crypto/bn/bn_recp.c

   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 "cryptlib.h"
  60 #include "bn_lcl.h"
  61
  62 void BN_RECP_CTX_init(BN_RECP_CTX *recp)
  63 {
  64     BN_init(&(recp->N));
  65     BN_init(&(recp->Nr));
  66     recp->num_bits = 0;
  67     recp->flags = 0;
  68 }
  69
  70 BN_RECP_CTX *BN_RECP_CTX_new(void)
  71 {
  72     BN_RECP_CTX *ret;
  73
  74     if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL)
  75         return (NULL);
  76
  77     BN_RECP_CTX_init(ret);
  78     ret->flags = BN_FLG_MALLOCED;
  79     return (ret);
  80 }
  81
  82 void BN_RECP_CTX_free(BN_RECP_CTX *recp)
  83 {
  84     if (recp == NULL)
  85         return;
  86
  87     BN_free(&(recp->N));
  88     BN_free(&(recp->Nr));
  89     if (recp->flags & BN_FLG_MALLOCED)
  90         OPENSSL_free(recp);
  91 }
  92
  93 int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *d, BN_CTX *ctx)
  94 {
  95     if (!BN_copy(&(recp->N), d))
  96         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)
 112         goto err;
 113     if (y != NULL) {
 114         if (x == y) {
 115             if (!BN_sqr(a, x, ctx))
 116                 goto err;
 117         } else {
 118             if (!BN_mul(a, x, y, ctx))
 119                 goto err;
 120         }
 121         ca = a;
 122     } else
 123         ca = x;                 /* Just do the mod */
 124
 125     ret = BN_div_recp(NULL, r, ca, recp, ctx);
 126  err:
 127     BN_CTX_end(ctx);
 128     bn_check_top(r);
 129     return (ret);
 130 }
 131
 132 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
 133                 BN_RECP_CTX *recp, BN_CTX *ctx)
 134 {
 135     int i, j, ret = 0;
 136     BIGNUM *a, *b, *d, *r;
 137
 138     BN_CTX_start(ctx);
 139     a = BN_CTX_get(ctx);
 140     b = BN_CTX_get(ctx);
 141     if (dv != NULL)
 142         d = dv;
 143     else
 144         d = BN_CTX_get(ctx);
 145     if (rem != NULL)
 146         r = rem;
 147     else
 148         r = BN_CTX_get(ctx);
 149     if (a == NULL || b == NULL || d == NULL || r == NULL)
 150         goto err;
 151
 152     if (BN_ucmp(m, &(recp->N)) < 0) {
 153         BN_zero(d);
 154         if (!BN_copy(r, m))
 155             return 0;
 156         BN_CTX_end(ctx);
 157         return (1);
 158     }
 159
 160     /*
 161      * We want the remainder Given input of ABCDEF / ab we need multiply
 162      * ABCDEF by 3 digests of the reciprocal of ab
 163      */
 164
 165     /* i := max(BN_num_bits(m), 2*BN_num_bits(N)) */
 166     i = BN_num_bits(m);
 167     j = recp->num_bits << 1;
 168     if (j > i)
 169         i = j;
 170
 171     /* Nr := round(2^i / N) */
 172     if (i != recp->shift)
 173         recp->shift = BN_reciprocal(&(recp->Nr), &(recp->N), i, ctx);
 174     /* BN_reciprocal could have returned -1 for an error */
 175     if (recp->shift == -1)
 176         goto err;
 177
 178     /*-
 179      * d := |round(round(m / 2^BN_num_bits(N)) * recp->Nr / 2^(i - BN_num_bits(N)))|
 180      *    = |round(round(m / 2^BN_num_bits(N)) * round(2^i / N) / 2^(i - BN_num_bits(N)))|
 181      *   <= |(m / 2^BN_num_bits(N)) * (2^i / N) * (2^BN_num_bits(N) / 2^i)|
 182      *    = |m/N|
 183      */
 184     if (!BN_rshift(a, m, recp->num_bits))
 185         goto err;
 186     if (!BN_mul(b, a, &(recp->Nr), ctx))
 187         goto err;
 188     if (!BN_rshift(d, b, i - recp->num_bits))
 189         goto err;
 190     d->neg = 0;
 191
 192     if (!BN_mul(b, &(recp->N), d, ctx))
 193         goto err;
 194     if (!BN_usub(r, m, b))
 195         goto err;
 196     r->neg = 0;
 197
 198     j = 0;
 199     while (BN_ucmp(r, &(recp->N)) >= 0) {
 200         if (j++ > 2) {
 201             BNerr(BN_F_BN_DIV_RECP, BN_R_BAD_RECIPROCAL);
 202             goto err;
 203         }
 204         if (!BN_usub(r, r, &(recp->N)))
 205             goto err;
 206         if (!BN_add_word(d, 1))
 207             goto err;
 208     }
 209
 210     r->neg = BN_is_zero(r) ? 0 : m->neg;
 211     d->neg = m->neg ^ recp->N.neg;
 212     ret = 1;
 213  err:
 214     BN_CTX_end(ctx);
 215     bn_check_top(dv);
 216     bn_check_top(rem);
 217     return (ret);
 218 }
 219
 220 /*
 221  * len is the expected size of the result We actually calculate with an extra
 222  * word of precision, so we can do faster division if the remainder is not
 223  * required.
 224  */
 225 /* r := 2^len / m */
 226 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx)
 227 {
 228     int ret = -1;
 229     BIGNUM *t;
 230
 231     BN_CTX_start(ctx);
 232     if ((t = BN_CTX_get(ctx)) == NULL)
 233         goto err;
 234
 235     if (!BN_set_bit(t, len))
 236         goto err;
 237
 238     if (!BN_div(r, NULL, t, m, ctx))
 239         goto err;
 240
 241     ret = len;
 242  err:
 243     bn_check_top(r);
 244     BN_CTX_end(ctx);
 245     return (ret);
 246 }