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 <stdio.h>
60#include "../bn/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 */
66int 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#ifdef BN_COUNT
73 fprintf(stderr, "BN_sqr %d * %d\n", a->top, a->top);
74#endif
75 bn_check_top(a);
76
77 al = a->top;
78 if (al <= 0) {
79 r->top = 0;
80 r->neg = 0;
81 return 1;
82 }
83
84 BN_CTX_start(ctx);
85 rr = (a != r) ? r : BN_CTX_get(ctx);
86 tmp = BN_CTX_get(ctx);
87 if (!rr || !tmp)
88 goto err;
89
90 max = 2 * al; /* Non-zero (from above) */
91 if (bn_wexpand(rr, max) == NULL)
92 goto err;
93
94 if (al == 4) {
95#ifndef BN_SQR_COMBA
96 BN_ULONG t[8];
97 bn_sqr_normal(rr->d, a->d, 4, t);
98#else
99 bn_sqr_comba4(rr->d, a->d);
100#endif
101 } else if (al == 8) {
102#ifndef BN_SQR_COMBA
103 BN_ULONG t[16];
104 bn_sqr_normal(rr->d, a->d, 8, t);
105#else
106 bn_sqr_comba8(rr->d, a->d);
107#endif
108 } else {
109#if defined(BN_RECURSION)
110 if (al < BN_SQR_RECURSIVE_SIZE_NORMAL) {
111 BN_ULONG t[BN_SQR_RECURSIVE_SIZE_NORMAL * 2];
112 bn_sqr_normal(rr->d, a->d, al, t);
113 } else {
114 int j, k;
115
116 j = BN_num_bits_word((BN_ULONG)al);
117 j = 1 << (j - 1);
118 k = j + j;
119 if (al == j) {
120 if (bn_wexpand(tmp, k * 2) == NULL)
121 goto err;
122 bn_sqr_recursive(rr->d, a->d, al, tmp->d);
123 } else {
124 if (bn_wexpand(tmp, max) == NULL)
125 goto err;
126 bn_sqr_normal(rr->d, a->d, al, tmp->d);
127 }
128 }
129#else
130 if (bn_wexpand(tmp, max) == NULL)
131 goto err;
132 bn_sqr_normal(rr->d, a->d, al, tmp->d);
133#endif
134 }
135
136 rr->neg = 0;
137 /*
138 * If the most-significant half of the top word of 'a' is zero, then the
139 * square of 'a' will max-1 words.
140 */
141 if (a->d[al - 1] == (a->d[al - 1] & BN_MASK2l))
142 rr->top = max - 1;
143 else
144 rr->top = max;
145 if (r != rr && BN_copy(r, rr) == NULL)
146 goto err;
147
148 ret = 1;
149 err:
150 bn_check_top(rr);
151 bn_check_top(tmp);
152 BN_CTX_end(ctx);
153 return (ret);
154}
155
156/* tmp must have 2*n words */
157void 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/*-
194 * r is 2*n words in size,
195 * a and b are both n words in size. (There's not actually a 'b' here ...)
196 * n must be a power of 2.
197 * We multiply and return the result.
198 * t must be 2*n words in size
199 * We calculate
200 * a[0]*b[0]
201 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
202 * a[1]*b[1]
203 */
204void 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 /*-
253 * t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero
254 * r[10] holds (a[0]*b[0])
255 * r[32] holds (b[1]*b[1])
256 */
257
258 c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
259
260 /* t[32] is negative */
261 c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
262
263 /*-
264 * t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1])
265 * r[10] holds (a[0]*a[0])
266 * r[32] holds (a[1]*a[1])
267 * c1 holds the carry bits
268 */
269 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
270 if (c1) {
271 p = &(r[n + n2]);
272 lo = *p;
273 ln = (lo + c1) & BN_MASK2;
274 *p = ln;
275
276 /*
277 * The overflow will stop before we over write words we should not
278 * overwrite
279 */
280 if (ln < (BN_ULONG)c1) {
281 do {
282 p++;
283 lo = *p;
284 ln = (lo + 1) & BN_MASK2;
285 *p = ln;
286 } while (ln == 0);
287 }
288 }
289}
290#endif
291