1 /* $OpenBSD: bn_recp.c,v 1.33 2025/02/04 20:22:20 tb Exp $ */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
3 * All rights reserved.
4 *
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.
8 *
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).
15 *
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.
22 *
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
25 * are met:
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)"
40 *
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
51 * SUCH DAMAGE.
52 *
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.]
57 */
58
59 #include <stdio.h>
60
61 #include <openssl/err.h>
62
63 #include "bn_local.h"
64
65 struct bn_recp_ctx_st {
66 BIGNUM *N; /* the divisor */
67 BIGNUM *Nr; /* the reciprocal 2^shift / N */
68 int num_bits; /* number of bits in N */
69 int shift;
70 } /* BN_RECP_CTX */;
71
72 BN_RECP_CTX *
BN_RECP_CTX_create(const BIGNUM * N)73 BN_RECP_CTX_create(const BIGNUM *N)
74 {
75 BN_RECP_CTX *recp;
76
77 if ((recp = calloc(1, sizeof(*recp))) == NULL)
78 goto err;
79
80 if ((recp->N = BN_dup(N)) == NULL)
81 goto err;
82 BN_set_negative(recp->N, 0);
83 recp->num_bits = BN_num_bits(recp->N);
84
85 if ((recp->Nr = BN_new()) == NULL)
86 goto err;
87
88 return recp;
89
90 err:
91 BN_RECP_CTX_free(recp);
92
93 return NULL;
94 }
95
96 void
BN_RECP_CTX_free(BN_RECP_CTX * recp)97 BN_RECP_CTX_free(BN_RECP_CTX *recp)
98 {
99 if (recp == NULL)
100 return;
101
102 BN_free(recp->N);
103 BN_free(recp->Nr);
104 freezero(recp, sizeof(*recp));
105 }
106
107 int
BN_div_reciprocal(BIGNUM * dv,BIGNUM * rem,const BIGNUM * m,BN_RECP_CTX * recp,BN_CTX * ctx)108 BN_div_reciprocal(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, BN_RECP_CTX *recp,
109 BN_CTX *ctx)
110 {
111 int i, j, ret = 0;
112 BIGNUM *a, *b, *d, *r;
113
114 if (BN_ucmp(m, recp->N) < 0) {
115 if (dv != NULL)
116 BN_zero(dv);
117 if (rem != NULL)
118 return bn_copy(rem, m);
119 return 1;
120 }
121
122 BN_CTX_start(ctx);
123 if ((a = BN_CTX_get(ctx)) == NULL)
124 goto err;
125 if ((b = BN_CTX_get(ctx)) == NULL)
126 goto err;
127
128 if ((d = dv) == NULL)
129 d = BN_CTX_get(ctx);
130 if (d == NULL)
131 goto err;
132
133 if ((r = rem) == NULL)
134 r = BN_CTX_get(ctx);
135 if (r == NULL)
136 goto err;
137
138 /*
139 * We want the remainder. Given input of ABCDEF / ab we need to
140 * multiply ABCDEF by 3 digits of the reciprocal of ab.
141 */
142
143 /* i := max(BN_num_bits(m), 2*BN_num_bits(N)) */
144 i = BN_num_bits(m);
145 j = recp->num_bits << 1;
146 if (j > i)
147 i = j;
148
149 /* Compute Nr := (1 << i) / N if necessary. */
150 if (i != recp->shift) {
151 BN_zero(recp->Nr);
152 if (!BN_set_bit(recp->Nr, i))
153 goto err;
154 if (!BN_div_ct(recp->Nr, NULL, recp->Nr, recp->N, ctx))
155 goto err;
156 recp->shift = i;
157 }
158
159 /*
160 * d := |((m >> BN_num_bits(N)) * recp->Nr) >> (i - BN_num_bits(N))|
161 * = |((m >> BN_num_bits(N)) * (1 << i) / N) >> (i - BN_num_bits(N))|
162 * <= |(m / 2^BN_num_bits(N)) * (2^i / N) * 2^BN_num_bits(N) / 2^i |
163 * = |m / N|
164 */
165 if (!BN_rshift(a, m, recp->num_bits))
166 goto err;
167 if (!BN_mul(b, a, recp->Nr, ctx))
168 goto err;
169 if (!BN_rshift(d, b, i - recp->num_bits))
170 goto err;
171 d->neg = 0;
172
173 if (!BN_mul(b, recp->N, d, ctx))
174 goto err;
175 if (!BN_usub(r, m, b))
176 goto err;
177 r->neg = 0;
178
179 #if 1
180 j = 0;
181 while (BN_ucmp(r, recp->N) >= 0) {
182 if (j++ > 2) {
183 BNerror(BN_R_BAD_RECIPROCAL);
184 goto err;
185 }
186 if (!BN_usub(r, r, recp->N))
187 goto err;
188 if (!BN_add_word(d, 1))
189 goto err;
190 }
191 #endif
192
193 BN_set_negative(r, m->neg);
194 BN_set_negative(d, m->neg ^ recp->N->neg);
195
196 ret = 1;
197
198 err:
199 BN_CTX_end(ctx);
200 return ret;
201 }
202
203 /* Compute r = (x * y) % m. */
204 int
BN_mod_mul_reciprocal(BIGNUM * r,const BIGNUM * x,const BIGNUM * y,BN_RECP_CTX * recp,BN_CTX * ctx)205 BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
206 BN_RECP_CTX *recp, BN_CTX *ctx)
207 {
208 if (!BN_mul(r, x, y, ctx))
209 return 0;
210
211 return BN_div_reciprocal(NULL, r, r, recp, ctx);
212 }
213
214 /* Compute r = x^2 % m. */
215 int
BN_mod_sqr_reciprocal(BIGNUM * r,const BIGNUM * x,BN_RECP_CTX * recp,BN_CTX * ctx)216 BN_mod_sqr_reciprocal(BIGNUM *r, const BIGNUM *x, BN_RECP_CTX *recp, BN_CTX *ctx)
217 {
218 if (!BN_sqr(r, x, ctx))
219 return 0;
220
221 return BN_div_reciprocal(NULL, r, r, recp, ctx);
222 }
223