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/* I've just gone over this and it is now %20 faster on x86 - eay - 27 Jun 96 */
65int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
66	{
67	int max,al;
68	int ret = 0;
69	BIGNUM *tmp,*rr;
70
71#ifdef BN_COUNT
72	fprintf(stderr,"BN_sqr %d * %d\n",a->top,a->top);
73#endif
74	bn_check_top(a);
75
76	al=a->top;
77	if (al <= 0)
78		{
79		r->top=0;
80		return 1;
81		}
82
83	BN_CTX_start(ctx);
84	rr=(a != r) ? r : BN_CTX_get(ctx);
85	tmp=BN_CTX_get(ctx);
86	if (!rr || !tmp) goto err;
87
88	max = 2 * al; /* Non-zero (from above) */
89	if (bn_wexpand(rr,max) == NULL) goto err;
90
91	if (al == 4)
92		{
93#ifndef BN_SQR_COMBA
94		BN_ULONG t[8];
95		bn_sqr_normal(rr->d,a->d,4,t);
96#else
97		bn_sqr_comba4(rr->d,a->d);
98#endif
99		}
100	else if (al == 8)
101		{
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		}
109	else
110		{
111#if defined(BN_RECURSION)
112		if (al < BN_SQR_RECURSIVE_SIZE_NORMAL)
113			{
114			BN_ULONG t[BN_SQR_RECURSIVE_SIZE_NORMAL*2];
115			bn_sqr_normal(rr->d,a->d,al,t);
116			}
117		else
118			{
119			int j,k;
120
121			j=BN_num_bits_word((BN_ULONG)al);
122			j=1<<(j-1);
123			k=j+j;
124			if (al == j)
125				{
126				if (bn_wexpand(tmp,k*2) == NULL) goto err;
127				bn_sqr_recursive(rr->d,a->d,al,tmp->d);
128				}
129			else
130				{
131				if (bn_wexpand(tmp,max) == NULL) goto err;
132				bn_sqr_normal(rr->d,a->d,al,tmp->d);
133				}
134			}
135#else
136		if (bn_wexpand(tmp,max) == NULL) goto err;
137		bn_sqr_normal(rr->d,a->d,al,tmp->d);
138#endif
139		}
140
141	rr->neg=0;
142	/* If the most-significant half of the top word of 'a' is zero, then
143	 * the square of 'a' will max-1 words. */
144	if(a->d[al - 1] == (a->d[al - 1] & BN_MASK2l))
145		rr->top = max - 1;
146	else
147		rr->top = max;
148	if (rr != r) BN_copy(r,rr);
149	ret = 1;
150 err:
151	bn_check_top(rr);
152	bn_check_top(tmp);
153	BN_CTX_end(ctx);
154	return(ret);
155	}
156
157/* tmp must have 2*n words */
158void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp)
159	{
160	int i,j,max;
161	const BN_ULONG *ap;
162	BN_ULONG *rp;
163
164	max=n*2;
165	ap=a;
166	rp=r;
167	rp[0]=rp[max-1]=0;
168	rp++;
169	j=n;
170
171	if (--j > 0)
172		{
173		ap++;
174		rp[j]=bn_mul_words(rp,ap,j,ap[-1]);
175		rp+=2;
176		}
177
178	for (i=n-2; i>0; i--)
179		{
180		j--;
181		ap++;
182		rp[j]=bn_mul_add_words(rp,ap,j,ap[-1]);
183		rp+=2;
184		}
185
186	bn_add_words(r,r,r,max);
187
188	/* There will not be a carry */
189
190	bn_sqr_words(tmp,a,n);
191
192	bn_add_words(r,r,tmp,max);
193	}
194
195#ifdef BN_RECURSION
196/* r is 2*n words in size,
197 * a and b are both n words in size.    (There's not actually a 'b' here ...)
198 * n must be a power of 2.
199 * We multiply and return the result.
200 * t must be 2*n words in size
201 * We calculate
202 * a[0]*b[0]
203 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
204 * a[1]*b[1]
205 */
206void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t)
207	{
208	int n=n2/2;
209	int zero,c1;
210	BN_ULONG ln,lo,*p;
211
212#ifdef BN_COUNT
213	fprintf(stderr," bn_sqr_recursive %d * %d\n",n2,n2);
214#endif
215	if (n2 == 4)
216		{
217#ifndef BN_SQR_COMBA
218		bn_sqr_normal(r,a,4,t);
219#else
220		bn_sqr_comba4(r,a);
221#endif
222		return;
223		}
224	else if (n2 == 8)
225		{
226#ifndef BN_SQR_COMBA
227		bn_sqr_normal(r,a,8,t);
228#else
229		bn_sqr_comba8(r,a);
230#endif
231		return;
232		}
233	if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL)
234		{
235		bn_sqr_normal(r,a,n2,t);
236		return;
237		}
238	/* r=(a[0]-a[1])*(a[1]-a[0]) */
239	c1=bn_cmp_words(a,&(a[n]),n);
240	zero=0;
241	if (c1 > 0)
242		bn_sub_words(t,a,&(a[n]),n);
243	else if (c1 < 0)
244		bn_sub_words(t,&(a[n]),a,n);
245	else
246		zero=1;
247
248	/* The result will always be negative unless it is zero */
249	p= &(t[n2*2]);
250
251	if (!zero)
252		bn_sqr_recursive(&(t[n2]),t,n,p);
253	else
254		memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
255	bn_sqr_recursive(r,a,n,p);
256	bn_sqr_recursive(&(r[n2]),&(a[n]),n,p);
257
258	/* t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero
259	 * r[10] holds (a[0]*b[0])
260	 * r[32] holds (b[1]*b[1])
261	 */
262
263	c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
264
265	/* t[32] is negative */
266	c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
267
268	/* t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1])
269	 * r[10] holds (a[0]*a[0])
270	 * r[32] holds (a[1]*a[1])
271	 * c1 holds the carry bits
272	 */
273	c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
274	if (c1)
275		{
276		p= &(r[n+n2]);
277		lo= *p;
278		ln=(lo+c1)&BN_MASK2;
279		*p=ln;
280
281		/* The overflow will stop before we over write
282		 * words we should not overwrite */
283		if (ln < (BN_ULONG)c1)
284			{
285			do	{
286				p++;
287				lo= *p;
288				ln=(lo+1)&BN_MASK2;
289				*p=ln;
290				} while (ln == 0);
291			}
292		}
293	}
294#endif
295