1 /* $OpenBSD: bn_sqr.c,v 1.12 2015/02/09 15:49:22 jsing 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 #include <string.h> 61 62 #include "bn_lcl.h" 63 64 /* r must not be a */ 65 /* I've just gone over this and it is now %20 faster on x86 - eay - 27 Jun 96 */ 66 int 67 BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) 68 { 69 int max, al; 70 int ret = 0; 71 BIGNUM *tmp, *rr; 72 73 #ifdef BN_COUNT 74 fprintf(stderr, "BN_sqr %d * %d\n", a->top, a->top); 75 #endif 76 bn_check_top(a); 77 78 al = a->top; 79 if (al <= 0) { 80 r->top = 0; 81 r->neg = 0; 82 return 1; 83 } 84 85 BN_CTX_start(ctx); 86 rr = (a != r) ? r : BN_CTX_get(ctx); 87 tmp = BN_CTX_get(ctx); 88 if (rr == NULL || tmp == NULL) 89 goto err; 90 91 max = 2 * al; /* Non-zero (from above) */ 92 if (bn_wexpand(rr, max) == NULL) 93 goto err; 94 95 if (al == 4) { 96 #ifndef BN_SQR_COMBA 97 BN_ULONG t[8]; 98 bn_sqr_normal(rr->d, a->d, 4, t); 99 #else 100 bn_sqr_comba4(rr->d, a->d); 101 #endif 102 } else if (al == 8) { 103 #ifndef BN_SQR_COMBA 104 BN_ULONG t[16]; 105 bn_sqr_normal(rr->d, a->d, 8, t); 106 #else 107 bn_sqr_comba8(rr->d, a->d); 108 #endif 109 } else { 110 #if defined(BN_RECURSION) 111 if (al < BN_SQR_RECURSIVE_SIZE_NORMAL) { 112 BN_ULONG t[BN_SQR_RECURSIVE_SIZE_NORMAL*2]; 113 bn_sqr_normal(rr->d, a->d, al, t); 114 } else { 115 int j, k; 116 117 j = BN_num_bits_word((BN_ULONG)al); 118 j = 1 << (j - 1); 119 k = j + j; 120 if (al == j) { 121 if (bn_wexpand(tmp, k * 2) == NULL) 122 goto err; 123 bn_sqr_recursive(rr->d, a->d, al, tmp->d); 124 } else { 125 if (bn_wexpand(tmp, max) == NULL) 126 goto err; 127 bn_sqr_normal(rr->d, a->d, al, tmp->d); 128 } 129 } 130 #else 131 if (bn_wexpand(tmp, max) == NULL) 132 goto err; 133 bn_sqr_normal(rr->d, a->d, al, tmp->d); 134 #endif 135 } 136 137 rr->neg = 0; 138 /* If the most-significant half of the top word of 'a' is zero, then 139 * the square of 'a' will max-1 words. */ 140 if (a->d[al - 1] == (a->d[al - 1] & BN_MASK2l)) 141 rr->top = max - 1; 142 else 143 rr->top = max; 144 if (rr != r) 145 BN_copy(r, rr); 146 ret = 1; 147 148 err: 149 bn_check_top(rr); 150 bn_check_top(tmp); 151 BN_CTX_end(ctx); 152 return (ret); 153 } 154 155 /* tmp must have 2*n words */ 156 void 157 bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp) 158 { 159 int i, j, max; 160 const BN_ULONG *ap; 161 BN_ULONG *rp; 162 163 max = n * 2; 164 ap = a; 165 rp = r; 166 rp[0] = rp[max - 1] = 0; 167 rp++; 168 j = n; 169 170 if (--j > 0) { 171 ap++; 172 rp[j] = bn_mul_words(rp, ap, j, ap[-1]); 173 rp += 2; 174 } 175 176 for (i = n - 2; i > 0; i--) { 177 j--; 178 ap++; 179 rp[j] = bn_mul_add_words(rp, ap, j, ap[-1]); 180 rp += 2; 181 } 182 183 bn_add_words(r, r, r, max); 184 185 /* There will not be a carry */ 186 187 bn_sqr_words(tmp, a, n); 188 189 bn_add_words(r, r, tmp, max); 190 } 191 192 #ifdef BN_RECURSION 193 /* r is 2*n words in size, 194 * a and b are both n words in size. (There's not actually a 'b' here ...) 195 * n must be a power of 2. 196 * We multiply and return the result. 197 * t must be 2*n words in size 198 * We calculate 199 * a[0]*b[0] 200 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0]) 201 * a[1]*b[1] 202 */ 203 void 204 bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t) 205 { 206 int n = n2 / 2; 207 int zero, c1; 208 BN_ULONG ln, lo, *p; 209 210 #ifdef BN_COUNT 211 fprintf(stderr, " bn_sqr_recursive %d * %d\n", n2, n2); 212 #endif 213 if (n2 == 4) { 214 #ifndef BN_SQR_COMBA 215 bn_sqr_normal(r, a, 4, t); 216 #else 217 bn_sqr_comba4(r, a); 218 #endif 219 return; 220 } else if (n2 == 8) { 221 #ifndef BN_SQR_COMBA 222 bn_sqr_normal(r, a, 8, t); 223 #else 224 bn_sqr_comba8(r, a); 225 #endif 226 return; 227 } 228 if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL) { 229 bn_sqr_normal(r, a, n2, t); 230 return; 231 } 232 /* r=(a[0]-a[1])*(a[1]-a[0]) */ 233 c1 = bn_cmp_words(a, &(a[n]), n); 234 zero = 0; 235 if (c1 > 0) 236 bn_sub_words(t, a, &(a[n]), n); 237 else if (c1 < 0) 238 bn_sub_words(t, &(a[n]), a, n); 239 else 240 zero = 1; 241 242 /* The result will always be negative unless it is zero */ 243 p = &(t[n2*2]); 244 245 if (!zero) 246 bn_sqr_recursive(&(t[n2]), t, n, p); 247 else 248 memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG)); 249 bn_sqr_recursive(r, a, n, p); 250 bn_sqr_recursive(&(r[n2]), &(a[n]), n, p); 251 252 /* t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero 253 * r[10] holds (a[0]*b[0]) 254 * r[32] holds (b[1]*b[1]) 255 */ 256 257 c1 = (int)(bn_add_words(t, r, &(r[n2]), n2)); 258 259 /* t[32] is negative */ 260 c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2)); 261 262 /* t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1]) 263 * r[10] holds (a[0]*a[0]) 264 * r[32] holds (a[1]*a[1]) 265 * c1 holds the carry bits 266 */ 267 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2)); 268 if (c1) { 269 p = &(r[n + n2]); 270 lo= *p; 271 ln = (lo + c1) & BN_MASK2; 272 *p = ln; 273 274 /* The overflow will stop before we over write 275 * words we should not overwrite */ 276 if (ln < (BN_ULONG)c1) { 277 do { 278 p++; 279 lo= *p; 280 ln = (lo + 1) & BN_MASK2; 281 *p = ln; 282 } while (ln == 0); 283 } 284 } 285 } 286 #endif 287