1 /* crypto/bn/bn_lib.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
60 # undef NDEBUG /* avoid conflicting definitions */
70 const char BN_version[] = "Big Number" OPENSSL_VERSION_PTEXT;
72 /* This stuff appears to be completely unused, so is deprecated */
73 #ifndef OPENSSL_NO_DEPRECATED
75 * For a 32 bit machine
84 static int bn_limit_bits = 0;
85 static int bn_limit_num = 8; /* (1<<bn_limit_bits) */
86 static int bn_limit_bits_low = 0;
87 static int bn_limit_num_low = 8; /* (1<<bn_limit_bits_low) */
88 static int bn_limit_bits_high = 0;
89 static int bn_limit_num_high = 8; /* (1<<bn_limit_bits_high) */
90 static int bn_limit_bits_mont = 0;
91 static int bn_limit_num_mont = 8; /* (1<<bn_limit_bits_mont) */
93 void BN_set_params(int mult, int high, int low, int mont)
96 if (mult > (int)(sizeof(int) * 8) - 1)
97 mult = sizeof(int) * 8 - 1;
99 bn_limit_num = 1 << mult;
102 if (high > (int)(sizeof(int) * 8) - 1)
103 high = sizeof(int) * 8 - 1;
104 bn_limit_bits_high = high;
105 bn_limit_num_high = 1 << high;
108 if (low > (int)(sizeof(int) * 8) - 1)
109 low = sizeof(int) * 8 - 1;
110 bn_limit_bits_low = low;
111 bn_limit_num_low = 1 << low;
114 if (mont > (int)(sizeof(int) * 8) - 1)
115 mont = sizeof(int) * 8 - 1;
116 bn_limit_bits_mont = mont;
117 bn_limit_num_mont = 1 << mont;
121 int BN_get_params(int which)
124 return (bn_limit_bits);
126 return (bn_limit_bits_high);
128 return (bn_limit_bits_low);
130 return (bn_limit_bits_mont);
136 const BIGNUM *BN_value_one(void)
138 static BN_ULONG data_one = 1L;
139 static BIGNUM const_one = { &data_one, 1, 1, 0, BN_FLG_STATIC_DATA };
144 int BN_num_bits_word(BN_ULONG l)
146 static const char bits[256] = {
147 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4,
148 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
149 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
150 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
151 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
152 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
153 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
154 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
155 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
156 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
157 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
158 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
159 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
160 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
161 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
162 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
165 #if defined(SIXTY_FOUR_BIT_LONG)
166 if (l & 0xffffffff00000000L) {
167 if (l & 0xffff000000000000L) {
168 if (l & 0xff00000000000000L) {
169 return (bits[(int)(l >> 56)] + 56);
171 return (bits[(int)(l >> 48)] + 48);
173 if (l & 0x0000ff0000000000L) {
174 return (bits[(int)(l >> 40)] + 40);
176 return (bits[(int)(l >> 32)] + 32);
180 # ifdef SIXTY_FOUR_BIT
181 if (l & 0xffffffff00000000LL) {
182 if (l & 0xffff000000000000LL) {
183 if (l & 0xff00000000000000LL) {
184 return (bits[(int)(l >> 56)] + 56);
186 return (bits[(int)(l >> 48)] + 48);
188 if (l & 0x0000ff0000000000LL) {
189 return (bits[(int)(l >> 40)] + 40);
191 return (bits[(int)(l >> 32)] + 32);
