1 /*
2 * Copyright 1998-2021 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
BN_nnmod(BIGNUM * r,const BIGNUM * m,const BIGNUM * d,BN_CTX * ctx)13 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
14 {
15 /*
16 * like BN_mod, but returns non-negative remainder (i.e., 0 <= r < |d|
17 * always holds)
18 */
19
20 if (!(BN_mod(r, m, d, ctx)))
21 return 0;
22 if (!r->neg)
23 return 1;
24 /* now -|d| < r < 0, so we have to set r := r + |d| */
25 return (d->neg ? BN_sub : BN_add) (r, r, d);
26 }
27
BN_mod_add(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BIGNUM * m,BN_CTX * ctx)28 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
29 BN_CTX *ctx)
30 {
31 if (!BN_add(r, a, b))
32 return 0;
33 return BN_nnmod(r, r, m, ctx);
34 }
35
36 /*
37 * BN_mod_add variant that may be used if both a and b are non-negative and
38 * less than m. The original algorithm was
39 *
40 * if (!BN_uadd(r, a, b))
41 * return 0;
42 * if (BN_ucmp(r, m) >= 0)
43 * return BN_usub(r, r, m);
44 *
45 * which is replaced with addition, subtracting modulus, and conditional
46 * move depending on whether or not subtraction borrowed.
47 */
bn_mod_add_fixed_top(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BIGNUM * m)48 int bn_mod_add_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
49 const BIGNUM *m)
50 {
51 size_t i, ai, bi, mtop = m->top;
52 BN_ULONG storage[1024 / BN_BITS2];
53 BN_ULONG carry, temp, mask, *rp, *tp = storage;
54 const BN_ULONG *ap, *bp;
55
56 if (bn_wexpand(r, mtop) == NULL)
57 return 0;
58
59 if (mtop > sizeof(storage) / sizeof(storage[0])) {
60 tp = OPENSSL_malloc(mtop * sizeof(BN_ULONG));
61 if (tp == NULL) {
62 ERR_raise(ERR_LIB_BN, ERR_R_MALLOC_FAILURE);
63 return 0;
64 }
65 }
66
67 ap = a->d != NULL ? a->d : tp;
68 bp = b->d != NULL ? b->d : tp;
69
70 for (i = 0, ai = 0, bi = 0, carry = 0; i < mtop;) {
71 mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
72 temp = ((ap[ai] & mask) + carry) & BN_MASK2;
73 carry = (temp < carry);
74
75 mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
76 tp[i] = ((bp[bi] & mask) + temp) & BN_MASK2;
77 carry += (tp[i] < temp);
78
79 i++;
80 ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
81 bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
82 }
83 rp = r->d;
84 carry -= bn_sub_words(rp, tp, m->d, mtop);
85 for (i = 0; i < mtop; i++) {
86 rp[i] = (carry & tp[i]) | (~carry & rp[i]);
87 ((volatile BN_ULONG *)tp)[i] = 0;
88 }
89 r->top = mtop;
90 r->flags |= BN_FLG_FIXED_TOP;
91 r->neg = 0;
92
93 if (tp != storage)
94 OPENSSL_free(tp);
95
96 return 1;
97 }
98
BN_mod_add_quick(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BIGNUM * m)99 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
100 const BIGNUM *m)
101 {
102 int ret = bn_mod_add_fixed_top(r, a, b, m);
103
104 if (ret)
105 bn_correct_top(r);
106
107 return ret;
108 }
109
BN_mod_sub(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BIGNUM * m,BN_CTX * ctx)110 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
111 BN_CTX *ctx)
112 {
113 if (!BN_sub(r, a, b))
114 return 0;
115 return BN_nnmod(r, r, m, ctx);
116 }
117
118 /*
119 * BN_mod_sub variant that may be used if both a and b are non-negative,
120 * a is less than m, while b is of same bit width as m. It's implemented
121 * as subtraction followed by two conditional additions.
122 *
123 * 0 <= a < m
124 * 0 <= b < 2^w < 2*m
125 *
126 * after subtraction
127 *
128 * -2*m < r = a - b < m
129 *
130 * Thus it takes up to two conditional additions to make |r| positive.
