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 */
17int 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
27int 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 */
109void 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 */
156void 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