]>
Commit | Line | Data |
---|---|---|
8240d5fa | 1 | /* |
8020d79b | 2 | * Copyright 2018-2021 The OpenSSL Project Authors. All Rights Reserved. |
8240d5fa SL |
3 | * Copyright (c) 2018-2019, Oracle and/or its affiliates. All rights reserved. |
4 | * | |
a6ed19dc | 5 | * Licensed under the Apache License 2.0 (the "License"). You may not use |
8240d5fa SL |
6 | * this file except in compliance with the License. You can obtain a copy |
7 | * in the file LICENSE in the source distribution or at | |
8 | * https://www.openssl.org/source/license.html | |
9 | */ | |
10 | ||
11 | /* | |
12 | * According to NIST SP800-131A "Transitioning the use of cryptographic | |
13 | * algorithms and key lengths" Generation of 1024 bit RSA keys are no longer | |
14 | * allowed for signatures (Table 2) or key transport (Table 5). In the code | |
15 | * below any attempt to generate 1024 bit RSA keys will result in an error (Note | |
16 | * that digital signature verification can still use deprecated 1024 bit keys). | |
17 | * | |
8240d5fa SL |
18 | * FIPS 186-4 relies on the use of the auxiliary primes p1, p2, q1 and q2 that |
19 | * must be generated before the module generates the RSA primes p and q. | |
5ae86f28 | 20 | * Table B.1 in FIPS 186-4 specifies RSA modulus lengths of 2048 and |
8240d5fa | 21 | * 3072 bits only, the min/max total length of the auxiliary primes. |
5ae86f28 SL |
22 | * FIPS 186-5 Table A.1 includes an additional entry for 4096 which has been |
23 | * included here. | |
8240d5fa SL |
24 | */ |
25 | #include <stdio.h> | |
26 | #include <openssl/bn.h> | |
706457b7 | 27 | #include "bn_local.h" |
25f2138b | 28 | #include "crypto/bn.h" |
fd4a6e7d KR |
29 | #include "internal/nelem.h" |
30 | ||
31 | #if BN_BITS2 == 64 | |
32 | # define BN_DEF(lo, hi) (BN_ULONG)hi<<32|lo | |
33 | #else | |
34 | # define BN_DEF(lo, hi) lo, hi | |
35 | #endif | |
36 | ||
37 | /* 1 / sqrt(2) * 2^256, rounded up */ | |
38 | static const BN_ULONG inv_sqrt_2_val[] = { | |
39 | BN_DEF(0x83339916UL, 0xED17AC85UL), BN_DEF(0x893BA84CUL, 0x1D6F60BAUL), | |
40 | BN_DEF(0x754ABE9FUL, 0x597D89B3UL), BN_DEF(0xF9DE6484UL, 0xB504F333UL) | |
41 | }; | |
42 | ||
94553e85 | 43 | const BIGNUM ossl_bn_inv_sqrt_2 = { |
fd4a6e7d KR |
44 | (BN_ULONG *)inv_sqrt_2_val, |
45 | OSSL_NELEM(inv_sqrt_2_val), | |
46 | OSSL_NELEM(inv_sqrt_2_val), | |
47 | 0, | |
48 | BN_FLG_STATIC_DATA | |
49 | }; | |
8240d5fa SL |
50 | |
51 | /* | |
5ae86f28 SL |
52 | * FIPS 186-5 Table A.1. "Min length of auxiliary primes p1, p2, q1, q2". |
53 | * (FIPS 186-5 has an entry for >= 4096 bits). | |
8240d5fa SL |
54 | * |
55 | * Params: | |
56 | * nbits The key size in bits. | |
57 | * Returns: | |
58 | * The minimum size of the auxiliary primes or 0 if nbits is invalid. | |
