bn_sqr.c revision 280304 
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 "cryptlib.h"
61#include "bn_lcl.h"
62
63/* r must not be a */
64/*
65 * I've just gone over this and it is now %20 faster on x86 - eay - 27 Jun 96
66 */
67int 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 || !tmp)
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    /*
139     * If the most-significant half of the top word of 'a' is zero, then the
140     * square of 'a' will max-1 words.
141     */
142    if (a->d[al - 1] == (a->d[al - 1] & BN_MASK2l))
143        rr->top = max - 1;
144    else
145        rr->top = max;
146    if (rr != r)
147        BN_copy(r, rr);
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