2 * Copyright 2018-2019 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2018-2019, Oracle and/or its affiliates. All rights reserved.
5 * Licensed under the OpenSSL license (the "License"). You may not use
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
11 #include <openssl/err.h>
12 #include <openssl/bn.h>
13 #include "internal/bn_int.h"
16 #define RSA_FIPS1864_MIN_KEYGEN_KEYSIZE 2048
17 #define RSA_FIPS1864_MIN_KEYGEN_STRENGTH 112
18 #define RSA_FIPS1864_MAX_KEYGEN_STRENGTH 256
21 * Generate probable primes 'p' & 'q'. See FIPS 186-4 Section B.3.6
22 * "Generation of Probable Primes with Conditions Based on Auxiliary Probable
26 * rsa Object used to store primes p & q.
27 * p1, p2 The returned auxiliary primes for p. If NULL they are not returned.
28 * Xpout An optionally returned random number used during generation of p.
29 * Xp An optional passed in value (that is random number used during
31 * Xp1, Xp2 Optionally passed in randomly generated numbers from which
32 * auxiliary primes p1 & p2 are calculated. If NULL these values
33 * are generated internally.
34 * q1, q2 The returned auxiliary primes for q. If NULL they are not returned.
35 * Xqout An optionally returned random number used during generation of q.
36 * Xq An optional passed in value (that is random number used during
38 * Xq1, Xq2 Optionally passed in randomly generated numbers from which
39 * auxiliary primes q1 & q2 are calculated. If NULL these values
40 * are generated internally.
41 * nbits The key size in bits (The size of the modulus n).
42 * e The public exponent.
43 * ctx A BN_CTX object.
44 * cb An optional BIGNUM callback.
45 * Returns: 1 if successful, or 0 otherwise.
47 * p1, p2, q1, q2, Xpout, Xqout are returned if they are not NULL.
48 * Xp, Xp1, Xp2, Xq, Xq1, Xq2 are optionally passed in.
49 * (Required for CAVS testing).
51 int rsa_fips186_4_gen_prob_primes(RSA *rsa, BIGNUM *p1, BIGNUM *p2,
52 BIGNUM *Xpout, const BIGNUM *Xp,
53 const BIGNUM *Xp1, const BIGNUM *Xp2,
54 BIGNUM *q1, BIGNUM *q2, BIGNUM *Xqout,
55 const BIGNUM *Xq, const BIGNUM *Xq1,
56 const BIGNUM *Xq2, int nbits,
57 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
60 BIGNUM *Xpo = NULL, *Xqo = NULL, *tmp = NULL;
62 /* (Step 1) Check key length
63 * NOTE: SP800-131A Rev1 Disallows key lengths of < 2048 bits for RSA
64 * Signature Generation and Key Agree/Transport.
66 if (nbits < RSA_FIPS1864_MIN_KEYGEN_KEYSIZE) {
67 RSAerr(RSA_F_RSA_FIPS186_4_GEN_PROB_PRIMES, RSA_R_INVALID_KEY_LENGTH);
71 if (!rsa_check_public_exponent(e)) {
72 RSAerr(RSA_F_RSA_FIPS186_4_GEN_PROB_PRIMES,
73 RSA_R_PUB_EXPONENT_OUT_OF_RANGE);
77 /* (Step 3) Determine strength and check rand generator strength is ok -
78 * this step is redundant because the generator always returns a higher
79 * strength than is required.
83 tmp = BN_CTX_get(ctx);
84 Xpo = (Xpout != NULL) ? Xpout : BN_CTX_get(ctx);
85 Xqo = (Xqout != NULL) ? Xqout : BN_CTX_get(ctx);
86 if (tmp == NULL || Xpo == NULL || Xqo == NULL)
90 rsa->p = BN_secure_new();
92 rsa->q = BN_secure_new();
93 if (rsa->p == NULL || rsa->q == NULL)
96 /* (Step 4) Generate p, Xp */
97 if (!bn_rsa_fips186_4_gen_prob_primes(rsa->p, Xpo, p1, p2, Xp, Xp1, Xp2,
101 /* (Step 5) Generate q, Xq*/
102 if (!bn_rsa_fips186_4_gen_prob_primes(rsa->q, Xqo, q1, q2, Xq, Xq1,
103 Xq2, nbits, e, ctx, cb))
106 /* (Step 6) |Xp - Xq| > 2^(nbitlen/2 - 100) */
107 ok = rsa_check_pminusq_diff(tmp, Xpo, Xqo, nbits);
113 /* (Step 6) |p - q| > 2^(nbitlen/2 - 100) */
114 ok = rsa_check_pminusq_diff(tmp, rsa->p, rsa->q, nbits);
119 break; /* successfully finished */
123 /* Zeroize any internally generated values that are not returned */
135 * Validates the RSA key size based on the target strength.
136 * See SP800-56Br1 6.3.1.1 (Steps 1a-1b)
139 * nbits The key size in bits.
140 * strength The target strength in bits. -1 means the target
141 * strength is unknown.
142 * Returns: 1 if the key size matches the target strength, or 0 otherwise.
144 int rsa_sp800_56b_validate_strength(int nbits, int strength)
146 int s = (int)rsa_compute_security_bits(nbits);
148 if (s < RSA_FIPS1864_MIN_KEYGEN_STRENGTH
149 || s > RSA_FIPS1864_MAX_KEYGEN_STRENGTH) {
150 RSAerr(RSA_F_RSA_SP800_56B_VALIDATE_STRENGTH, RSA_R_INVALID_MODULUS);
153 if (strength != -1 && s != strength) {
154 RSAerr(RSA_F_RSA_SP800_56B_VALIDATE_STRENGTH, RSA_R_INVALID_STRENGTH);
162 * Using p & q, calculate other required parameters such as n, d.
