2 * Copyright 2018-2021 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 ossl_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 */
41 BN_set_flags(r, BN_FLG_CONSTTIME);
42 BN_set_flags(p1, BN_FLG_CONSTTIME);
43 BN_set_flags(q1, BN_FLG_CONSTTIME);
50 && (BN_copy(p1, rsa->p) != NULL)
53 && (BN_copy(q1, rsa->q) != NULL)
55 /* (a) 1 < dP < (p – 1). */
56 && (BN_cmp(rsa->dmp1, BN_value_one()) > 0)
57 && (BN_cmp(rsa->dmp1, p1) < 0)
58 /* (b) 1 < dQ < (q - 1). */
59 && (BN_cmp(rsa->dmq1, BN_value_one()) > 0)
60 && (BN_cmp(rsa->dmq1, q1) < 0)
61 /* (c) 1 < qInv < p */
62 && (BN_cmp(rsa->iqmp, BN_value_one()) > 0)
63 && (BN_cmp(rsa->iqmp, rsa->p) < 0)
64 /* (d) 1 = (dP . e) mod (p - 1)*/
65 && BN_mod_mul(r, rsa->dmp1, rsa->e, p1, ctx)
67 /* (e) 1 = (dQ . e) mod (q - 1) */
68 && BN_mod_mul(r, rsa->dmq1, rsa->e, q1, ctx)
70 /* (f) 1 = (qInv . q) mod p */
71 && BN_mod_mul(r, rsa->iqmp, rsa->q, rsa->p, ctx)
81 * Part of the RSA keypair test.
82 * Check that (√2)(2^(nbits/2 - 1) <= p <= 2^(nbits/2) - 1
84 * See SP800-5bBr1 6.4.1.2.1 Part 5 (c) & (g) - used for both p and q.
86 * (√2)(2^(nbits/2 - 1) = (√2/2)(2^(nbits/2))
88 int ossl_rsa_check_prime_factor_range(const BIGNUM *p, int nbits, BN_CTX *ctx)
95 shift = nbits - BN_num_bits(&ossl_bn_inv_sqrt_2);
97 /* Upper bound check */
98 if (BN_num_bits(p) != nbits)
102 low = BN_CTX_get(ctx);
106 /* set low = (√2)(2^(nbits/2 - 1) */
107 if (!BN_copy(low, &ossl_bn_inv_sqrt_2))
112 * We don't have all the bits. ossl_bn_inv_sqrt_2 contains a rounded up
113 * value, so there is a very low probability that we'll reject a valid
116 if (!BN_lshift(low, low, shift))
118 } else if (!BN_rshift(low, low, -shift)) {
121 if (BN_cmp(p, low) <= 0)
130 * Part of the RSA keypair test.
131 * Check the prime factor (for either p or q)
132 * i.e: p is prime AND GCD(p - 1, e) = 1
134 * See SP800-56Br1 6.4.1.2.3 Step 5 (a to d) & (e to h).
136 int ossl_rsa_check_prime_factor(BIGNUM *p, BIGNUM *e, int nbits, BN_CTX *ctx)
139 BIGNUM *p1 = NULL, *gcd = NULL;
141 /* (Steps 5 a-b) prime test */
142 if (BN_check_prime(p, ctx, NULL) != 1
143 /* (Step 5c) (√2)(2^(nbits/2 - 1) <= p <= 2^(nbits/2 - 1) */
144 || ossl_rsa_check_prime_factor_range(p, nbits, ctx) != 1)
148 p1 = BN_CTX_get(ctx);
149 gcd = BN_CTX_get(ctx);
151 BN_set_flags(p1, BN_FLG_CONSTTIME);
152 BN_set_flags(gcd, BN_FLG_CONSTTIME);
158 /* (Step 5d) GCD(p-1, e) = 1 */
159 && (BN_copy(p1, p) != NULL)
160 && BN_sub_word(p1, 1)
161 && BN_gcd(gcd, p1, e, ctx)
170 * See SP800-56Br1 6.4.1.2.3 Part 6(a-b) Check the private exponent d
172 * (Step 6a) 2^(nBit/2) < d < LCM(p–1, q–1).