59 | */ | |
5ae86f28 | 60 | static int bn_rsa_fips186_5_aux_prime_min_size(int nbits) |
8240d5fa | 61 | { |
5ae86f28 SL |
62 | if (nbits >= 4096) |
63 | return 201; | |
8240d5fa SL |
64 | if (nbits >= 3072) |
65 | return 171; | |
7c9a7cf1 | 66 | if (nbits >= 2048) |
8240d5fa SL |
67 | return 141; |
68 | return 0; | |
69 | } | |
70 | ||
71 | /* | |
5ae86f28 | 72 | * FIPS 186-5 Table A.1 "Max of len(p1) + len(p2) and |
8240d5fa | 73 | * len(q1) + len(q2) for p,q Probable Primes". |
5ae86f28 | 74 | * (FIPS 186-5 has an entry for >= 4096 bits). |
8240d5fa SL |
75 | * Params: |
76 | * nbits The key size in bits. | |
77 | * Returns: | |
78 | * The maximum length or 0 if nbits is invalid. | |
79 | */ | |
5ae86f28 | 80 | static int bn_rsa_fips186_5_aux_prime_max_sum_size_for_prob_primes(int nbits) |
8240d5fa | 81 | { |
5ae86f28 SL |
82 | if (nbits >= 4096) |
83 | return 2030; | |
8240d5fa SL |
84 | if (nbits >= 3072) |
85 | return 1518; | |
7c9a7cf1 | 86 | if (nbits >= 2048) |
8240d5fa SL |
87 | return 1007; |
88 | return 0; | |
89 | } | |
90 | ||
8240d5fa SL |
91 | /* |
92 | * Find the first odd integer that is a probable prime. | |
93 | * | |
94 | * See section FIPS 186-4 B.3.6 (Steps 4.2/5.2). | |
95 | * | |
96 | * Params: | |
97 | * Xp1 The passed in starting point to find a probably prime. | |
98 | * p1 The returned probable prime (first odd integer >= Xp1) | |
99 | * ctx A BN_CTX object. | |
100 | * cb An optional BIGNUM callback. | |
101 | * Returns: 1 on success otherwise it returns 0. | |
102 | */ | |
103 | static int bn_rsa_fips186_4_find_aux_prob_prime(const BIGNUM *Xp1, | |
104 | BIGNUM *p1, BN_CTX *ctx, | |
105 | BN_GENCB *cb) | |
106 | { | |
107 | int ret = 0; | |
108 | int i = 0; | |
8240d5fa | 109 | |
42619397 | 110 | if (BN_copy(p1, Xp1) == NULL) |
8240d5fa | 111 | return 0; |
d4bf0d57 | 112 | BN_set_flags(p1, BN_FLG_CONSTTIME); |
8240d5fa SL |
113 | |
114 | /* Find the first odd number >= Xp1 that is probably prime */ | |
1287dabd | 115 | for (;;) { |
8240d5fa SL |
116 | i++; |
117 | BN_GENCB_call(cb, 0, i); | |
118 | /* MR test with trial division */ | |
42619397 | 119 | if (BN_check_prime(p1, ctx, cb)) |
8240d5fa SL |
120 | break; |
121 | /* Get next odd number */ | |
122 | if (!BN_add_word(p1, 2)) | |
123 | goto err; | |
124 | } | |
125 | BN_GENCB_call(cb, 2, i); | |
126 | ret = 1; | |
127 | err: | |
128 | return ret; | |
129 | } | |
130 | ||
131 | /* | |
132 | * Generate a probable prime (p or q). | |
133 | * | |
134 | * See FIPS 186-4 B.3.6 (Steps 4 & 5) | |
135 | * | |
136 | * Params: | |
137 | * p The returned probable prime. | |
138 | * Xpout An optionally returned random number used during generation of p. | |
139 | * p1, p2 The returned auxiliary primes. If NULL they are not returned. | |
