1/* 2 * Copyright (c) 2000-2001,2011,2014 Apple Inc. All Rights Reserved. 3 * 4 * The contents of this file constitute Original Code as defined in and are 5 * subject to the Apple Public Source License Version 1.2 (the 'License'). 6 * You may not use this file except in compliance with the License. Please obtain 7 * a copy of the License at http://www.apple.com/publicsource and read it before 8 * using this file. 9 * 10 * This Original Code and all software distributed under the License are 11 * distributed on an 'AS IS' basis, WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESS 12 * OR IMPLIED, AND APPLE HEREBY DISCLAIMS ALL SUCH WARRANTIES, INCLUDING WITHOUT 13 * LIMITATION, ANY WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR 14 * PURPOSE, QUIET ENJOYMENT OR NON-INFRINGEMENT. Please see the License for the 15 * specific language governing rights and limitations under the License. 16 */ 17 18 19/* crypto/bn/bn_gcd.c */ 20/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) 21 * All rights reserved. 22 * 23 * This package is an SSL implementation written 24 * by Eric Young (eay@cryptsoft.com). 25 * The implementation was written so as to conform with Netscapes SSL. 26 * 27 * This library is free for commercial and non-commercial use as long as 28 * the following conditions are aheared to. The following conditions 29 * apply to all code found in this distribution, be it the RC4, RSA, 30 * lhash, DES, etc., code; not just the SSL code. The SSL documentation 31 * included with this distribution is covered by the same copyright terms 32 * except that the holder is Tim Hudson (tjh@cryptsoft.com). 33 * 34 * Copyright remains Eric Young's, and as such any Copyright notices in 35 * the code are not to be removed. 36 * If this package is used in a product, Eric Young should be given attribution 37 * as the author of the parts of the library used. 38 * This can be in the form of a textual message at program startup or 39 * in documentation (online or textual) provided with the package. 40 * 41 * Redistribution and use in source and binary forms, with or without 42 * modification, are permitted provided that the following conditions 43 * are met: 44 * 1. Redistributions of source code must retain the copyright 45 * notice, this list of conditions and the following disclaimer. 46 * 2. Redistributions in binary form must reproduce the above copyright 47 * notice, this list of conditions and the following disclaimer in the 48 * documentation and/or other materials provided with the distribution. 49 * 3. All advertising materials mentioning features or use of this software 50 * must display the following acknowledgement: 51 * "This product includes cryptographic software written by 52 * Eric Young (eay@cryptsoft.com)" 53 * The word 'cryptographic' can be left out if the rouines from the library 54 * being used are not cryptographic related :-). 55 * 4. If you include any Windows specific code (or a derivative thereof) from 56 * the apps directory (application code) you must include an acknowledgement: 57 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" 58 * 59 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND 60 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 61 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 62 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 63 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 64 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 65 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 66 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 67 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 68 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 69 * SUCH DAMAGE. 