163 * as well as the CRT parameters dP, dQ, qInv.
166 * 6.3.1.1 rsakpg1 - basic (Steps 3-4)
167 * 6.3.1.3 rsakpg1 - crt (Step 5)
171 * nbits The key size.
172 * e The public exponent.
173 * ctx A BN_CTX object.
175 * There is a small chance that the generated d will be too small.
176 * Returns: -1 = error,
177 * 0 = d is too small,
180 int rsa_sp800_56b_derive_params_from_pq(RSA *rsa, int nbits,
181 const BIGNUM *e, BN_CTX *ctx)
184 BIGNUM *p1, *q1, *lcm, *p1q1, *gcd;
187 p1 = BN_CTX_get(ctx);
188 q1 = BN_CTX_get(ctx);
189 lcm = BN_CTX_get(ctx);
190 p1q1 = BN_CTX_get(ctx);
191 gcd = BN_CTX_get(ctx);
195 /* LCM((p-1, q-1)) */
196 if (rsa_get_lcm(ctx, rsa->p, rsa->q, lcm, gcd, p1, q1, p1q1) != 1)
205 BN_clear_free(rsa->d);
206 /* (Step 3) d = (e^-1) mod (LCM(p-1, q-1)) */
207 rsa->d = BN_secure_new();
208 if (rsa->d == NULL || BN_mod_inverse(rsa->d, e, lcm, ctx) == NULL)
211 /* (Step 3) return an error if d is too small */
212 if (BN_num_bits(rsa->d) <= (nbits >> 1)) {
217 /* (Step 4) n = pq */
220 if (rsa->n == NULL || !BN_mul(rsa->n, rsa->p, rsa->q, ctx))
223 /* (Step 5a) dP = d mod (p-1) */
224 if (rsa->dmp1 == NULL)
225 rsa->dmp1 = BN_new();
226 if (rsa->dmp1 == NULL || !BN_mod(rsa->dmp1, rsa->d, p1, ctx))
229 /* (Step 5b) dQ = d mod (q-1) */
230 if (rsa->dmq1 == NULL)
231 rsa->dmq1 = BN_secure_new();
232 if (rsa->dmq1 == NULL || !BN_mod(rsa->dmq1, rsa->d, q1, ctx))
235 /* (Step 5c) qInv = (inverse of q) mod p */
237 rsa->iqmp = BN_secure_new();
238 if (rsa->iqmp == NULL
239 || BN_mod_inverse(rsa->iqmp, rsa->q, rsa->p, ctx) == NULL)
269 * Generate a SP800-56B RSA key.
271 * See SP800-56Br1 6.3.1 "RSA Key-Pair Generation with a Fixed Public Exponent"
272 * 6.3.1.1 rsakpg1 - basic
273 * 6.3.1.3 rsakpg1 - crt
275 * See also FIPS 186-4 Section B.3.6
276 * "Generation of Probable Primes with Conditions Based on Auxiliary
280 * rsa The rsa object.
281 * nbits The intended key size in bits.
282 * efixed The public exponent. If NULL a default of 65537 is used.
283 * cb An optional BIGNUM callback.
284 * Returns: 1 if successfully generated otherwise it returns 0.
286 int rsa_sp800_56b_generate_key(RSA *rsa, int nbits, const BIGNUM *efixed,
294 /* (Steps 1a-1b) : Currently ignores the strength check */
295 if (!rsa_sp800_56b_validate_strength(nbits, -1))
302 /* Set default if e is not passed in */
303 if (efixed == NULL) {
305 if (e == NULL || !BN_set_word(e, 65537))
308 e = (BIGNUM *)efixed;
310 /* (Step 1c) fixed exponent is checked later . */
313 /* (Step 2) Generate prime factors */
314 if (!rsa_fips186_4_gen_prob_primes(rsa, NULL, NULL, NULL, NULL, NULL,
315 NULL, NULL, NULL, NULL, NULL, NULL,
316 NULL, nbits, e, ctx, cb))
318 /* (Steps 3-5) Compute params d, n, dP, dQ, qInv */
319 ok = rsa_sp800_56b_derive_params_from_pq(rsa, nbits, e, ctx);
324 /* Gets here if computed d is too small - so try again */
327 /* (Step 6) Do pairwise test - optional validity test has been omitted */
328 ret = rsa_sp800_56b_pairwise_test(rsa, ctx);
337 * See SP800-56Br1 6.3.1.3 (Step 6) Perform a pair-wise consistency test by
338 * verifying that: k = (k^e)^d mod n for some integer k where 1 < k < n-1.
340 * Returns 1 if the RSA key passes the pairwise test or 0 it it fails.
342 int rsa_sp800_56b_pairwise_test(RSA *rsa, BN_CTX *ctx)
348 tmp = BN_CTX_get(ctx);
353 ret = (BN_set_word(k, 2)
354 && BN_mod_exp(tmp, k, rsa->e, rsa->n, ctx)
355 && BN_mod_exp(tmp, tmp, rsa->d, rsa->n, ctx)
356 && BN_cmp(k, tmp) == 0);
358 RSAerr(RSA_F_RSA_SP800_56B_PAIRWISE_TEST, RSA_R_PAIRWISE_TEST_FAILURE);