1 /* crypto/bn/bn_sqr.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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.
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).
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.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
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)"
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
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.]
59 #include "internal/cryptlib.h"
64 * 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
)
82 rr
= (a
!= r
) ? r
: BN_CTX_get(ctx
);
83 tmp
= BN_CTX_get(ctx
);
87 max
= 2 * al
; /* Non-zero (from above) */
88 if (bn_wexpand(rr
, max
) == NULL
)
94 bn_sqr_normal(rr
->d
, a
->d
, 4, t
);
96 bn_sqr_comba4(rr
->d
, a
->d
);
101 bn_sqr_normal(rr
->d
, a
->d
, 8, t
);
103 bn_sqr_comba8(rr
->d
, a
->d
);
106 #if defined(BN_RECURSION)
107 if (al
< BN_SQR_RECURSIVE_SIZE_NORMAL
) {
108 BN_ULONG t
[BN_SQR_RECURSIVE_SIZE_NORMAL
* 2];
109 bn_sqr_normal(rr
->d
, a
->d
, al
, t
);
113 j
= BN_num_bits_word((BN_ULONG
)al
);
117 if (bn_wexpand(tmp
, k
* 2) == NULL
)
119 bn_sqr_recursive(rr
->d
, a
->d
, al
, tmp
->d
);
121 if (bn_wexpand(tmp
, max
) == NULL
)
123 bn_sqr_normal(rr
->d
, a
->d
, al
, tmp
->d
);
127 if (bn_wexpand(tmp
, max
) == NULL
)
129 bn_sqr_normal(rr
->d
, a
->d
, al
, tmp
->d
);
135 * If the most-significant half of the top word of 'a' is zero, then the
136 * square of 'a' will max-1 words.
138 if (a
->d
[al
- 1] == (a
->d
[al
- 1] & BN_MASK2l
))
152 /* tmp must have 2*n words */
153 void bn_sqr_normal(BN_ULONG
*r
, const BN_ULONG
*a
, int n
, BN_ULONG
*tmp
)
162 rp
[0] = rp
[max
- 1] = 0;
168 rp
[j
] = bn_mul_words(rp
, ap
, j
, ap
[-1]);
172 for (i
= n
- 2; i
> 0; i
--) {
175 rp
[j
] = bn_mul_add_words(rp
, ap
, j
, ap
[-1]);
179 bn_add_words(r
, r
, r
, max
);
181 /* There will not be a carry */
183 bn_sqr_words(tmp
, a
, n
);
185 bn_add_words(r
, r
, tmp
, max
);
190 * r is 2*n words in size,
191 * a and b are both n words in size. (There's not actually a 'b' here ...)
192 * n must be a power of 2.
193 * We multiply and return the result.
194 * t must be 2*n words in size
197 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
200 void bn_sqr_recursive(BN_ULONG
*r
, const BN_ULONG
*a
, int n2
, BN_ULONG
*t
)
207 # ifndef BN_SQR_COMBA
208 bn_sqr_normal(r
, a
, 4, t
);
213 } else if (n2
== 8) {
214 # ifndef BN_SQR_COMBA
215 bn_sqr_normal(r
, a
, 8, t
);
221 if (n2
< BN_SQR_RECURSIVE_SIZE_NORMAL
) {
222 bn_sqr_normal(r
, a
, n2
, t
);
225 /* r=(a[0]-a[1])*(a[1]-a[0]) */
226 c1
= bn_cmp_words(a
, &(a
[n
]), n
);
229 bn_sub_words(t
, a
, &(a
[n
]), n
);
231 bn_sub_words(t
, &(a
[n
]), a
, n
);
235 /* The result will always be negative unless it is zero */
239 bn_sqr_recursive(&(t
[n2
]), t
, n
, p
);
241 memset(&t
[n2
], 0, sizeof(*t
) * n2
);
242 bn_sqr_recursive(r
, a
, n
, p
);
243 bn_sqr_recursive(&(r
[n2
]), &(a
[n
]), n
, p
);
246 * t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero
247 * r[10] holds (a[0]*b[0])
248 * r[32] holds (b[1]*b[1])
251 c1
= (int)(bn_add_words(t
, r
, &(r
[n2
]), n2
));
253 /* t[32] is negative */
254 c1
-= (int)(bn_sub_words(&(t
[n2
]), t
, &(t
[n2
]), n2
));
257 * t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1])
258 * r[10] holds (a[0]*a[0])
259 * r[32] holds (a[1]*a[1])
260 * c1 holds the carry bits
262 c1
+= (int)(bn_add_words(&(r
[n
]), &(r
[n
]), &(t
[n2
]), n2
));
266 ln
= (lo
+ c1
) & BN_MASK2
;
270 * The overflow will stop before we over write words we should not
273 if (ln
< (BN_ULONG
)c1
) {
277 ln
= (lo
+ 1) & BN_MASK2
;