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"
17 * Part of the RSA keypair test.
18 * Check the Chinese Remainder Theorem components are valid.
21 * 6.4.1.2.3: rsakpv1-crt Step 7
22 * 6.4.1.3.3: rsakpv2-crt Step 7
24 int rsa_check_crt_components(const RSA *rsa, BN_CTX *ctx)
27 BIGNUM *r = NULL, *p1 = NULL, *q1 = NULL;
29 /* check if only some of the crt components are set */
30 if (rsa->dmp1 == NULL || rsa->dmq1 == NULL || rsa->iqmp == NULL) {
31 if (rsa->dmp1 != NULL || rsa->dmq1 != NULL || rsa->iqmp != NULL)
33 return 1; /* return ok if all components are NULL */
42 && (BN_copy(p1, rsa->p) != NULL)
45 && (BN_copy(q1, rsa->q) != NULL)
47 /* (a) 1 < dP < (p – 1). */
48 && (BN_cmp(rsa->dmp1, BN_value_one()) > 0)
49 && (BN_cmp(rsa->dmp1, p1) < 0)
50 /* (b) 1 < dQ < (q - 1). */
51 && (BN_cmp(rsa->dmq1, BN_value_one()) > 0)
52 && (BN_cmp(rsa->dmq1, q1) < 0)
53 /* (c) 1 < qInv < p */
54 && (BN_cmp(rsa->iqmp, BN_value_one()) > 0)
55 && (BN_cmp(rsa->iqmp, rsa->p) < 0)
56 /* (d) 1 = (dP . e) mod (p - 1)*/
57 && BN_mod_mul(r, rsa->dmp1, rsa->e, p1, ctx)
59 /* (e) 1 = (dQ . e) mod (q - 1) */
60 && BN_mod_mul(r, rsa->dmq1, rsa->e, q1, ctx)
62 /* (f) 1 = (qInv . q) mod p */
63 && BN_mod_mul(r, rsa->iqmp, rsa->q, rsa->p, ctx)
72 * Part of the RSA keypair test.
73 * Check that (√2)(2^(nbits/2 - 1) <= p <= 2^(nbits/2) - 1
75 * See SP800-5bBr1 6.4.1.2.1 Part 5 (c) & (g) - used for both p and q.
77 * (√2)(2^(nbits/2 - 1) = (√2/2)(2^(nbits/2))
78 * √2/2 = 0.707106781186547524400 = 0.B504F333F9DE6484597D8
79 * 0.B504F334 gives an approximation to 11 decimal places.
80 * The range is then from
81 * 0xB504F334_0000.......................000 to
82 * 0xFFFFFFFF_FFFF.......................FFF
84 int rsa_check_prime_factor_range(const BIGNUM *p, int nbits, BN_CTX *ctx)
91 /* Upper bound check */
92 if (BN_num_bits(p) != nbits)
96 tmp = BN_CTX_get(ctx);
97 low = BN_CTX_get(ctx);
99 /* set low = (√2)(2^(nbits/2 - 1) */
100 if (low == NULL || !BN_set_word(tmp, 0xB504F334))
104 if (!BN_lshift(low, tmp, nbits - 32))
106 } else if (!BN_rshift(low, tmp, 32 - nbits)) {
109 if (BN_cmp(p, low) < 0)
118 * Part of the RSA keypair test.
119 * Check the prime factor (for either p or q)
120 * i.e: p is prime AND GCD(p - 1, e) = 1
122 * See SP800-5bBr1 6.4.1.2.3 Step 5 (a to d) & (e to h).