131 */
bn_mod_sub_fixed_top(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BIGNUM * m)132 int bn_mod_sub_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
133 const BIGNUM *m)
134 {
135 size_t i, ai, bi, mtop = m->top;
136 BN_ULONG borrow, carry, ta, tb, mask, *rp;
137 const BN_ULONG *ap, *bp;
138
139 if (bn_wexpand(r, mtop) == NULL)
140 return 0;
141
142 rp = r->d;
143 ap = a->d != NULL ? a->d : rp;
144 bp = b->d != NULL ? b->d : rp;
145
146 for (i = 0, ai = 0, bi = 0, borrow = 0; i < mtop;) {
147 mask = (BN_ULONG)0 - ((i - a->top) >> (8 * sizeof(i) - 1));
148 ta = ap[ai] & mask;
149
150 mask = (BN_ULONG)0 - ((i - b->top) >> (8 * sizeof(i) - 1));
151 tb = bp[bi] & mask;
152 rp[i] = ta - tb - borrow;
153 if (ta != tb)
154 borrow = (ta < tb);
155
156 i++;
157 ai += (i - a->dmax) >> (8 * sizeof(i) - 1);
158 bi += (i - b->dmax) >> (8 * sizeof(i) - 1);
159 }
160 ap = m->d;
161 for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
162 ta = ((ap[i] & mask) + carry) & BN_MASK2;
163 carry = (ta < carry);
164 rp[i] = (rp[i] + ta) & BN_MASK2;
165 carry += (rp[i] < ta);
166 }
167 borrow -= carry;
168 for (i = 0, mask = 0 - borrow, carry = 0; i < mtop; i++) {
169 ta = ((ap[i] & mask) + carry) & BN_MASK2;
170 carry = (ta < carry);
171 rp[i] = (rp[i] + ta) & BN_MASK2;
172 carry += (rp[i] < ta);
173 }
174
175 r->top = mtop;
176 r->flags |= BN_FLG_FIXED_TOP;
177 r->neg = 0;
178
179 return 1;
180 }
181
182 /*
183 * BN_mod_sub variant that may be used if both a and b are non-negative and
184 * less than m
185 */
BN_mod_sub_quick(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BIGNUM * m)186 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
187 const BIGNUM *m)
188 {
189 if (!BN_sub(r, a, b))
190 return 0;
191 if (r->neg)
192 return BN_add(r, r, m);
193 return 1;
194 }
195
196 /* slow but works */
BN_mod_mul(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BIGNUM * m,BN_CTX * ctx)197 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
198 BN_CTX *ctx)
199 {
200 BIGNUM *t;
201 int ret = 0;
202
203 bn_check_top(a);
204 bn_check_top(b);
205 bn_check_top(m);
206
207 BN_CTX_start(ctx);
208 if ((t = BN_CTX_get(ctx)) == NULL)
209 goto err;
210 if (a == b) {
211 if (!BN_sqr(t, a, ctx))
212 goto err;
213 } else {
214 if (!BN_mul(t, a, b, ctx))
215 goto err;
216 }
217 if (!BN_nnmod(r, t, m, ctx))
218 goto err;
219 bn_check_top(r);
220 ret = 1;
221 err:
222 BN_CTX_end(ctx);
223 return ret;
224 }
225
BN_mod_sqr(BIGNUM * r,const BIGNUM * a,const BIGNUM * m,BN_CTX * ctx)226 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
227 {
228 if (!BN_sqr(r, a, ctx))
229 return 0;
230 /* r->neg == 0, thus we don't need BN_nnmod */
231 return BN_mod(r, r, m, ctx);
232 }
233
BN_mod_lshift1(BIGNUM * r,const BIGNUM * a,const BIGNUM * m,BN_CTX * ctx)234 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx)
235 {
236 if (!BN_lshift1(r, a))
237 return 0;
238 bn_check_top(r);
239 return BN_nnmod(r, r, m, ctx);
240 }
241
242 /*
243 * BN_mod_lshift1 variant that may be used if a is non-negative and less than
244 * m
245 */
BN_mod_lshift1_quick(BIGNUM * r,const BIGNUM * a,const BIGNUM * m)246 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m)
247 {
248 if (!BN_lshift1(r, a))
249 return 0;
250 bn_check_top(r);
251 if (BN_cmp(r, m) >= 0)
252 return BN_sub(r, r, m);
253 return 1;
254 }
255
BN_mod_lshift(BIGNUM * r,const BIGNUM * a,int n,const BIGNUM * m,BN_CTX * ctx)256 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
257 BN_CTX *ctx)
258 {
259 BIGNUM *abs_m = NULL;
260 int ret;
261
262 if (!BN_nnmod(r, a, m, ctx))
263 return 0;
264
265 if (m->neg) {
266 abs_m = BN_dup(m);
267 if (abs_m == NULL)
268 return 0;
269 abs_m->neg = 0;
270 }
271
272 ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m));
273 bn_check_top(r);
274
275 BN_free(abs_m);
276 return ret;
277 }
278
279 /*
280 * BN_mod_lshift variant that may be used if a is non-negative and less than
281 * m
282 */
BN_mod_lshift_quick(BIGNUM * r,const BIGNUM * a,int n,const BIGNUM * m)283 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m)
284 {
285 if (r != a) {
286 if (BN_copy(r, a) == NULL)
287 return 0;
288 }
289
290 while (n > 0) {
291 int max_shift;
292
293 /* 0 < r < m */
294 max_shift = BN_num_bits(m) - BN_num_bits(r);
295 /* max_shift >= 0 */
296
297 if (max_shift < 0) {
298 ERR_raise(ERR_LIB_BN, BN_R_INPUT_NOT_REDUCED);
299 return 0;
300 }
301
302 if (max_shift > n)
303 max_shift = n;
304
305 if (max_shift) {
306 if (!BN_lshift(r, r, max_shift))
307 return 0;
308 n -= max_shift;
309 } else {
310 if (!BN_lshift1(r, r))
311 return 0;
312 --n;
313 }
314
315 /* BN_num_bits(r) <= BN_num_bits(m) */
316
317 if (BN_cmp(r, m) >= 0) {
318 if (!BN_sub(r, r, m))
319 return 0;
320 }
321 }
322 bn_check_top(r);
323
324 return 1;
325 }
326