70 * 71 * The licence and distribution terms for any publically available version or 72 * derivative of this code cannot be changed. i.e. this code cannot simply be 73 * copied and put under another distribution licence 74 * [including the GNU Public Licence.] 75 */ 76 77#include <stdio.h> 78#include "cryptlib.h" 79#include "bn_lcl.h" 80 81static BIGNUM *euclid(BIGNUM *a, BIGNUM *b); 82 83int BN_gcd(BIGNUM *r, BIGNUM *in_a, BIGNUM *in_b, BN_CTX *ctx) 84 { 85 BIGNUM *a,*b,*t; 86 int ret=0; 87 88 bn_check_top(in_a); 89 bn_check_top(in_b); 90 91 BN_CTX_start(ctx); 92 a = BN_CTX_get(ctx); 93 b = BN_CTX_get(ctx); 94 if (a == NULL || b == NULL) goto err; 95 96 if (BN_copy(a,in_a) == NULL) goto err; 97 if (BN_copy(b,in_b) == NULL) goto err; 98 99 if (BN_cmp(a,b) < 0) { t=a; a=b; b=t; } 100 t=euclid(a,b); 101 if (t == NULL) goto err; 102 103 if (BN_copy(r,t) == NULL) goto err; 104 ret=1; 105err: 106 BN_CTX_end(ctx); 107 return(ret); 108 } 109 110static BIGNUM *euclid(BIGNUM *a, BIGNUM *b) 111 { 112 BIGNUM *t; 113 int shifts=0; 114 115 bn_check_top(a); 116 bn_check_top(b); 117 118 for (;;) 119 { 120 if (BN_is_zero(b)) 121 break; 122 123 if (BN_is_odd(a)) 124 { 125 if (BN_is_odd(b)) 126 { 127 if (!BN_sub(a,a,b)) goto err; 128 if (!BN_rshift1(a,a)) goto err; 129 if (BN_cmp(a,b) < 0) 130 { t=a; a=b; b=t; } 131 } 132 else /* a odd - b even */ 133 { 134 if (!BN_rshift1(b,b)) goto err; 135 if (BN_cmp(a,b) < 0) 136 { t=a; a=b; b=t; } 137 } 138 } 139 else /* a is even */ 140 { 141 if (BN_is_odd(b)) 142 { 143 if (!BN_rshift1(a,a)) goto err; 144 if (BN_cmp(a,b) < 0) 145 { t=a; a=b; b=t; } 146 } 147 else /* a even - b even */ 148 { 149 if (!BN_rshift1(a,a)) goto err; 150 if (!BN_rshift1(b,b)) goto err; 151 shifts++; 152 } 153 } 154 } 155 if (shifts) 156 { 157 if (!BN_lshift(a,a,shifts)) goto err; 158 } 159 return(a); 160err: 161 return(NULL); 162 } 163 164/* solves ax == 1 (mod n) */ 165BIGNUM *BN_mod_inverse(BIGNUM *in, BIGNUM *a, const BIGNUM *n, BN_CTX *ctx) 166 { 167 BIGNUM *A,*B,*X,*Y,*M,*D,*R=NULL; 168 BIGNUM *T,*ret=NULL; 169 int sign; 170 171 bn_check_top(a); 172 bn_check_top(n); 173 174 BN_CTX_start(ctx); 175 A = BN_CTX_get(ctx); 176 B = BN_CTX_get(ctx); 177 X = BN_CTX_get(ctx); 178 D = BN_CTX_get(ctx); 179 M = BN_CTX_get(ctx); 180 Y = BN_CTX_get(ctx); 181 if (Y == NULL) goto err; 182 183 if (in == NULL) 184 R=BN_new(); 185 else 186 R=in; 187 if (R == NULL) goto err; 188 189 BN_zero(X); 190 BN_one(Y); 191 if (BN_copy(A,a) == NULL) goto err; 192 if (BN_copy(B,n) == NULL) goto err; 193 sign=1; 194 195 while (!BN_is_zero(B)) 196 { 197 if (!BN_div(D,M,A,B,ctx)) goto err; 198 T=A; 199 A=B; 200 B=M; 201 /* T has a struct, M does not */ 202 203 if (!BN_mul(T,D,X,ctx)) goto err; 204 if (!BN_add(T,T,Y)) goto err; 205 M=Y; 206 Y=X; 207 X=T; 208 sign= -sign; 209 } 210 if (sign < 0) 211 { 212 if (!BN_sub(Y,n,Y)) goto err; 213 } 214 215 if (BN_is_one(A)) 216 { if (!BN_mod(R,Y,n,ctx)) goto err; } 217 else 218 { 219 BNerr(BN_F_BN_MOD_INVERSE,BN_R_NO_INVERSE); 220 goto err; 221 } 222 ret=R; 223err: 224 if ((ret == NULL) && (in == NULL)) BN_free(R); 225 BN_CTX_end(ctx); 226 return(ret); 227 } 228 229