124 int rsa_check_prime_factor(BIGNUM *p, BIGNUM *e, int nbits, BN_CTX *ctx)
126 int checks = bn_rsa_fips186_4_prime_MR_min_checks(nbits);
128 BIGNUM *p1 = NULL, *gcd = NULL;
130 /* (Steps 5 a-b) prime test */
131 if (BN_is_prime_fasttest_ex(p, checks, ctx, 1, NULL) != 1
132 /* (Step 5c) (√2)(2^(nbits/2 - 1) <= p <= 2^(nbits/2 - 1) */
133 || rsa_check_prime_factor_range(p, nbits, ctx) != 1)
137 p1 = BN_CTX_get(ctx);
138 gcd = BN_CTX_get(ctx);
140 /* (Step 5d) GCD(p-1, e) = 1 */
141 && (BN_copy(p1, p) != NULL)
142 && BN_sub_word(p1, 1)
143 && BN_gcd(gcd, p1, e, ctx)
152 * See SP800-56Br1 6.4.1.2.3 Part 6(a-b) Check the private exponent d
154 * (Step 6a) 2^(nBit/2) < d < LCM(p–1, q–1).
155 * (Step 6b) 1 = (d*e) mod LCM(p–1, q–1)
157 int rsa_check_private_exponent(const RSA *rsa, int nbits, BN_CTX *ctx)
160 BIGNUM *r, *p1, *q1, *lcm, *p1q1, *gcd;
162 /* (Step 6a) 2^(nbits/2) < d */
163 if (BN_num_bits(rsa->d) <= (nbits >> 1))
168 p1 = BN_CTX_get(ctx);
169 q1 = BN_CTX_get(ctx);
170 lcm = BN_CTX_get(ctx);
171 p1q1 = BN_CTX_get(ctx);
172 gcd = BN_CTX_get(ctx);
174 /* LCM(p - 1, q - 1) */
175 && (rsa_get_lcm(ctx, rsa->p, rsa->q, lcm, gcd, p1, q1, p1q1) == 1)
176 /* (Step 6a) d < LCM(p - 1, q - 1) */
177 && (BN_cmp(rsa->d, lcm) < 0)
178 /* (Step 6b) 1 = (e . d) mod LCM(p - 1, q - 1) */
179 && BN_mod_mul(r, rsa->e, rsa->d, lcm, ctx)
190 /* Check exponent is odd, and has a bitlen ranging from [17..256] */
191 int rsa_check_public_exponent(const BIGNUM *e)
193 int bitlen = BN_num_bits(e);
195 return (BN_is_odd(e) && bitlen > 16 && bitlen < 257);
199 * SP800-56Br1 6.4.1.2.1 (Step 5i): |p - q| > 2^(nbits/2 - 100)
200 * i.e- numbits(p-q-1) > (nbits/2 -100)
202 int rsa_check_pminusq_diff(BIGNUM *diff, const BIGNUM *p, const BIGNUM *q,
205 int bitlen = (nbits >> 1) - 100;
207 if (!BN_sub(diff, p, q))
209 BN_set_negative(diff, 0);
211 if (BN_is_zero(diff))
214 if (!BN_sub_word(diff, 1))
216 return (BN_num_bits(diff) > bitlen);
219 /* return LCM(p-1, q-1) */
220 int rsa_get_lcm(BN_CTX *ctx, const BIGNUM *p, const BIGNUM *q,
221 BIGNUM *lcm, BIGNUM *gcd, BIGNUM *p1, BIGNUM *q1,
224 return BN_sub(p1, p, BN_value_one()) /* p-1 */
225 && BN_sub(q1, q, BN_value_one()) /* q-1 */
226 && BN_mul(p1q1, p1, q1, ctx) /* (p-1)(q-1) */
227 && BN_gcd(gcd, p1, q1, ctx)
228 && BN_div(lcm, NULL, p1q1, gcd, ctx); /* LCM((p-1, q-1)) */
232 * SP800-56Br1 6.4.2.2 Partial Public Key Validation for RSA refers to
233 * SP800-89 5.3.3 (Explicit) Partial Public Key Validation for RSA
234 * caveat is that the modulus must be as specified in SP800-56Br1
236 int rsa_sp800_56b_check_public(const RSA *rsa)
238 int ret = 0, nbits, iterations, status;
242 if (rsa->n == NULL || rsa->e == NULL)
246 * (Step a): modulus must be 2048 or 3072 (caveat from SP800-56Br1)
247 * NOTE: changed to allow keys >= 2048
249 nbits = BN_num_bits(rsa->n);
250 if (!rsa_sp800_56b_validate_strength(nbits, -1)) {
251 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC, RSA_R_INVALID_KEY_LENGTH);
254 if (!BN_is_odd(rsa->n)) {
255 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC, RSA_R_INVALID_MODULUS);
259 /* (Steps b-c): 2^16 < e < 2^256, n and e must be odd */
260 if (!rsa_check_public_exponent(rsa->e)) {
261 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC,
262 RSA_R_PUB_EXPONENT_OUT_OF_RANGE);
268 if (ctx == NULL || gcd == NULL)
271 iterations = bn_rsa_fips186_4_prime_MR_min_checks(nbits);
273 * The modulus is composite, but not a power of a prime.