140 | * Xp An optional passed in value (that is random number used during | |
141 | * generation of p). | |
142 | * Xp1, Xp2 Optional passed in values that are normally generated | |
143 | * internally. Used to find p1, p2. | |
144 | * nlen The bit length of the modulus (the key size). | |
145 | * e The public exponent. | |
146 | * ctx A BN_CTX object. | |
147 | * cb An optional BIGNUM callback. | |
148 | * Returns: 1 on success otherwise it returns 0. | |
149 | */ | |
94553e85 SL |
150 | int ossl_bn_rsa_fips186_4_gen_prob_primes(BIGNUM *p, BIGNUM *Xpout, |
151 | BIGNUM *p1, BIGNUM *p2, | |
152 | const BIGNUM *Xp, const BIGNUM *Xp1, | |
153 | const BIGNUM *Xp2, int nlen, | |
154 | const BIGNUM *e, BN_CTX *ctx, | |
155 | BN_GENCB *cb) | |
8240d5fa SL |
156 | { |
157 | int ret = 0; | |
158 | BIGNUM *p1i = NULL, *p2i = NULL, *Xp1i = NULL, *Xp2i = NULL; | |
159 | int bitlen; | |
160 | ||
161 | if (p == NULL || Xpout == NULL) | |
162 | return 0; | |
163 | ||
164 | BN_CTX_start(ctx); | |
165 | ||
166 | p1i = (p1 != NULL) ? p1 : BN_CTX_get(ctx); | |
167 | p2i = (p2 != NULL) ? p2 : BN_CTX_get(ctx); | |
168 | Xp1i = (Xp1 != NULL) ? (BIGNUM *)Xp1 : BN_CTX_get(ctx); | |
169 | Xp2i = (Xp2 != NULL) ? (BIGNUM *)Xp2 : BN_CTX_get(ctx); | |
170 | if (p1i == NULL || p2i == NULL || Xp1i == NULL || Xp2i == NULL) | |
171 | goto err; | |
172 | ||
5ae86f28 | 173 | bitlen = bn_rsa_fips186_5_aux_prime_min_size(nlen); |
8240d5fa SL |
174 | if (bitlen == 0) |
175 | goto err; | |
176 | ||
177 | /* (Steps 4.1/5.1): Randomly generate Xp1 if it is not passed in */ | |
178 | if (Xp1 == NULL) { | |
179 | /* Set the top and bottom bits to make it odd and the correct size */ | |
2934be91 | 180 | if (!BN_priv_rand_ex(Xp1i, bitlen, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD, |
5cbd2ea3 | 181 | 0, ctx)) |
8240d5fa SL |
182 | goto err; |
183 | } | |
184 | /* (Steps 4.1/5.1): Randomly generate Xp2 if it is not passed in */ | |
185 | if (Xp2 == NULL) { | |
186 | /* Set the top and bottom bits to make it odd and the correct size */ | |
2934be91 | 187 | if (!BN_priv_rand_ex(Xp2i, bitlen, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD, |
5cbd2ea3 | 188 | 0, ctx)) |
8240d5fa SL |
189 | goto err; |
190 | } | |
191 | ||
192 | /* (Steps 4.2/5.2) - find first auxiliary probable primes */ | |
193 | if (!bn_rsa_fips186_4_find_aux_prob_prime(Xp1i, p1i, ctx, cb) | |
194 | || !bn_rsa_fips186_4_find_aux_prob_prime(Xp2i, p2i, ctx, cb)) | |
195 | goto err; | |
196 | /* (Table B.1) auxiliary prime Max length check */ | |
197 | if ((BN_num_bits(p1i) + BN_num_bits(p2i)) >= | |
5ae86f28 | 198 | bn_rsa_fips186_5_aux_prime_max_sum_size_for_prob_primes(nlen)) |
8240d5fa SL |
199 | goto err; |
