1 /* $OpenBSD: bn_recp.c,v 1.25 2025/01/08 20:21:28 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 void 66 BN_RECP_CTX_init(BN_RECP_CTX *recp) 67 { 68 BN_init(&recp->N); 69 BN_init(&recp->Nr); 70 recp->num_bits = 0; 71 recp->flags = 0; 72 } 73 74 BN_RECP_CTX * 75 BN_RECP_CTX_new(void) 76 { 77 BN_RECP_CTX *ret; 78 79 if ((ret = malloc(sizeof(BN_RECP_CTX))) == NULL) 80 return NULL; 81 82 BN_RECP_CTX_init(ret); 83 ret->flags = BN_FLG_MALLOCED; 84 return ret; 85 } 86 87 void 88 BN_RECP_CTX_free(BN_RECP_CTX *recp) 89 { 90 if (recp == NULL) 91 return; 92 93 BN_free(&recp->N); 94 BN_free(&recp->Nr); 95 if (recp->flags & BN_FLG_MALLOCED) 96 free(recp); 97 } 98 99 int 100 BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *d, BN_CTX *ctx) 101 { 102 if (!bn_copy(&recp->N, d)) 103 return 0; 104 recp->num_bits = BN_num_bits(&recp->N); 105 106 BN_zero(&recp->Nr); 107 recp->shift = 0; 108 109 return 1; 110 } 111 112 /* len is the expected size of the result 113 * We actually calculate with an extra word of precision, so 114 * we can do faster division if the remainder is not required. 115 */ 116 /* r := 2^len / m */ 117 static int 118 BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx) 119 { 120 int ret = -1; 121 BIGNUM *t; 122 123 BN_CTX_start(ctx); 124 if ((t = BN_CTX_get(ctx)) == NULL) 125 goto err; 126 127 if (!BN_set_bit(t, len)) 128 goto err; 129 130 if (!BN_div_ct(r, NULL, t, m, ctx)) 131 goto err; 132 133 ret = len; 134 135 err: 136 BN_CTX_end(ctx); 137 return ret; 138 } 139 140 int 141 BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, BN_RECP_CTX *recp, 142 BN_CTX *ctx) 143 { 144 int i, j, ret = 0; 145 BIGNUM *a, *b, *d, *r; 146 147 BN_CTX_start(ctx); 148 a = BN_CTX_get(ctx); 149 b = BN_CTX_get(ctx); 150 if (dv != NULL) 151 d = dv; 152 else 153 d = BN_CTX_get(ctx); 154 if (rem != NULL) 155 r = rem; 156 else 157 r = BN_CTX_get(ctx); 158 if (a == NULL || b == NULL || d == NULL || r == NULL) 159 goto err; 160 161 if (BN_ucmp(m, &recp->N) < 0) { 162 BN_zero(d); 163 if (!bn_copy(r, m)) { 164 BN_CTX_end(ctx); 165 return 0; 166 } 167 BN_CTX_end(ctx); 168 return 1; 169 } 170 171 /* We want the remainder 172 * Given input of ABCDEF / ab 173 * we need multiply ABCDEF by 3 digests of the reciprocal of ab 174 * 175 */ 176 177 /* i := max(BN_num_bits(m), 2*BN_num_bits(N)) */ 178 i = BN_num_bits(m); 179 j = recp->num_bits << 1; 180 if (j > i) 181 i = j; 182 183 /* Nr := round(2^i / N) */ 184 if (i != recp->shift) 185 recp->shift = BN_reciprocal(&recp->Nr, &recp->N, i, ctx); 186 187 /* BN_reciprocal returns i, or -1 for an error */ 188 if (recp->shift == -1) 189 goto err; 190 191 /* d := |round(round(m / 2^BN_num_bits(N)) * recp->Nr / 2^(i - BN_num_bits(N)))| 192 * = |round(round(m / 2^BN_num_bits(N)) * round(2^i / N) / 2^(i - BN_num_bits(N)))| 193 * <= |(m / 2^BN_num_bits(N)) * (2^i / N) * (2^BN_num_bits(N) / 2^i)| 194 * = |m/N| 195 */ 196 if (!BN_rshift(a, m, recp->num_bits)) 197 goto err; 198 if (!BN_mul(b, a, &recp->Nr, ctx)) 199 goto err; 200 if (!BN_rshift(d, b, i - recp->num_bits)) 201 goto err; 202 d->neg = 0; 203 204 if (!BN_mul(b, &recp->N, d, ctx)) 205 goto err; 206 if (!BN_usub(r, m, b)) 207 goto err; 208 r->neg = 0; 209 210 #if 1 211 j = 0; 212 while (BN_ucmp(r, &recp->N) >= 0) { 213 if (j++ > 2) { 214 BNerror(BN_R_BAD_RECIPROCAL); 215 goto err; 216 } 217 if (!BN_usub(r, r, &recp->N)) 218 goto err; 219 if (!BN_add_word(d, 1)) 220 goto err; 221 } 222 #endif 223 224 BN_set_negative(r, m->neg); 225 BN_set_negative(d, m->neg ^ recp->N.neg); 226 227 ret = 1; 228 229 err: 230 BN_CTX_end(ctx); 231 return ret; 232 } 233 234 int 235 BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y, 236 BN_RECP_CTX *recp, BN_CTX *ctx) 237 { 238 int ret = 0; 239 BIGNUM *a; 240 const BIGNUM *ca; 241 242 BN_CTX_start(ctx); 243 if ((a = BN_CTX_get(ctx)) == NULL) 244 goto err; 245 if (y != NULL) { 246 if (x == y) { 247 if (!BN_sqr(a, x, ctx)) 248 goto err; 249 } else { 250 if (!BN_mul(a, x, y, ctx)) 251 goto err; 252 } 253 ca = a; 254 } else 255 ca = x; /* Just do the mod */ 256 257 ret = BN_div_recp(NULL, r, ca, recp, ctx); 258 259 err: 260 BN_CTX_end(ctx); 261 return ret; 262 } 263