274 * The modulus has no factors smaller than 752.
276 if (!BN_gcd(gcd, rsa->n, bn_get0_small_factors(), ctx) || !BN_is_one(gcd)) {
277 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC, RSA_R_INVALID_MODULUS);
281 ret = bn_miller_rabin_is_prime(rsa->n, iterations, ctx, NULL, 1, &status);
282 if (ret != 1 || status != BN_PRIMETEST_COMPOSITE_NOT_POWER_OF_PRIME) {
283 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC, RSA_R_INVALID_MODULUS);
296 * Perform validation of the RSA private key to check that 0 < D < N.
298 int rsa_sp800_56b_check_private(const RSA *rsa)
300 if (rsa->d == NULL || rsa->n == NULL)
302 return BN_cmp(rsa->d, BN_value_one()) >= 0 && BN_cmp(rsa->d, rsa->n) < 0;
306 * RSA key pair validation.
309 * 6.4.1.2 "RSAKPV1 Family: RSA Key - Pair Validation with a Fixed Exponent"
310 * 6.4.1.3 "RSAKPV2 Family: RSA Key - Pair Validation with a Random Exponent"
313 * 6.4.1.2.3 "rsakpv1 - crt"
314 * 6.4.1.3.3 "rsakpv2 - crt"
316 int rsa_sp800_56b_check_keypair(const RSA *rsa, const BIGNUM *efixed,
317 int strength, int nbits)
328 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR, RSA_R_INVALID_REQUEST);
331 /* (Step 1): Check Ranges */
332 if (!rsa_sp800_56b_validate_strength(nbits, strength))
335 /* If the exponent is known */
336 if (efixed != NULL) {
337 /* (2): Check fixed exponent matches public exponent. */
338 if (BN_cmp(efixed, rsa->e) != 0) {
339 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR, RSA_R_INVALID_REQUEST);
343 /* (Step 1.c): e is odd integer 65537 <= e < 2^256 */
344 if (!rsa_check_public_exponent(rsa->e)) {
345 /* exponent out of range */
346 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR,
347 RSA_R_PUB_EXPONENT_OUT_OF_RANGE);
350 /* (Step 3.b): check the modulus */
351 if (nbits != BN_num_bits(rsa->n)) {
352 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR, RSA_R_INVALID_KEYPAIR);
362 if (r == NULL || !BN_mul(r, rsa->p, rsa->q, ctx))
364 /* (Step 4.c): Check n = pq */
365 if (BN_cmp(rsa->n, r) != 0) {
366 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR, RSA_R_INVALID_REQUEST);
370 /* (Step 5): check prime factors p & q */
371 ret = rsa_check_prime_factor(rsa->p, rsa->e, nbits, ctx)
372 && rsa_check_prime_factor(rsa->q, rsa->e, nbits, ctx)
373 && (rsa_check_pminusq_diff(r, rsa->p, rsa->q, nbits) > 0)
374 /* (Step 6): Check the private exponent d */
375 && rsa_check_private_exponent(rsa, nbits, ctx)
376 /* 6.4.1.2.3 (Step 7): Check the CRT components */
377 && rsa_check_crt_components(rsa, ctx);
379 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR, RSA_R_INVALID_KEYPAIR);