200 | /* (Steps 4.3/5.3) - generate prime */ | |
94553e85 SL |
201 | if (!ossl_bn_rsa_fips186_4_derive_prime(p, Xpout, Xp, p1i, p2i, nlen, e, |
202 | ctx, cb)) | |
8240d5fa SL |
203 | goto err; |
204 | ret = 1; | |
205 | err: | |
206 | /* Zeroize any internally generated values that are not returned */ | |
207 | if (p1 == NULL) | |
208 | BN_clear(p1i); | |
209 | if (p2 == NULL) | |
210 | BN_clear(p2i); | |
211 | if (Xp1 == NULL) | |
212 | BN_clear(Xp1i); | |
213 | if (Xp2 == NULL) | |
214 | BN_clear(Xp2i); | |
215 | BN_CTX_end(ctx); | |
216 | return ret; | |
217 | } | |
218 | ||
219 | /* | |
220 | * Constructs a probable prime (a candidate for p or q) using 2 auxiliary | |
221 | * prime numbers and the Chinese Remainder Theorem. | |
222 | * | |
223 | * See FIPS 186-4 C.9 "Compute a Probable Prime Factor Based on Auxiliary | |
224 | * Primes". Used by FIPS 186-4 B.3.6 Section (4.3) for p and Section (5.3) for q. | |
225 | * | |
226 | * Params: | |
227 | * Y The returned prime factor (private_prime_factor) of the modulus n. | |
228 | * X The returned random number used during generation of the prime factor. | |
229 | * Xin An optional passed in value for X used for testing purposes. | |
230 | * r1 An auxiliary prime. | |
231 | * r2 An auxiliary prime. | |
232 | * nlen The desired length of n (the RSA modulus). | |
233 | * e The public exponent. | |
234 | * ctx A BN_CTX object. | |
235 | * cb An optional BIGNUM callback object. | |
236 | * Returns: 1 on success otherwise it returns 0. | |
237 | * Assumptions: | |
238 | * Y, X, r1, r2, e are not NULL. | |
239 | */ | |
94553e85 SL |
240 | int ossl_bn_rsa_fips186_4_derive_prime(BIGNUM *Y, BIGNUM *X, const BIGNUM *Xin, |
241 | const BIGNUM *r1, const BIGNUM *r2, | |
242 | int nlen, const BIGNUM *e, BN_CTX *ctx, | |
243 | BN_GENCB *cb) | |
8240d5fa SL |
244 | { |
245 | int ret = 0; | |
246 | int i, imax; | |
247 | int bits = nlen >> 1; | |
8240d5fa | 248 | BIGNUM *tmp, *R, *r1r2x2, *y1, *r1x2; |
fd4a6e7d | 249 | BIGNUM *base, *range; |
8240d5fa | 250 | |
8240d5fa SL |
251 | BN_CTX_start(ctx); |
252 | ||
fd4a6e7d KR |
253 | base = BN_CTX_get(ctx); |
254 | range = BN_CTX_get(ctx); | |
8240d5fa SL |
255 | R = BN_CTX_get(ctx); |
256 | tmp = BN_CTX_get(ctx); | |
257 | r1r2x2 = BN_CTX_get(ctx); | |
258 | y1 = BN_CTX_get(ctx); | |
259 | r1x2 = BN_CTX_get(ctx); | |
260 | if (r1x2 == NULL) | |
261 | goto err; | |
262 | ||
263 | if (Xin != NULL && BN_copy(X, Xin) == NULL) | |
264 | goto err; | |
265 | ||
fd4a6e7d KR |
266 | /* |
267 | * We need to generate a random number X in the range | |
268 | * 1/sqrt(2) * 2^(nlen/2) <= X < 2^(nlen/2). | |
269 | * We can rewrite that as: | |
270 | * base = 1/sqrt(2) * 2^(nlen/2) | |
271 | * range = ((2^(nlen/2))) - (1/sqrt(2) * 2^(nlen/2)) | |
