1 /* crypto/bn/bn_recp.c */ 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 #include "cryptlib.h" 61 #include "bn_lcl.h" 62 63 void BN_RECP_CTX_init(BN_RECP_CTX *recp) 64 { 65 BN_init(&(recp->N)); 66 BN_init(&(recp->Nr)); 67 recp->num_bits=0; 68 recp->flags=0; 69 } 70 71 BN_RECP_CTX *BN_RECP_CTX_new(void) 72 { 73 BN_RECP_CTX *ret; 74 75 if ((ret=(BN_RECP_CTX *)OPENSSL_malloc(sizeof(BN_RECP_CTX))) == NULL) 76 return(NULL); 77 78 BN_RECP_CTX_init(ret); 79 ret->flags=BN_FLG_MALLOCED; 80 return(ret); 81 } 82 83 void BN_RECP_CTX_free(BN_RECP_CTX *recp) 84 { 85 if(recp == NULL) 86 return; 87 88 BN_free(&(recp->N)); 89 BN_free(&(recp->Nr)); 90 if (recp->flags & BN_FLG_MALLOCED) 91 OPENSSL_free(recp); 92 } 93 94 int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *d, BN_CTX *ctx) 95 { 96 if (!BN_copy(&(recp->N),d)) return 0; 97 BN_zero(&(recp->Nr)); 98 recp->num_bits=BN_num_bits(d); 99 recp->shift=0; 100 return(1); 101 } 102 103 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y, 104 BN_RECP_CTX *recp, BN_CTX *ctx) 105 { 106 int ret=0; 107 BIGNUM *a; 108 const BIGNUM *ca; 109 110 BN_CTX_start(ctx); 111 if ((a = BN_CTX_get(ctx)) == NULL) goto err; 112 if (y != NULL) 113 { 114 if (x == y) 115 { if (!BN_sqr(a,x,ctx)) goto err; } 116 else 117 { if (!BN_mul(a,x,y,ctx)) goto err; } 118 ca = a; 119 } 120 else 121 ca=x; /* Just do the mod */ 122 123 ret = BN_div_recp(NULL,r,ca,recp,ctx); 124 err: 125 BN_CTX_end(ctx); 126 bn_check_top(r); 127 return(ret); 128 } 129 130 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, 131 BN_RECP_CTX *recp, BN_CTX *ctx) 132 { 133 int i,j,ret=0; 134 BIGNUM *a,*b,*d,*r; 135 136 BN_CTX_start(ctx); 137 a=BN_CTX_get(ctx); 138 b=BN_CTX_get(ctx); 139 if (dv != NULL) 140 d=dv; 141 else 142 d=BN_CTX_get(ctx); 143 if (rem != NULL) 144 r=rem; 145 else 146 r=BN_CTX_get(ctx); 147 if (a == NULL || b == NULL || d == NULL || r == NULL) goto err; 148 149 if (BN_ucmp(m,&(recp->N)) < 0) 150 { 151 BN_zero(d); 152 if (!BN_copy(r,m)) return 0; 153 BN_CTX_end(ctx); 154 return(1); 155 } 156 157 /* We want the remainder 158 * Given input of ABCDEF / ab 159 * we need multiply ABCDEF by 3 digests of the reciprocal of ab 160 * 161 */ 162 163 /* i := max(BN_num_bits(m), 2*BN_num_bits(N)) */ 164 i=BN_num_bits(m); 165 j=recp->num_bits<<1; 166 if (j>i) i=j; 167 168 /* Nr := round(2^i / N) */ 169 if (i != recp->shift) 170 recp->shift=BN_reciprocal(&(recp->Nr),&(recp->N), 171 i,ctx); /* BN_reciprocal returns i, or -1 for an error */ 172 if (recp->shift == -1) goto err; 173 174 /* d := |round(round(m / 2^BN_num_bits(N)) * recp->Nr / 2^(i - BN_num_bits(N)))| 175 * = |round(round(m / 2^BN_num_bits(N)) * round(2^i / N) / 2^(i - BN_num_bits(N)))| 176 * <= |(m / 2^BN_num_bits(N)) * (2^i / N) * (2^BN_num_bits(N) / 2^i)| 177 * = |m/N| 178 */ 179 if (!BN_rshift(a,m,recp->num_bits)) goto err; 180 if (!BN_mul(b,a,&(recp->Nr),ctx)) goto err; 181 if (!BN_rshift(d,b,i-recp->num_bits)) goto err; 182 d->neg=0; 183 184 if (!BN_mul(b,&(recp->N),d,ctx)) goto err; 185 if (!BN_usub(r,m,b)) goto err; 186 r->neg=0; 187 188 #if 1 189 j=0; 190 while (BN_ucmp(r,&(recp->N)) >= 0) 191 { 192 if (j++ > 2) 193 { 194 BNerr(BN_F_BN_DIV_RECP,BN_R_BAD_RECIPROCAL); 195 goto err; 196 } 197 if (!BN_usub(r,r,&(recp->N))) goto err; 198 if (!BN_add_word(d,1)) goto err; 199 } 200 #endif 201 202 r->neg=BN_is_zero(r)?0:m->neg; 203 d->neg=m->neg^recp->N.neg; 204 ret=1; 205 err: 206 BN_CTX_end(ctx); 207 bn_check_top(dv); 208 bn_check_top(rem); 209 return(ret); 210 } 211 212 /* len is the expected size of the result 213 * We actually calculate with an extra word of precision, so 214 * we can do faster division if the remainder is not required. 215 */ 216 /* r := 2^len / m */ 217 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx) 218 { 219 int ret= -1; 220 BIGNUM *t; 221 222 BN_CTX_start(ctx); 223 if((t = BN_CTX_get(ctx)) == NULL) goto err; 224 225 if (!BN_set_bit(t,len)) goto err; 226 227 if (!BN_div(r,NULL,t,m,ctx)) goto err; 228 229 ret=len; 230 err: 231 bn_check_top(r); 232 BN_CTX_end(ctx); 233 return(ret); 234 } 235