173 * (Step 6b) 1 = (d*e) mod LCM(p–1, q–1)
175 int ossl_rsa_check_private_exponent(const RSA *rsa, int nbits, BN_CTX *ctx)
178 BIGNUM *r, *p1, *q1, *lcm, *p1q1, *gcd;
180 /* (Step 6a) 2^(nbits/2) < d */
181 if (BN_num_bits(rsa->d) <= (nbits >> 1))
186 p1 = BN_CTX_get(ctx);
187 q1 = BN_CTX_get(ctx);
188 lcm = BN_CTX_get(ctx);
189 p1q1 = BN_CTX_get(ctx);
190 gcd = BN_CTX_get(ctx);
192 BN_set_flags(r, BN_FLG_CONSTTIME);
193 BN_set_flags(p1, BN_FLG_CONSTTIME);
194 BN_set_flags(q1, BN_FLG_CONSTTIME);
195 BN_set_flags(lcm, BN_FLG_CONSTTIME);
196 BN_set_flags(p1q1, BN_FLG_CONSTTIME);
197 BN_set_flags(gcd, BN_FLG_CONSTTIME);
203 /* LCM(p - 1, q - 1) */
204 && (ossl_rsa_get_lcm(ctx, rsa->p, rsa->q, lcm, gcd, p1, q1,
206 /* (Step 6a) d < LCM(p - 1, q - 1) */
207 && (BN_cmp(rsa->d, lcm) < 0)
208 /* (Step 6b) 1 = (e . d) mod LCM(p - 1, q - 1) */
209 && BN_mod_mul(r, rsa->e, rsa->d, lcm, ctx)
222 static int bn_is_three(const BIGNUM *bn)
224 BIGNUM *num = BN_dup(bn);
225 int ret = (num != NULL && BN_sub_word(num, 3) && BN_is_zero(num));
230 #endif /* FIPS_MODULE */
232 /* Check exponent is odd, and has a bitlen ranging from [17..256] */
233 int ossl_rsa_check_public_exponent(const BIGNUM *e)
237 /* For legacy purposes RSA_3 is allowed in non fips mode */
241 #endif /* FIPS_MODULE */
243 bitlen = BN_num_bits(e);
244 return (BN_is_odd(e) && bitlen > 16 && bitlen < 257);
248 * SP800-56Br1 6.4.1.2.1 (Step 5i): |p - q| > 2^(nbits/2 - 100)
249 * i.e- numbits(p-q-1) > (nbits/2 -100)
251 int ossl_rsa_check_pminusq_diff(BIGNUM *diff, const BIGNUM *p, const BIGNUM *q,
254 int bitlen = (nbits >> 1) - 100;
256 if (!BN_sub(diff, p, q))
258 BN_set_negative(diff, 0);
260 if (BN_is_zero(diff))
263 if (!BN_sub_word(diff, 1))
265 return (BN_num_bits(diff) > bitlen);
269 * return LCM(p-1, q-1)
271 * Caller should ensure that lcm, gcd, p1, q1, p1q1 are flagged with
274 int ossl_rsa_get_lcm(BN_CTX *ctx, const BIGNUM *p, const BIGNUM *q,
275 BIGNUM *lcm, BIGNUM *gcd, BIGNUM *p1, BIGNUM *q1,
278 return BN_sub(p1, p, BN_value_one()) /* p-1 */
279 && BN_sub(q1, q, BN_value_one()) /* q-1 */
280 && BN_mul(p1q1, p1, q1, ctx) /* (p-1)(q-1) */
281 && BN_gcd(gcd, p1, q1, ctx)
282 && BN_div(lcm, NULL, p1q1, gcd, ctx); /* LCM((p-1, q-1)) */
286 * SP800-56Br1 6.4.2.2 Partial Public Key Validation for RSA refers to
287 * SP800-89 5.3.3 (Explicit) Partial Public Key Validation for RSA
288 * caveat is that the modulus must be as specified in SP800-56Br1
290 int ossl_rsa_sp800_56b_check_public(const RSA *rsa)
297 if (rsa->n == NULL || rsa->e == NULL)
300 nbits = BN_num_bits(rsa->n);
303 * (Step a): modulus must be 2048 or 3072 (caveat from SP800-56Br1)
304 * NOTE: changed to allow keys >= 2048
306 if (!ossl_rsa_sp800_56b_validate_strength(nbits, -1)) {
307 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_KEY_LENGTH);
311 if (!BN_is_odd(rsa->n)) {
312 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_MODULUS);
315 /* (Steps b-c): 2^16 < e < 2^256, n and e must be odd */
316 if (!ossl_rsa_check_public_exponent(rsa->e)) {
317 ERR_raise(ERR_LIB_RSA, RSA_R_PUB_EXPONENT_OUT_OF_RANGE);
321 ctx = BN_CTX_new_ex(rsa->libctx);
323 if (ctx == NULL || gcd == NULL)
327 * The modulus is composite, but not a power of a prime.
