crypto/bn/bn_sqr.c

   1 /* crypto/bn/bn_sqr.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 "internal/cryptlib.h"
  60 #include "bn_lcl.h"
  61
  62 /* r must not be a */
  63 /*
  64  * I've just gone over this and it is now %20 faster on x86 - eay - 27 Jun 96
  65  */
  66 int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
  67 {
  68     int max, al;
  69     int ret = 0;
  70     BIGNUM *tmp, *rr;
  71
  72     bn_check_top(a);
  73
  74     al = a->top;
  75     if (al <= 0) {
  76         r->top = 0;
  77         r->neg = 0;
  78         return 1;
  79     }
  80
  81     BN_CTX_start(ctx);
  82     rr = (a != r) ? r : BN_CTX_get(ctx);
  83     tmp = BN_CTX_get(ctx);
  84     if (!rr || !tmp)
  85         goto err;
  86
  87     max = 2 * al;               /* Non-zero (from above) */
  88     if (bn_wexpand(rr, max) == NULL)
  89         goto err;
  90
  91     if (al == 4) {
  92 #ifndef BN_SQR_COMBA
  93         BN_ULONG t[8];
  94         bn_sqr_normal(rr->d, a->d, 4, t);
  95 #else
  96         bn_sqr_comba4(rr->d, a->d);
  97 #endif
  98     } else if (al == 8) {
  99 #ifndef BN_SQR_COMBA
 100         BN_ULONG t[16];
 101         bn_sqr_normal(rr->d, a->d, 8, t);
 102 #else
 103         bn_sqr_comba8(rr->d, a->d);
 104 #endif
 105     } else {
 106 #if defined(BN_RECURSION)
 107         if (al < BN_SQR_RECURSIVE_SIZE_NORMAL) {
 108             BN_ULONG t[BN_SQR_RECURSIVE_SIZE_NORMAL * 2];
 109             bn_sqr_normal(rr->d, a->d, al, t);
 110         } else {
 111             int j, k;
 112
 113             j = BN_num_bits_word((BN_ULONG)al);
 114             j = 1 << (j - 1);
 115             k = j + j;
 116             if (al == j) {
 117                 if (bn_wexpand(tmp, k * 2) == NULL)
 118                     goto err;
 119                 bn_sqr_recursive(rr->d, a->d, al, tmp->d);
 120             } else {
 121                 if (bn_wexpand(tmp, max) == NULL)
 122                     goto err;
 123                 bn_sqr_normal(rr->d, a->d, al, tmp->d);
 124             }
 125         }
 126 #else
 127         if (bn_wexpand(tmp, max) == NULL)
 128             goto err;
 129         bn_sqr_normal(rr->d, a->d, al, tmp->d);
 130 #endif
 131     }
 132
 133     rr->neg = 0;
 134     /*
 135      * If the most-significant half of the top word of 'a' is zero, then the
 136      * square of 'a' will max-1 words.
 137      */
 138     if (a->d[al - 1] == (a->d[al - 1] & BN_MASK2l))
 139         rr->top = max - 1;
 140     else
 141         rr->top = max;
 142     if (rr != r)
 143         BN_copy(r, rr);
 144     ret = 1;
 145  err:
 146     bn_check_top(rr);
 147     bn_check_top(tmp);
 148     BN_CTX_end(ctx);
 149     return (ret);
 150 }
 151
 152 /* tmp must have 2*n words */
 153 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp)
 154 {
 155     int i, j, max;
 156     const BN_ULONG *ap;
 157     BN_ULONG *rp;
 158
 159     max = n * 2;
 160     ap = a;
 161     rp = r;
 162     rp[0] = rp[max - 1] = 0;
 163     rp++;
 164     j = n;
 165
 166     if (--j > 0) {
 167         ap++;
 168         rp[j] = bn_mul_words(rp, ap, j, ap[-1]);
 169         rp += 2;
 170     }
 171
 172     for (i = n - 2; i > 0; i--) {
 173         j--;
 174         ap++;
 175         rp[j] = bn_mul_add_words(rp, ap, j, ap[-1]);
 176         rp += 2;
 177     }
 178
 179     bn_add_words(r, r, r, max);
 180
 181     /* There will not be a carry */
 182
 183     bn_sqr_words(tmp, a, n);
 184
 185     bn_add_words(r, r, tmp, max);
 186 }
 187
 188 #ifdef BN_RECURSION
 189 /*-
 190  * r is 2*n words in size,
 191  * a and b are both n words in size.    (There's not actually a 'b' here ...)
 192  * n must be a power of 2.
 193  * We multiply and return the result.
 194  * t must be 2*n words in size
 195  * We calculate
 196  * a[0]*b[0]
 197  * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
 198  * a[1]*b[1]
 199  */
 200 void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t)
 201 {
 202     int n = n2 / 2;
 203     int zero, c1;
 204     BN_ULONG ln, lo, *p;
 205
 206     if (n2 == 4) {
 207 # ifndef BN_SQR_COMBA
 208         bn_sqr_normal(r, a, 4, t);
 209 # else
 210         bn_sqr_comba4(r, a);
 211 # endif
 212         return;
 213     } else if (n2 == 8) {
 214 # ifndef BN_SQR_COMBA
 215         bn_sqr_normal(r, a, 8, t);
 216 # else
 217         bn_sqr_comba8(r, a);
 218 # endif
 219         return;
 220     }
 221     if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL) {
 222         bn_sqr_normal(r, a, n2, t);
 223         return;
 224     }
 225     /* r=(a[0]-a[1])*(a[1]-a[0]) */
 226     c1 = bn_cmp_words(a, &(a[n]), n);
 227     zero = 0;
 228     if (c1 > 0)
 229         bn_sub_words(t, a, &(a[n]), n);
 230     else if (c1 < 0)
 231         bn_sub_words(t, &(a[n]), a, n);
 232     else
 233         zero = 1;
 234
 235     /* The result will always be negative unless it is zero */
 236     p = &(t[n2 * 2]);
 237
 238     if (!zero)
 239         bn_sqr_recursive(&(t[n2]), t, n, p);
 240     else
 241         memset(&t[n2], 0, sizeof(*t) * n2);
 242     bn_sqr_recursive(r, a, n, p);
 243     bn_sqr_recursive(&(r[n2]), &(a[n]), n, p);
 244
 245     /*-
 246      * t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero
 247      * r[10] holds (a[0]*b[0])
 248      * r[32] holds (b[1]*b[1])
 249      */
 250
 251     c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
 252
 253     /* t[32] is negative */
 254     c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
 255
 256     /*-
 257      * t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1])
 258      * r[10] holds (a[0]*a[0])
 259      * r[32] holds (a[1]*a[1])
 260      * c1 holds the carry bits
 261      */
 262     c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
 263     if (c1) {
 264         p = &(r[n + n2]);
 265         lo = *p;
 266         ln = (lo + c1) & BN_MASK2;
 267         *p = ln;
 268
 269         /*
 270          * The overflow will stop before we over write words we should not
 271          * overwrite
 272          */
 273         if (ln < (BN_ULONG)c1) {
 274             do {
 275                 p++;
 276                 lo = *p;
 277                 ln = (lo + 1) & BN_MASK2;
 278                 *p = ln;
 279             } while (ln == 0);
 280         }
 281     }
 282 }
 283 #endif