197 #if defined(THIRTY_TWO_BIT) || defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
198 if (l & 0xffff0000L) {
200 return (bits[(int)(l >> 24L)] + 24);
202 return (bits[(int)(l >> 16L)] + 16);
206 #if defined(SIXTEEN_BIT) || defined(THIRTY_TWO_BIT) || defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
208 return (bits[(int)(l >> 8)] + 8);
211 return (bits[(int)(l)]);
216 int BN_num_bits(const BIGNUM *a)
223 return ((i * BN_BITS2) + BN_num_bits_word(a->d[i]));
226 void BN_clear_free(BIGNUM *a)
234 OPENSSL_cleanse(a->d, a->dmax * sizeof(a->d[0]));
235 if (!(BN_get_flags(a, BN_FLG_STATIC_DATA)))
238 i = BN_get_flags(a, BN_FLG_MALLOCED);
239 OPENSSL_cleanse(a, sizeof(BIGNUM));
244 void BN_free(BIGNUM *a)
249 if ((a->d != NULL) && !(BN_get_flags(a, BN_FLG_STATIC_DATA)))
251 if (a->flags & BN_FLG_MALLOCED)
254 #ifndef OPENSSL_NO_DEPRECATED
255 a->flags |= BN_FLG_FREE;
261 void BN_init(BIGNUM *a)
263 memset(a, 0, sizeof(BIGNUM));
271 if ((ret = (BIGNUM *)OPENSSL_malloc(sizeof(BIGNUM))) == NULL) {
272 BNerr(BN_F_BN_NEW, ERR_R_MALLOC_FAILURE);
275 ret->flags = BN_FLG_MALLOCED;
284 /* This is used both by bn_expand2() and bn_dup_expand() */
285 /* The caller MUST check that words > b->dmax before calling this */
286 static BN_ULONG *bn_expand_internal(const BIGNUM *b, int words)
288 BN_ULONG *A, *a = NULL;
294 if (words > (INT_MAX / (4 * BN_BITS2))) {
295 BNerr(BN_F_BN_EXPAND_INTERNAL, BN_R_BIGNUM_TOO_LONG);
298 if (BN_get_flags(b, BN_FLG_STATIC_DATA)) {
299 BNerr(BN_F_BN_EXPAND_INTERNAL, BN_R_EXPAND_ON_STATIC_BIGNUM_DATA);
302 a = A = (BN_ULONG *)OPENSSL_malloc(sizeof(BN_ULONG) * words);
304 BNerr(BN_F_BN_EXPAND_INTERNAL, ERR_R_MALLOC_FAILURE);
309 * Valgrind complains in BN_consttime_swap because we process the whole
310 * array even if it's not initialised yet. This doesn't matter in that
311 * function - what's important is constant time operation (we're not
312 * actually going to use the data)
314 memset(a, 0, sizeof(BN_ULONG) * words);
319 /* Check if the previous number needs to be copied */
321 for (i = b->top >> 2; i > 0; i--, A += 4, B += 4) {
323 * The fact that the loop is unrolled
324 * 4-wise is a tribute to Intel. It's
325 * the one that doesn't have enough
326 * registers to accomodate more data.
327 * I'd unroll it 8-wise otherwise:-)
329 * <appro@fy.chalmers.se>
331 BN_ULONG a0, a1, a2, a3;
342 * workaround for ultrix cc: without 'case 0', the optimizer does
343 * the switch table by doing a=top&3; a--; goto jump_table[a];
344 * which fails for top== 0
346 switch (b->top & 3) {
358 memset(A, 0, sizeof(BN_ULONG) * words);
359 memcpy(A, b->d, sizeof(b->d[0]) * b->top);
366 * This is an internal function that can be used instead of bn_expand2() when
367 * there is a need to copy BIGNUMs instead of only expanding the data part,
368 * while still expanding them. Especially useful when needing to expand
369 * BIGNUMs that are declared 'const' and should therefore not be changed. The
370 * reason to use this instead of a BN_dup() followed by a bn_expand2() is
371 * memory allocation overhead. A BN_dup() followed by a bn_expand2() will
372 * allocate new memory for the BIGNUM data twice, and free it once, while
373 * bn_dup_expand() makes sure allocation is made only once.
