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
BN_sqr(BIGNUM * r,const BIGNUM * a,BN_CTX * ctx)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
bn_sqr_normal(BN_ULONG * r,const BN_ULONG * a,int n,BN_ULONG * tmp)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
bn_sqr_recursive(BN_ULONG * r,const BN_ULONG * a,int n2,BN_ULONG * t)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