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1/* $OpenBSD: bn_sqr.c,v 1.36 2023/07/08 12:21:58 beck 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 <assert.h>
60#include <stdio.h>
61#include <string.h>
62
63#include "bn_arch.h"
64#include "bn_local.h"
65#include "bn_internal.h"
66
67int bn_sqr(BIGNUM *r, const BIGNUM *a, int max, BN_CTX *ctx);
68
69/*
70 * bn_sqr_comba4() computes r[] = a[] * a[] using Comba multiplication
71 * (https://everything2.com/title/Comba+multiplication), where a is a
72 * four word array, producing an eight word array result.
73 */
74#ifndef HAVE_BN_SQR_COMBA4
75void
76bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
77{
78 BN_ULONG c2, c1, c0;
79
80 bn_mulw_addtw(a[0], a[0], 0, 0, 0, &c2, &c1, &r[0]);
81
82 bn_mul2_mulw_addtw(a[1], a[0], 0, c2, c1, &c2, &c1, &r[1]);
83
84 bn_mulw_addtw(a[1], a[1], 0, c2, c1, &c2, &c1, &c0);
85 bn_mul2_mulw_addtw(a[2], a[0], c2, c1, c0, &c2, &c1, &r[2]);
86
87 bn_mul2_mulw_addtw(a[3], a[0], 0, c2, c1, &c2, &c1, &c0);
88 bn_mul2_mulw_addtw(a[2], a[1], c2, c1, c0, &c2, &c1, &r[3]);
89
90 bn_mulw_addtw(a[2], a[2], 0, c2, c1, &c2, &c1, &c0);
91 bn_mul2_mulw_addtw(a[3], a[1], c2, c1, c0, &c2, &c1, &r[4]);
92
93 bn_mul2_mulw_addtw(a[3], a[2], 0, c2, c1, &c2, &c1, &r[5]);
94
95 bn_mulw_addtw(a[3], a[3], 0, c2, c1, &c2, &r[7], &r[6]);
96}
97#endif
98
99/*
100 * bn_sqr_comba8() computes r[] = a[] * a[] using Comba multiplication
101 * (https://everything2.com/title/Comba+multiplication), where a is an
102 * eight word array, producing an 16 word array result.
103 */
104#ifndef HAVE_BN_SQR_COMBA8
105void
106bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
107{
108 BN_ULONG c2, c1, c0;
109
110 bn_mulw_addtw(a[0], a[0], 0, 0, 0, &c2, &c1, &r[0]);
111
112 bn_mul2_mulw_addtw(a[1], a[0], 0, c2, c1, &c2, &c1, &r[1]);
113
114 bn_mulw_addtw(a[1], a[1], 0, c2, c1, &c2, &c1, &c0);
115 bn_mul2_mulw_addtw(a[2], a[0], c2, c1, c0, &c2, &c1, &r[2]);
116
117 bn_mul2_mulw_addtw(a[3], a[0], 0, c2, c1, &c2, &c1, &c0);
118 bn_mul2_mulw_addtw(a[2], a[1], c2, c1, c0, &c2, &c1, &r[3]);
119
120 bn_mulw_addtw(a[2], a[2], 0, c2, c1, &c2, &c1, &c0);
121 bn_mul2_mulw_addtw(a[3], a[1], c2, c1, c0, &c2, &c1, &c0);
122 bn_mul2_mulw_addtw(a[4], a[0], c2, c1, c0, &c2, &c1, &r[4]);
123
124 bn_mul2_mulw_addtw(a[5], a[0], 0, c2, c1, &c2, &c1, &c0);
125 bn_mul2_mulw_addtw(a[4], a[1], c2, c1, c0, &c2, &c1, &c0);
126 bn_mul2_mulw_addtw(a[3], a[2], c2, c1, c0, &c2, &c1, &r[5]);
127
128 bn_mulw_addtw(a[3], a[3], 0, c2, c1, &c2, &c1, &c0);
129 bn_mul2_mulw_addtw(a[4], a[2], c2, c1, c0, &c2, &c1, &c0);
130 bn_mul2_mulw_addtw(a[5], a[1], c2, c1, c0, &c2, &c1, &c0);
131 bn_mul2_mulw_addtw(a[6], a[0], c2, c1, c0, &c2, &c1, &r[6]);
132
133 bn_mul2_mulw_addtw(a[7], a[0], 0, c2, c1, &c2, &c1, &c0);
134 bn_mul2_mulw_addtw(a[6], a[1], c2, c1, c0, &c2, &c1, &c0);
135 bn_mul2_mulw_addtw(a[5], a[2], c2, c1, c0, &c2, &c1, &c0);
136 bn_mul2_mulw_addtw(a[4], a[3], c2, c1, c0, &c2, &c1, &r[7]);
137
138 bn_mulw_addtw(a[4], a[4], 0, c2, c1, &c2, &c1, &c0);
139 bn_mul2_mulw_addtw(a[5], a[3], c2, c1, c0, &c2, &c1, &c0);
140 bn_mul2_mulw_addtw(a[6], a[2], c2, c1, c0, &c2, &c1, &c0);
141 bn_mul2_mulw_addtw(a[7], a[1], c2, c1, c0, &c2, &c1, &r[8]);
142
143 bn_mul2_mulw_addtw(a[7], a[2], 0, c2, c1, &c2, &c1, &c0);
144 bn_mul2_mulw_addtw(a[6], a[3], c2, c1, c0, &c2, &c1, &c0);
145 bn_mul2_mulw_addtw(a[5], a[4], c2, c1, c0, &c2, &c1, &r[9]);
146
147 bn_mulw_addtw(a[5], a[5], 0, c2, c1, &c2, &c1, &c0);
148 bn_mul2_mulw_addtw(a[6], a[4], c2, c1, c0, &c2, &c1, &c0);
149 bn_mul2_mulw_addtw(a[7], a[3], c2, c1, c0, &c2, &c1, &r[10]);
150
151 bn_mul2_mulw_addtw(a[7], a[4], 0, c2, c1, &c2, &c1, &c0);
152 bn_mul2_mulw_addtw(a[6], a[5], c2, c1, c0, &c2, &c1, &r[11]);
153
154 bn_mulw_addtw(a[6], a[6], 0, c2, c1, &c2, &c1, &c0);
155 bn_mul2_mulw_addtw(a[7], a[5], c2, c1, c0, &c2, &c1, &r[12]);
156
157 bn_mul2_mulw_addtw(a[7], a[6], 0, c2, c1, &c2, &c1, &r[13]);
158
159 bn_mulw_addtw(a[7], a[7], 0, c2, c1, &c2, &r[15], &r[14]);
160}
161#endif
162
163#ifndef HAVE_BN_SQR
164/*
165 * bn_sqr_add_words() computes (r[i*2+1]:r[i*2]) = (r[i*2+1]:r[i*2]) + a[i] * a[i].
