2 * Copyright 2018-2020 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2018-2019, Oracle and/or its affiliates. All rights reserved.
5 * Licensed under the Apache License 2.0 (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 "crypto/bn.h"
14 #include "rsa_local.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))
79 int rsa_check_prime_factor_range(const BIGNUM *p, int nbits, BN_CTX *ctx)
86 shift = nbits - BN_num_bits(&bn_inv_sqrt_2);
88 /* Upper bound check */
89 if (BN_num_bits(p) != nbits)
93 low = BN_CTX_get(ctx);
97 /* set low = (√2)(2^(nbits/2 - 1) */
98 if (!BN_copy(low, &bn_inv_sqrt_2))
103 * We don't have all the bits. bn_inv_sqrt_2 contains a rounded up
104 * value, so there is a very low probability that we'll reject a valid
107 if (!BN_lshift(low, low, shift))
109 } else if (!BN_rshift(low, low, -shift)) {
112 if (BN_cmp(p, low) <= 0)
121 * Part of the RSA keypair test.
122 * Check the prime factor (for either p or q)
123 * i.e: p is prime AND GCD(p - 1, e) = 1
125 * See SP800-56Br1 6.4.1.2.3 Step 5 (a to d) & (e to h).
127 int rsa_check_prime_factor(BIGNUM *p, BIGNUM *e, int nbits, BN_CTX *ctx)
130 BIGNUM *p1 = NULL, *gcd = NULL;
132 /* (Steps 5 a-b) prime test */
133 if (BN_check_prime(p, ctx, NULL) != 1
134 /* (Step 5c) (√2)(2^(nbits/2 - 1) <= p <= 2^(nbits/2 - 1) */
135 || rsa_check_prime_factor_range(p, nbits, ctx) != 1)
139 p1 = BN_CTX_get(ctx);
140 gcd = BN_CTX_get(ctx);
142 /* (Step 5d) GCD(p-1, e) = 1 */
143 && (BN_copy(p1, p) != NULL)
144 && BN_sub_word(p1, 1)
145 && BN_gcd(gcd, p1, e, ctx)
154 * See SP800-56Br1 6.4.1.2.3 Part 6(a-b) Check the private exponent d
156 * (Step 6a) 2^(nBit/2) < d < LCM(p–1, q–1).
157 * (Step 6b) 1 = (d*e) mod LCM(p–1, q–1)
159 int rsa_check_private_exponent(const RSA *rsa, int nbits, BN_CTX *ctx)
162 BIGNUM *r, *p1, *q1, *lcm, *p1q1, *gcd;
164 /* (Step 6a) 2^(nbits/2) < d */
165 if (BN_num_bits(rsa->d) <= (nbits >> 1))
170 p1 = BN_CTX_get(ctx);
171 q1 = BN_CTX_get(ctx);
172 lcm = BN_CTX_get(ctx);
173 p1q1 = BN_CTX_get(ctx);
174 gcd = BN_CTX_get(ctx);
176 /* LCM(p - 1, q - 1) */
177 && (rsa_get_lcm(ctx, rsa->p, rsa->q, lcm, gcd, p1, q1, p1q1) == 1)
178 /* (Step 6a) d < LCM(p - 1, q - 1) */
179 && (BN_cmp(rsa->d, lcm) < 0)
180 /* (Step 6b) 1 = (e . d) mod LCM(p - 1, q - 1) */
181 && BN_mod_mul(r, rsa->e, rsa->d, lcm, ctx)
193 static int bn_is_three(const BIGNUM *bn)
195 BIGNUM *num = BN_dup(bn);
196 int ret = (num != NULL && BN_sub_word(num, 3) && BN_is_zero(num));
201 #endif /* FIPS_MODULE */
203 /* Check exponent is odd, and has a bitlen ranging from [17..256] */
204 int rsa_check_public_exponent(const BIGNUM *e)
208 /* For legacy purposes RSA_3 is allowed in non fips mode */
212 #endif /* FIPS_MODULE */
214 bitlen = BN_num_bits(e);
215 return (BN_is_odd(e) && bitlen > 16 && bitlen < 257);
219 * SP800-56Br1 6.4.1.2.1 (Step 5i): |p - q| > 2^(nbits/2 - 100)
220 * i.e- numbits(p-q-1) > (nbits/2 -100)
222 int rsa_check_pminusq_diff(BIGNUM *diff, const BIGNUM *p, const BIGNUM *q,
225 int bitlen = (nbits >> 1) - 100;
227 if (!BN_sub(diff, p, q))
229 BN_set_negative(diff, 0);
231 if (BN_is_zero(diff))
234 if (!BN_sub_word(diff, 1))
236 return (BN_num_bits(diff) > bitlen);
239 /* return LCM(p-1, q-1) */
240 int rsa_get_lcm(BN_CTX *ctx, const BIGNUM *p, const BIGNUM *q,
241 BIGNUM *lcm, BIGNUM *gcd, BIGNUM *p1, BIGNUM *q1,
244 return BN_sub(p1, p, BN_value_one()) /* p-1 */
245 && BN_sub(q1, q, BN_value_one()) /* q-1 */
246 && BN_mul(p1q1, p1, q1, ctx) /* (p-1)(q-1) */
247 && BN_gcd(gcd, p1, q1, ctx)
248 && BN_div(lcm, NULL, p1q1, gcd, ctx); /* LCM((p-1, q-1)) */
252 * SP800-56Br1 6.4.2.2 Partial Public Key Validation for RSA refers to
