1 /*
2 * Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved.
3 *
4 * Licensed under the Apache License 2.0 (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
8 */
9
10 #include "internal/cryptlib.h"
11 #include "bn_local.h"
12
13 /* r must not be a */
14 /*
15 * I've just gone over this and it is now %20 faster on x86 - eay - 27 Jun 96
16 */
BN_sqr(BIGNUM * r,const BIGNUM * a,BN_CTX * ctx)17 int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
18 {
19 int ret = bn_sqr_fixed_top(r, a, ctx);
20
21 bn_correct_top(r);
22 bn_check_top(r);
23
24 return ret;
25 }
26
bn_sqr_fixed_top(BIGNUM * r,const BIGNUM * a,BN_CTX * ctx)27 int bn_sqr_fixed_top(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
28 {
29 int max, al;
30 int ret = 0;
31 BIGNUM *tmp, *rr;
32
33 bn_check_top(a);
34
35 al = a->top;
36 if (al <= 0) {
37 r->top = 0;
38 r->neg = 0;
39 return 1;
40 }
41
42 BN_CTX_start(ctx);
43 rr = (a != r) ? r : BN_CTX_get(ctx);
44 tmp = BN_CTX_get(ctx);
45 if (rr == NULL || tmp == NULL)
46 goto err;
47
48 max = 2 * al; /* Non-zero (from above) */
49 if (bn_wexpand(rr, max) == NULL)
50 goto err;
51
52 if (al == 4) {
53 #ifndef BN_SQR_COMBA
54 BN_ULONG t[8];
55 bn_sqr_normal(rr->d, a->d, 4, t);
56 #else
57 bn_sqr_comba4(rr->d, a->d);
58 #endif
59 } else if (al == 8) {
60 #ifndef BN_SQR_COMBA
61 BN_ULONG t[16];
62 bn_sqr_normal(rr->d, a->d, 8, t);
63 #else
64 bn_sqr_comba8(rr->d, a->d);
65 #endif
66 } else {
67 #if defined(BN_RECURSION)
68 if (al < BN_SQR_RECURSIVE_SIZE_NORMAL) {
69 BN_ULONG t[BN_SQR_RECURSIVE_SIZE_NORMAL * 2];
70 bn_sqr_normal(rr->d, a->d, al, t);
71 } else {
72 int j, k;
73
74 j = BN_num_bits_word((BN_ULONG)al);
75 j = 1 << (j - 1);
76 k = j + j;
77 if (al == j) {
78 if (bn_wexpand(tmp, k * 2) == NULL)
79 goto err;
80 bn_sqr_recursive(rr->d, a->d, al, tmp->d);
81 } else {
82 if (bn_wexpand(tmp, max) == NULL)
83 goto err;
84 bn_sqr_normal(rr->d, a->d, al, tmp->d);
85 }
86 }
87 #else
88 if (bn_wexpand(tmp, max) == NULL)
89 goto err;
90 bn_sqr_normal(rr->d, a->d, al, tmp->d);
91 #endif
92 }
93
94 rr->neg = 0;
95 rr->top = max;
96 rr->flags |= BN_FLG_FIXED_TOP;
97 if (r != rr && BN_copy(r, rr) == NULL)
98 goto err;
99
100 ret = 1;
101 err:
102 bn_check_top(rr);
103 bn_check_top(tmp);
104 BN_CTX_end(ctx);
105 return ret;
106 }
107
108 /* tmp must have 2*n words */
bn_sqr_normal(BN_ULONG * r,const BN_ULONG * a,int n,BN_ULONG * tmp)109 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp)
110 {
111 int i, j, max;
112 const BN_ULONG *ap;
113 BN_ULONG *rp;
114
115 max = n * 2;
116 ap = a;
117 rp = r;
118 rp[0] = rp[max - 1] = 0;
119 rp++;
120 j = n;
121
122 if (--j > 0) {
123 ap++;
124 rp[j] = bn_mul_words(rp, ap, j, ap[-1]);
125 rp += 2;
126 }
127
128 for (i = n - 2; i > 0; i--) {
129 j--;
130 ap++;
131 rp[j] = bn_mul_add_words(rp, ap, j, ap[-1]);
132 rp += 2;
133 }
134
135 bn_add_words(r, r, r, max);
136
137 /* There will not be a carry */
138
139 bn_sqr_words(tmp, a, n);
140
141 bn_add_words(r, r, tmp, max);
142 }
143
144 #ifdef BN_RECURSION
145 /*-
146 * r is 2*n words in size,
147 * a and b are both n words in size. (There's not actually a 'b' here ...)
148 * n must be a power of 2.
149 * We multiply and return the result.
150 * t must be 2*n words in size
151 * We calculate
152 * a[0]*b[0]
153 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
154 * a[1]*b[1]
155 */
bn_sqr_recursive(BN_ULONG * r,const BN_ULONG * a,int n2,BN_ULONG * t)156 void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t)
157 {
158 int n = n2 / 2;
159 int zero, c1;
160 BN_ULONG ln, lo, *p;
161
162 if (n2 == 4) {
163 # ifndef BN_SQR_COMBA
164 bn_sqr_normal(r, a, 4, t);
165 # else
166 bn_sqr_comba4(r, a);
167 # endif
168 return;
169 } else if (n2 == 8) {
170 # ifndef BN_SQR_COMBA
171 bn_sqr_normal(r, a, 8, t);
172 # else
173 bn_sqr_comba8(r, a);
174 # endif
175 return;
176 }
177 if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL) {
178 bn_sqr_normal(r, a, n2, t);
179 return;
180 }
181 /* r=(a[0]-a[1])*(a[1]-a[0]) */
182 c1 = bn_cmp_words(a, &(a[n]), n);
183 zero = 0;
184 if (c1 > 0)
185 bn_sub_words(t, a, &(a[n]), n);
186 else if (c1 < 0)
187 bn_sub_words(t, &(a[n]), a, n);
188 else
189 zero = 1;
190
191 /* The result will always be negative unless it is zero */
192 p = &(t[n2 * 2]);
193
194 if (!zero)
195 bn_sqr_recursive(&(t[n2]), t, n, p);
196 else
197 memset(&t[n2], 0, sizeof(*t) * n2);
198 bn_sqr_recursive(r, a, n, p);
199 bn_sqr_recursive(&(r[n2]), &(a[n]), n, p);
200
201 /*-
202 * t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero
203 * r[10] holds (a[0]*b[0])
204 * r[32] holds (b[1]*b[1])
205 */
206
207 c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
208
209 /* t[32] is negative */
210 c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
211
212 /*-
213 * t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1])
214 * r[10] holds (a[0]*a[0])
215 * r[32] holds (a[1]*a[1])
216 * c1 holds the carry bits
217 */
218 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
219 if (c1) {
220 p = &(r[n + n2]);
221 lo = *p;
222 ln = (lo + c1) & BN_MASK2;
223 *p = ln;
224
225 /*
226 * The overflow will stop before we over write words we should not
227 * overwrite
228 */
229 if (ln < (BN_ULONG)c1) {
230 do {
231 p++;
232 lo = *p;
233 ln = (lo + 1) & BN_MASK2;
234 *p = ln;
235 } while (ln == 0);
236 }
237 }
238 }
239 #endif
240