328 * The modulus has no factors smaller than 752.
330 if (!BN_gcd(gcd, rsa->n, ossl_bn_get0_small_factors(), ctx)
331 || !BN_is_one(gcd)) {
332 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_MODULUS);
336 ret = ossl_bn_miller_rabin_is_prime(rsa->n, 0, ctx, NULL, 1, &status);
338 if (ret != 1 || status != BN_PRIMETEST_COMPOSITE_NOT_POWER_OF_PRIME) {
340 if (ret != 1 || (status != BN_PRIMETEST_COMPOSITE_NOT_POWER_OF_PRIME
341 && (nbits >= RSA_MIN_MODULUS_BITS
342 || status != BN_PRIMETEST_COMPOSITE_WITH_FACTOR))) {
344 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_MODULUS);
357 * Perform validation of the RSA private key to check that 0 < D < N.
359 int ossl_rsa_sp800_56b_check_private(const RSA *rsa)
361 if (rsa->d == NULL || rsa->n == NULL)
363 return BN_cmp(rsa->d, BN_value_one()) >= 0 && BN_cmp(rsa->d, rsa->n) < 0;
367 * RSA key pair validation.
370 * 6.4.1.2 "RSAKPV1 Family: RSA Key - Pair Validation with a Fixed Exponent"
371 * 6.4.1.3 "RSAKPV2 Family: RSA Key - Pair Validation with a Random Exponent"
374 * 6.4.1.2.3 "rsakpv1 - crt"
375 * 6.4.1.3.3 "rsakpv2 - crt"
377 int ossl_rsa_sp800_56b_check_keypair(const RSA *rsa, const BIGNUM *efixed,
378 int strength, int nbits)
389 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_REQUEST);
392 /* (Step 1): Check Ranges */
393 if (!ossl_rsa_sp800_56b_validate_strength(nbits, strength))
396 /* If the exponent is known */
397 if (efixed != NULL) {
398 /* (2): Check fixed exponent matches public exponent. */
399 if (BN_cmp(efixed, rsa->e) != 0) {
400 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_REQUEST);
404 /* (Step 1.c): e is odd integer 65537 <= e < 2^256 */
405 if (!ossl_rsa_check_public_exponent(rsa->e)) {
406 /* exponent out of range */
407 ERR_raise(ERR_LIB_RSA, RSA_R_PUB_EXPONENT_OUT_OF_RANGE);
410 /* (Step 3.b): check the modulus */
411 if (nbits != BN_num_bits(rsa->n)) {
412 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_KEYPAIR);
416 ctx = BN_CTX_new_ex(rsa->libctx);
422 if (r == NULL || !BN_mul(r, rsa->p, rsa->q, ctx))
424 /* (Step 4.c): Check n = pq */
425 if (BN_cmp(rsa->n, r) != 0) {
426 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_REQUEST);
430 /* (Step 5): check prime factors p & q */
431 ret = ossl_rsa_check_prime_factor(rsa->p, rsa->e, nbits, ctx)
432 && ossl_rsa_check_prime_factor(rsa->q, rsa->e, nbits, ctx)
433 && (ossl_rsa_check_pminusq_diff(r, rsa->p, rsa->q, nbits) > 0)
434 /* (Step 6): Check the private exponent d */
435 && ossl_rsa_check_private_exponent(rsa, nbits, ctx)
436 /* 6.4.1.2.3 (Step 7): Check the CRT components */
437 && ossl_rsa_check_crt_components(rsa, ctx);
439 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_KEYPAIR);