/* $OpenBSD: bn_lib.c,v 1.31 2014/07/10 22:45:56 jsing Exp $ */ /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) * All rights reserved. * * This package is an SSL implementation written * by Eric Young (eay@cryptsoft.com). * The implementation was written so as to conform with Netscapes SSL. * * This library is free for commercial and non-commercial use as long as * the following conditions are aheared to. The following conditions * apply to all code found in this distribution, be it the RC4, RSA, * lhash, DES, etc., code; not just the SSL code. The SSL documentation * included with this distribution is covered by the same copyright terms * except that the holder is Tim Hudson (tjh@cryptsoft.com). * * Copyright remains Eric Young's, and as such any Copyright notices in * the code are not to be removed. * If this package is used in a product, Eric Young should be given attribution * as the author of the parts of the library used. * This can be in the form of a textual message at program startup or * in documentation (online or textual) provided with the package. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. All advertising materials mentioning features or use of this software * must display the following acknowledgement: * "This product includes cryptographic software written by * Eric Young (eay@cryptsoft.com)" * The word 'cryptographic' can be left out if the rouines from the library * being used are not cryptographic related :-). * 4. If you include any Windows specific code (or a derivative thereof) from * the apps directory (application code) you must include an acknowledgement: * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" * * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * * The licence and distribution terms for any publically available version or * derivative of this code cannot be changed. i.e. this code cannot simply be * copied and put under another distribution licence * [including the GNU Public Licence.] */ #ifndef BN_DEBUG # undef NDEBUG /* avoid conflicting definitions */ # define NDEBUG #endif #include #include #include #include #include #include #include "bn_lcl.h" /* This stuff appears to be completely unused, so is deprecated */ #ifndef OPENSSL_NO_DEPRECATED /* 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, }; #ifdef _LP64 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 #endif { if (l & 0xffff0000L) { if (l & 0xff000000L) return (bits[(int)(l >> 24L)] + 24); else return (bits[(int)(l >> 16L)] + 16); } else { if (l & 0xff00L) return (bits[(int)(l >> 8)] + 8); else 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])); } void BN_clear_free(BIGNUM *a) { int i; if (a == NULL) return; bn_check_top(a); if (a->d != NULL && !(BN_get_flags(a, BN_FLG_STATIC_DATA))) { OPENSSL_cleanse(a->d, a->dmax * sizeof(a->d[0])); free(a->d); } i = BN_get_flags(a, BN_FLG_MALLOCED); OPENSSL_cleanse(a, sizeof(BIGNUM)); if (i) free(a); } void BN_free(BIGNUM *a) { BN_clear_free(a); } void BN_init(BIGNUM *a) { memset(a, 0, sizeof(BIGNUM)); bn_check_top(a); } BIGNUM * BN_new(void) { BIGNUM *ret; if ((ret = malloc(sizeof(BIGNUM))) == NULL) { BNerr(BN_F_BN_NEW, ERR_R_MALLOC_FAILURE); return (NULL); } ret->flags = BN_FLG_MALLOCED; ret->top = 0; ret->neg = 0; ret->dmax = 0; ret->d = NULL; bn_check_top(ret); return (ret); } /* This is used both by bn_expand2() and bn_dup_expand() */ /* 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, *a = NULL; const BN_ULONG *B; int i; 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); } a = A = reallocarray(NULL, words, sizeof(BN_ULONG)); if (A == NULL) { BNerr(BN_F_BN_EXPAND_INTERNAL, ERR_R_MALLOC_FAILURE); return (NULL); } #if 1 B = b->d; /* Check if the previous number needs to be copied */ if (B != NULL) { for (i = b->top >> 2; i > 0; i--, A += 4, B += 4) { /* * The fact that the loop is unrolled * 4-wise is a tribute to Intel. It's * the one that doesn't have enough * registers to accomodate more data. * I'd unroll it 8-wise otherwise:-) * * */ BN_ULONG a0, a1, a2, a3; a0 = B[0]; a1 = B[1]; a2 = B[2]; a3 = B[3]; A[0] = a0; A[1] = a1; A[2] = a2; A[3] = a3; } switch (b->top & 3) { case 3: A[2] = B[2]; case 2: A[1] = B[1]; case 1: A[0] = B[0]; } } #else memset(A, 0, sizeof(BN_ULONG) * words); memcpy(A, b->d, sizeof(b->d[0]) * b->top); #endif return (a); } /* This is an internal function that can be used instead of bn_expand2() * when there is a need to copy BIGNUMs instead of only expanding the * data part, while still expanding them. * Especially useful when needing to expand BIGNUMs that are declared * 'const' and should therefore not be changed. * The reason to use this instead of a BN_dup() followed by a bn_expand2() * is memory allocation overhead. A BN_dup() followed by a bn_expand2() * will allocate new memory for the BIGNUM data twice, and free it once, * while bn_dup_expand() makes sure allocation is made only once. */ #ifndef OPENSSL_NO_DEPRECATED BIGNUM * bn_dup_expand(const BIGNUM *b, int words) { BIGNUM *r = NULL; bn_check_top(b); /* This function does not work if * words <= b->dmax && top < words * because BN_dup() does not preserve 'dmax'! * (But bn_dup_expand() is not used anywhere yet.) */ if (words > b->dmax) { BN_ULONG *a = bn_expand_internal(b, words); if (a) { r = BN_new(); if (r) { r->top = b->top; r->dmax = words; r->neg = b->neg; r->d = a; } else { /* r == NULL, BN_new failure */ free(a); } } /* If a == NULL, there was an error in allocation in bn_expand_internal(), and NULL should be returned */ } else { r = BN_dup(b); } bn_check_top(r); return r; } #endif /* 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])); free(b->d); } b->d = a; b->dmax = words; } /* None of this should be necessary because of what b->top means! */ #if 0 /* NB: bn_wexpand() calls this only if the BIGNUM really has to grow */ if (b->top < b->dmax) { int i; BN_ULONG *A = &(b->d[b->top]); for (i = (b->dmax - b->top) >> 3; i > 0; i--, A += 8) { A[0] = 0; A[1] = 0; A[2] = 0; A[3] = 0; A[4] = 0; A[5] = 0; A[6] = 0; A[7] = 0; } for (i = (b->dmax - b->top)&7; i > 0; i--, A++) A[0] = 0; assert(A == &(b->d[b->dmax])); } #endif 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_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) { int i; BN_ULONG *A; const BN_ULONG *B; bn_check_top(b); if (a == b) return (a); if (bn_wexpand(a, b->top) == NULL) return (NULL); #if 1 A = a->d; B = b->d; for (i = b->top >> 2; i > 0; i--, A += 4, B += 4) { BN_ULONG a0, a1, a2, a3; a0 = B[0]; a1 = B[1]; a2 = B[2]; a3 = B[3]; A[0] = a0; A[1] = a1; A[2] = a2; A[3] = a3; } switch (b->top & 3) { case 3: A[2] = B[2]; case 2: A[1] = B[1]; case 1: A[0] = B[0]; } #else memcpy(a->d, b->d, sizeof(b->d[0]) * b->top); #endif 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) memset(a->d, 0, a->dmax * sizeof(a->d[0])); 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); l = 0; 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) { if (bn) BN_free(bn); return NULL; } ret->top = i; ret->neg = 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 */ int BN_bn2bin(const BIGNUM *a, unsigned char *to) { int n, i; BN_ULONG l; bn_check_top(a); n = i=BN_num_bytes(a); while (i--) { l = a->d[i / BN_BYTES]; *(to++) = (unsigned char)(l >> (8 * (i % BN_BYTES))) & 0xff; } return (n); } 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 property of performing the operation on arrays of different sizes. The sizes of those arrays is expressed through cl, which is the common length ( basicall, 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 }