272 | * X = base + random(range) | |
273 | * We only have the first 256 bit of 1/sqrt(2) | |
274 | */ | |
275 | if (Xin == NULL) { | |
94553e85 | 276 | if (bits < BN_num_bits(&ossl_bn_inv_sqrt_2)) |
fd4a6e7d | 277 | goto err; |
94553e85 SL |
278 | if (!BN_lshift(base, &ossl_bn_inv_sqrt_2, |
279 | bits - BN_num_bits(&ossl_bn_inv_sqrt_2)) | |
fd4a6e7d KR |
280 | || !BN_lshift(range, BN_value_one(), bits) |
281 | || !BN_sub(range, range, base)) | |
282 | goto err; | |
283 | } | |
284 | ||
8240d5fa SL |
285 | if (!(BN_lshift1(r1x2, r1) |
286 | /* (Step 1) GCD(2r1, r2) = 1 */ | |
287 | && BN_gcd(tmp, r1x2, r2, ctx) | |
288 | && BN_is_one(tmp) | |
289 | /* (Step 2) R = ((r2^-1 mod 2r1) * r2) - ((2r1^-1 mod r2)*2r1) */ | |
290 | && BN_mod_inverse(R, r2, r1x2, ctx) | |
291 | && BN_mul(R, R, r2, ctx) /* R = (r2^-1 mod 2r1) * r2 */ | |
292 | && BN_mod_inverse(tmp, r1x2, r2, ctx) | |
293 | && BN_mul(tmp, tmp, r1x2, ctx) /* tmp = (2r1^-1 mod r2)*2r1 */ | |
294 | && BN_sub(R, R, tmp) | |
295 | /* Calculate 2r1r2 */ | |
296 | && BN_mul(r1r2x2, r1x2, r2, ctx))) | |
297 | goto err; | |
298 | /* Make positive by adding the modulus */ | |
299 | if (BN_is_negative(R) && !BN_add(R, R, r1r2x2)) | |
300 | goto err; | |
301 | ||
302 | imax = 5 * bits; /* max = 5/2 * nbits */ | |
303 | for (;;) { | |
304 | if (Xin == NULL) { | |
305 | /* | |
306 | * (Step 3) Choose Random X such that | |
fd4a6e7d | 307 | * sqrt(2) * 2^(nlen/2-1) <= Random X <= (2^(nlen/2)) - 1. |
8240d5fa | 308 | */ |
5cbd2ea3 | 309 | if (!BN_priv_rand_range_ex(X, range, 0, ctx) || !BN_add(X, X, base)) |
8240d5fa SL |
310 | goto end; |
311 | } | |
312 | /* (Step 4) Y = X + ((R - X) mod 2r1r2) */ | |
313 | if (!BN_mod_sub(Y, R, X, r1r2x2, ctx) || !BN_add(Y, Y, X)) | |
314 | goto err; | |
315 | /* (Step 5) */ | |
316 | i = 0; | |
317 | for (;;) { | |
318 | /* (Step 6) */ | |
319 | if (BN_num_bits(Y) > bits) { | |
320 | if (Xin == NULL) | |
321 | break; /* Randomly Generated X so Go back to Step 3 */ | |
322 | else | |
323 | goto err; /* X is not random so it will always fail */ | |
324 | } | |
325 | BN_GENCB_call(cb, 0, 2); | |
326 | ||
327 | /* (Step 7) If GCD(Y-1) == 1 & Y is probably prime then return Y */ | |
328 | if (BN_copy(y1, Y) == NULL | |
329 | || !BN_sub_word(y1, 1) | |
330 | || !BN_gcd(tmp, y1, e, ctx)) | |
331 | goto err; | |
42619397 | 332 | if (BN_is_one(tmp) && BN_check_prime(Y, ctx, cb)) |
8240d5fa SL |
333 | goto end; |
334 | /* (Step 8-10) */ | |
335 | if (++i >= imax || !BN_add(Y, Y, r1r2x2)) | |
336 | goto err; | |
337 | } | |
338 | } | |
339 | end: | |
340 | ret = 1; | |
341 | BN_GENCB_call(cb, 3, 0); | |
342 | err: | |
343 | BN_clear(y1); | |
344 | BN_CTX_end(ctx); | |
345 | return ret; | |
346 | } |