166 */
167static void
168bn_sqr_add_words(BN_ULONG *r, const BN_ULONG *a, int n)
169{
170 BN_ULONG x3, x2, x1, x0;
171 BN_ULONG carry = 0;
172
173 assert(n >= 0);
174 if (n <= 0)
175 return;
176
177 while (n & ~3) {
178 bn_mulw(a[0], a[0], &x1, &x0);
179 bn_mulw(a[1], a[1], &x3, &x2);
180 bn_qwaddqw(x3, x2, x1, x0, r[3], r[2], r[1], r[0], carry,
181 &carry, &r[3], &r[2], &r[1], &r[0]);
182 bn_mulw(a[2], a[2], &x1, &x0);
183 bn_mulw(a[3], a[3], &x3, &x2);
184 bn_qwaddqw(x3, x2, x1, x0, r[7], r[6], r[5], r[4], carry,
185 &carry, &r[7], &r[6], &r[5], &r[4]);
186
187 a += 4;
188 r += 8;
189 n -= 4;
190 }
191 while (n) {
192 bn_mulw_addw_addw(a[0], a[0], r[0], carry, &carry, &r[0]);
193 bn_addw(r[1], carry, &carry, &r[1]);
194 a++;
195 r += 2;
196 n--;
197 }
198}
199
200static void
201bn_sqr_normal(BN_ULONG *r, int r_len, const BN_ULONG *a, int a_len)
202{
203 const BN_ULONG *ap;
204 BN_ULONG *rp;
205 BN_ULONG w;
206 int n;
207
208 if (a_len <= 0)
209 return;
210
211 ap = a;
212 w = ap[0];
213 ap++;
214
215 rp = r;
216 rp[0] = rp[r_len - 1] = 0;
217 rp++;
218
219 /* Compute initial product - r[n:1] = a[n:1] * a[0] */
220 n = a_len - 1;
221 if (n > 0) {
222 rp[n] = bn_mul_words(rp, ap, n, w);
223 }
224 rp += 2;
225 n--;
226
227 /* Compute and sum remaining products. */
228 while (n > 0) {
229 w = ap[0];
230 ap++;
231
232 rp[n] = bn_mul_add_words(rp, ap, n, w);
233 rp += 2;
234 n--;
235 }
236
237 /* Double the sum of products. */
238 bn_add_words(r, r, r, r_len);
239
240 /* Add squares. */
241 bn_sqr_add_words(r, a, a_len);
242}
243
244/*
245 * bn_sqr() computes a * a, storing the result in r. The caller must ensure that
246 * r is not the same BIGNUM as a and that r has been expanded to rn = a->top * 2
247 * words.
248 */
249int
250bn_sqr(BIGNUM *r, const BIGNUM *a, int r_len, BN_CTX *ctx)
251{
252 bn_sqr_normal(r->d, r_len, a->d, a->top);
253
254 return 1;
255}
256#endif
257
258int
259BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
260{
261 BIGNUM *rr;
262 int r_len;
263 int ret = 1;
264
265 BN_CTX_start(ctx);
266
267 if (a->top < 1) {
268 BN_zero(r);
269 goto done;
270 }
271
272 if ((rr = r) == a)
273 rr = BN_CTX_get(ctx);
274 if (rr == NULL)
275 goto err;
276
277 if ((r_len = a->top * 2) < a->top)
278 goto err;
279 if (!bn_wexpand(rr, r_len))
280 goto err;
281
282 if (a->top == 4) {
283 bn_sqr_comba4(rr->d, a->d);
284 } else if (a->top == 8) {
285 bn_sqr_comba8(rr->d, a->d);
286 } else {
287 if (!bn_sqr(rr, a, r_len, ctx))
288 goto err;
289 }
290
291 rr->top = r_len;
292 bn_correct_top(rr);
293
294 rr->neg = 0;
295
296 if (!bn_copy(r, rr))
297 goto err;
298 done:
299 ret = 1;
300 err:
301 BN_CTX_end(ctx);
302
303 return ret;
304}
305LCRYPTO_ALIAS(BN_sqr);
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-12-23 13:52:57 +0000