIME_SWAP(4); /* Fallthrough */ case 4: BN_CONSTTIME_SWAP(3); /* Fallthrough */ case 3: BN_CONSTTIME_SWAP(2); /* Fallthrough */ case 2: BN_CONSTTIME_SWAP(1); /* Fallthrough */ case 1: BN_CONSTTIME_SWAP(0); } #undef BN_CONSTTIME_SWAP } /* Bits of security, see SP800-57 */ int BN_security_bits(int L, int N) { int secbits, bits; if (L >= 15360) secbits = 256; else if (L >= 7690) secbits = 192; else if (L >= 3072) secbits = 128; else if (L >= 2048) secbits = 112; else if (L >= 1024) secbits = 80; else return 0; if (N == -1) return secbits; bits = N / 2; if (bits < 80) return 0; return bits >= secbits ? secbits : bits; } void BN_zero_ex(BIGNUM *a) { a->top = 0; a->neg = 0; } int BN_abs_is_word(const BIGNUM *a, const BN_ULONG w) { return ((a->top == 1) && (a->d[0] == w)) || ((w == 0) && (a->top == 0)); } int BN_is_zero(const BIGNUM *a) { return a->top == 0; } int BN_is_one(const BIGNUM *a) { return BN_abs_is_word(a, 1) && !a->neg; } int BN_is_word(const BIGNUM *a, const BN_ULONG w) { return BN_abs_is_word(a, w) && (!w || !a->neg); } int BN_is_odd(const BIGNUM *a) { return (a->top > 0) && (a->d[0] & 1); } int BN_is_negative(const BIGNUM *a) { return (a->neg != 0); } int BN_to_montgomery(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont, BN_CTX *ctx) { return BN_mod_mul_montgomery(r, a, &(mont->RR), mont, ctx); } void BN_with_flags(BIGNUM *dest, const BIGNUM *b, int flags) { dest->d = b->d; dest->top = b->top; dest->dmax = b->dmax; dest->neg = b->neg; dest->flags = ((dest->flags & BN_FLG_MALLOCED) | (b->flags & ~BN_FLG_MALLOCED) | BN_FLG_STATIC_DATA | flags); } BN_GENCB *BN_GENCB_new(void) { BN_GENCB *ret; if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL) { BNerr(BN_F_BN_GENCB_NEW, ERR_R_MALLOC_FAILURE); return (NULL); } return ret; } void BN_GENCB_free(BN_GENCB *cb) { if (cb == NULL) return; OPENSSL_free(cb); } void BN_set_flags(BIGNUM *b, int n) { b->flags |= n; } int BN_get_flags(const BIGNUM *b, int n) { return b->flags & n; } /* Populate a BN_GENCB structure with an "old"-style callback */ void BN_GENCB_set_old(BN_GENCB *gencb, void (*callback) (int, int, void *), void *cb_arg) { BN_GENCB *tmp_gencb = gencb; tmp_gencb->ver = 1; tmp_gencb->arg = cb_arg; tmp_gencb->cb.cb_1 = callback; } /* Populate a BN_GENCB structure with a "new"-style callback */ void BN_GENCB_set(BN_GENCB *gencb, int (*callback) (int, int, BN_GENCB *), void *cb_arg) { BN_GENCB *tmp_gencb = gencb; tmp_gencb->ver = 2; tmp_gencb->arg = cb_arg; tmp_gencb->cb.cb_2 = callback; } void *BN_GENCB_get_arg(BN_GENCB *cb) { return cb->arg; } BIGNUM *bn_wexpand(BIGNUM *a, int words) { return (words <= a->dmax) ? a : bn_expand2(a, words); } void bn_correct_top(BIGNUM *a) { BN_ULONG *ftl; int tmp_top = a->top; if (tmp_top > 0) { for (ftl = &(a->d[tmp_top]); tmp_top > 0; tmp_top--) { ftl--; if (*ftl != 0) break; } a->top = tmp_top; } if (a->top == 0) a->neg = 0; bn_pollute(a); }