376 #ifndef OPENSSL_NO_DEPRECATED
377 BIGNUM *bn_dup_expand(const BIGNUM *b, int words)
384 * This function does not work if words <= b->dmax && top < words because
385 * BN_dup() does not preserve 'dmax'! (But bn_dup_expand() is not used
389 if (words > b->dmax) {
390 BN_ULONG *a = bn_expand_internal(b, words);
400 /* r == NULL, BN_new failure */
405 * If a == NULL, there was an error in allocation in
406 * bn_expand_internal(), and NULL should be returned
418 * This is an internal function that should not be used in applications. It
419 * ensures that 'b' has enough room for a 'words' word number and initialises
420 * any unused part of b->d with leading zeros. It is mostly used by the
421 * various BIGNUM routines. If there is an error, NULL is returned. If not,
425 BIGNUM *bn_expand2(BIGNUM *b, int words)
429 if (words > b->dmax) {
430 BN_ULONG *a = bn_expand_internal(b, words);
439 /* None of this should be necessary because of what b->top means! */
442 * NB: bn_wexpand() calls this only if the BIGNUM really has to grow
444 if (b->top < b->dmax) {
446 BN_ULONG *A = &(b->d[b->top]);
447 for (i = (b->dmax - b->top) >> 3; i > 0; i--, A += 8) {
457 for (i = (b->dmax - b->top) & 7; i > 0; i--, A++)
459 assert(A == &(b->d[b->dmax]));
466 BIGNUM *BN_dup(const BIGNUM *a)
477 if (!BN_copy(t, a)) {
485 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b)
495 if (bn_wexpand(a, b->top) == NULL)
501 for (i = b->top >> 2; i > 0; i--, A += 4, B += 4) {
502 BN_ULONG a0, a1, a2, a3;
512 /* ultrix cc workaround, see comments in bn_expand_internal */
513 switch (b->top & 3) {
523 memcpy(a->d, b->d, sizeof(b->d[0]) * b->top);
532 void BN_swap(BIGNUM *a, BIGNUM *b)
534 int flags_old_a, flags_old_b;
536 int tmp_top, tmp_dmax, tmp_neg;
541 flags_old_a = a->flags;
542 flags_old_b = b->flags;
560 (flags_old_a & BN_FLG_MALLOCED) | (flags_old_b & BN_FLG_STATIC_DATA);
562 (flags_old_b & BN_FLG_MALLOCED) | (flags_old_a & BN_FLG_STATIC_DATA);
567 void BN_clear(BIGNUM *a)
571 memset(a->d, 0, a->dmax * sizeof(a->d[0]));
576 BN_ULONG BN_get_word(const BIGNUM *a)
580 else if (a->top == 1)
586 int BN_set_word(BIGNUM *a, BN_ULONG w)
589 if (bn_expand(a, (int)sizeof(BN_ULONG) * 8) == NULL)
593 a->top = (w ? 1 : 0);
598 BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret)
616 i = ((n - 1) / BN_BYTES) + 1;
617 m = ((n - 1) % (BN_BYTES));
618 if (bn_wexpand(ret, (int)i) == NULL) {
626 l = (l << 8L) | *(s++);
634 * need to call this due to clear byte at top if avoiding having the top
635 * bit set (-ve number)
641 /* ignore negative */
642 int BN_bn2bin(const BIGNUM *a, unsigned char *to)
648 n = i = BN_num_bytes(a);
650 l = a->d[i / BN_BYTES];
651 *(to++) = (unsigned char)(l >> (8 * (i % BN_BYTES))) & 0xff;
656 int BN_ucmp(const BIGNUM *a, const BIGNUM *b)
659 BN_ULONG t1, t2, *ap, *bp;
669 for (i = a->top - 1; i >= 0; i--) {
673 return ((t1 > t2) ? 1 : -1);
678 int BN_cmp(const BIGNUM *a, const BIGNUM *b)
684 if ((a == NULL) || (b == NULL)) {
696 if (a->neg != b->neg) {
714 for (i = a->top - 1; i >= 0; i--) {
725 int BN_set_bit(BIGNUM *a, int n)
735 if (bn_wexpand(a, i + 1) == NULL)
737 for (k = a->top; k < i + 1; k++)
742 a->d[i] |= (((BN_ULONG)1) << j);
747 int BN_clear_bit(BIGNUM *a, int n)
760 a->d[i] &= (~(((BN_ULONG)1) << j));
765 int BN_is_bit_set(const BIGNUM *a, int n)
776 return (((a->d[i]) >> j) & ((BN_ULONG)1));
779 int BN_mask_bits(BIGNUM *a, int n)
795 a->d[w] &= ~(BN_MASK2 << b);
801 void BN_set_negative(BIGNUM *a, int b)
803 if (b && !BN_is_zero(a))
809 int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n)
817 return ((aa > bb) ? 1 : -1);
818 for (i = n - 2; i >= 0; i--) {
822 return ((aa > bb) ? 1 : -1);
828 * Here follows a specialised variants of bn_cmp_words(). It has the
829 * property of performing the operation on arrays of different sizes. The
830 * sizes of those arrays is expressed through cl, which is the common length
831 * ( basicall, min(len(a),len(b)) ), and dl, which is the delta between the
832 * two lengths, calculated as len(a)-len(b). All lengths are the number of
836 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl)
842 for (i = dl; i < 0; i++) {
844 return -1; /* a < b */
848 for (i = dl; i > 0; i--) {
850 return 1; /* a > b */
853 return bn_cmp_words(a, b, cl);