253 * SP800-89 5.3.3 (Explicit) Partial Public Key Validation for RSA
254 * caveat is that the modulus must be as specified in SP800-56Br1
256 int rsa_sp800_56b_check_public(const RSA *rsa)
265 if (rsa->n == NULL || rsa->e == NULL)
270 * (Step a): modulus must be 2048 or 3072 (caveat from SP800-56Br1)
271 * NOTE: changed to allow keys >= 2048
273 nbits = BN_num_bits(rsa->n);
274 if (!rsa_sp800_56b_validate_strength(nbits, -1)) {
275 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC, RSA_R_INVALID_KEY_LENGTH);
279 if (!BN_is_odd(rsa->n)) {
280 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC, RSA_R_INVALID_MODULUS);
283 /* (Steps b-c): 2^16 < e < 2^256, n and e must be odd */
284 if (!rsa_check_public_exponent(rsa->e)) {
285 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC,
286 RSA_R_PUB_EXPONENT_OUT_OF_RANGE);
290 ctx = BN_CTX_new_ex(rsa->libctx);
292 if (ctx == NULL || gcd == NULL)
296 * The modulus is composite, but not a power of a prime.
297 * The modulus has no factors smaller than 752.
299 if (!BN_gcd(gcd, rsa->n, bn_get0_small_factors(), ctx) || !BN_is_one(gcd)) {
300 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC, RSA_R_INVALID_MODULUS);
304 ret = bn_miller_rabin_is_prime(rsa->n, 0, ctx, NULL, 1, &status);
305 if (ret != 1 || status != BN_PRIMETEST_COMPOSITE_NOT_POWER_OF_PRIME) {
306 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC, RSA_R_INVALID_MODULUS);
319 * Perform validation of the RSA private key to check that 0 < D < N.
321 int rsa_sp800_56b_check_private(const RSA *rsa)
323 if (rsa->d == NULL || rsa->n == NULL)
325 return BN_cmp(rsa->d, BN_value_one()) >= 0 && BN_cmp(rsa->d, rsa->n) < 0;
329 * RSA key pair validation.
332 * 6.4.1.2 "RSAKPV1 Family: RSA Key - Pair Validation with a Fixed Exponent"
333 * 6.4.1.3 "RSAKPV2 Family: RSA Key - Pair Validation with a Random Exponent"
336 * 6.4.1.2.3 "rsakpv1 - crt"
337 * 6.4.1.3.3 "rsakpv2 - crt"
339 int rsa_sp800_56b_check_keypair(const RSA *rsa, const BIGNUM *efixed,
340 int strength, int nbits)
351 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR, RSA_R_INVALID_REQUEST);
354 /* (Step 1): Check Ranges */
355 if (!rsa_sp800_56b_validate_strength(nbits, strength))
358 /* If the exponent is known */
359 if (efixed != NULL) {
360 /* (2): Check fixed exponent matches public exponent. */
361 if (BN_cmp(efixed, rsa->e) != 0) {
362 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR, RSA_R_INVALID_REQUEST);
366 /* (Step 1.c): e is odd integer 65537 <= e < 2^256 */
367 if (!rsa_check_public_exponent(rsa->e)) {
368 /* exponent out of range */
369 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR,
370 RSA_R_PUB_EXPONENT_OUT_OF_RANGE);
373 /* (Step 3.b): check the modulus */
374 if (nbits != BN_num_bits(rsa->n)) {
375 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR, RSA_R_INVALID_KEYPAIR);
379 ctx = BN_CTX_new_ex(rsa->libctx);
385 if (r == NULL || !BN_mul(r, rsa->p, rsa->q, ctx))
387 /* (Step 4.c): Check n = pq */
388 if (BN_cmp(rsa->n, r) != 0) {
389 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR, RSA_R_INVALID_REQUEST);
393 /* (Step 5): check prime factors p & q */
394 ret = rsa_check_prime_factor(rsa->p, rsa->e, nbits, ctx)
395 && rsa_check_prime_factor(rsa->q, rsa->e, nbits, ctx)
396 && (rsa_check_pminusq_diff(r, rsa->p, rsa->q, nbits) > 0)
397 /* (Step 6): Check the private exponent d */
398 && rsa_check_private_exponent(rsa, nbits, ctx)
399 /* 6.4.1.2.3 (Step 7): Check the CRT components */
400 && rsa_check_crt_components(rsa, ctx);
402 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR, RSA_R_INVALID_KEYPAIR);