1 /* crypto/bn/bn_recp.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.]
63 void BN_RECP_CTX_init(BN_RECP_CTX *recp)
71 BN_RECP_CTX *BN_RECP_CTX_new(void)
75 if ((ret = (BN_RECP_CTX *)OPENSSL_malloc(sizeof(BN_RECP_CTX))) == NULL)
78 BN_RECP_CTX_init(ret);
79 ret->flags = BN_FLG_MALLOCED;
83 void BN_RECP_CTX_free(BN_RECP_CTX *recp)
90 if (recp->flags & BN_FLG_MALLOCED)
94 int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *d, BN_CTX *ctx)
96 if (!BN_copy(&(recp->N), d))
99 recp->num_bits = BN_num_bits(d);
104 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
105 BN_RECP_CTX *recp, BN_CTX *ctx)
112 if ((a = BN_CTX_get(ctx)) == NULL)
116 if (!BN_sqr(a, x, ctx))
119 if (!BN_mul(a, x, y, ctx))
124 ca = x; /* Just do the mod */
126 ret = BN_div_recp(NULL, r, ca, recp, ctx);
133 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
134 BN_RECP_CTX *recp, BN_CTX *ctx)
137 BIGNUM *a, *b, *d, *r;
150 if (a == NULL || b == NULL || d == NULL || r == NULL)
153 if (BN_ucmp(m, &(recp->N)) < 0) {
162 * We want the remainder Given input of ABCDEF / ab we need multiply
163 * ABCDEF by 3 digests of the reciprocal of ab
166 /* i := max(BN_num_bits(m), 2*BN_num_bits(N)) */
168 j = recp->num_bits << 1;
172 /* Nr := round(2^i / N) */
173 if (i != recp->shift)
174 recp->shift = BN_reciprocal(&(recp->Nr), &(recp->N), i, ctx);
175 /* BN_reciprocal could have returned -1 for an error */
176 if (recp->shift == -1)
180 * d := |round(round(m / 2^BN_num_bits(N)) * recp->Nr / 2^(i - BN_num_bits(N)))|
181 * = |round(round(m / 2^BN_num_bits(N)) * round(2^i / N) / 2^(i - BN_num_bits(N)))|
182 * <= |(m / 2^BN_num_bits(N)) * (2^i / N) * (2^BN_num_bits(N) / 2^i)|
185 if (!BN_rshift(a, m, recp->num_bits))
187 if (!BN_mul(b, a, &(recp->Nr), ctx))
189 if (!BN_rshift(d, b, i - recp->num_bits))
193 if (!BN_mul(b, &(recp->N), d, ctx))
195 if (!BN_usub(r, m, b))
201 while (BN_ucmp(r, &(recp->N)) >= 0) {
203 BNerr(BN_F_BN_DIV_RECP, BN_R_BAD_RECIPROCAL);
206 if (!BN_usub(r, r, &(recp->N)))
208 if (!BN_add_word(d, 1))
213 r->neg = BN_is_zero(r) ? 0 : m->neg;
214 d->neg = m->neg ^ recp->N.neg;
224 * len is the expected size of the result We actually calculate with an extra
225 * word of precision, so we can do faster division if the remainder is not
229 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx)
235 if ((t = BN_CTX_get(ctx)) == NULL)
238 if (!BN_set_bit(t, len))
241 if (!BN_div(r, NULL, t, m, ctx))