crypto/rsa/rsa_sp800_56b_check.c

   1 /*
   2  * Copyright 2018-2020 The OpenSSL Project Authors. All Rights Reserved.
   3  * Copyright (c) 2018-2019, Oracle and/or its affiliates.  All rights reserved.
   4  *
   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
   9  */
  10
  11 #include <openssl/err.h>
  12 #include <openssl/bn.h>
  13 #include "crypto/bn.h"
  14 #include "rsa_local.h"
  15
  16 /*
  17  * Part of the RSA keypair test.
  18  * Check the Chinese Remainder Theorem components are valid.
  19  *
  20  * See SP800-5bBr1
  21  *   6.4.1.2.3: rsakpv1-crt Step 7
  22  *   6.4.1.3.3: rsakpv2-crt Step 7
  23  */
  24 int rsa_check_crt_components(const RSA *rsa, BN_CTX *ctx)
  25 {
  26     int ret = 0;
  27     BIGNUM *r = NULL, *p1 = NULL, *q1 = NULL;
  28
  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)
  32             return 0;
  33         return 1; /* return ok if all components are NULL */
  34     }
  35
  36     BN_CTX_start(ctx);
  37     r = BN_CTX_get(ctx);
  38     p1 = BN_CTX_get(ctx);
  39     q1 = BN_CTX_get(ctx);
  40     if (q1 != 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);
  44         ret = 1;
  45     } else {
  46         ret = 0;
  47     }
  48     ret = ret
  49           /* p1 = p -1 */
  50           && (BN_copy(p1, rsa->p) != NULL)
  51           && BN_sub_word(p1, 1)
  52           /* q1 = q - 1 */
  53           && (BN_copy(q1, rsa->q) != NULL)
  54           && BN_sub_word(q1, 1)
  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)
  66           && BN_is_one(r)
  67           /* (e) 1 = (dQ . e) mod (q - 1) */
  68           && BN_mod_mul(r, rsa->dmq1, rsa->e, q1, ctx)
  69           && BN_is_one(r)
  70           /* (f) 1 = (qInv . q) mod p */
  71           && BN_mod_mul(r, rsa->iqmp, rsa->q, rsa->p, ctx)
  72           && BN_is_one(r);
  73     BN_clear(r);
  74     BN_clear(p1);
  75     BN_clear(q1);
  76     BN_CTX_end(ctx);
  77     return ret;
  78 }
  79
  80 /*
  81  * Part of the RSA keypair test.
  82  * Check that (√2)(2^(nbits/2 - 1) <= p <= 2^(nbits/2) - 1
  83  *
  84  * See SP800-5bBr1 6.4.1.2.1 Part 5 (c) & (g) - used for both p and q.
  85  *
  86  * (√2)(2^(nbits/2 - 1) = (√2/2)(2^(nbits/2))
  87  */
  88 int rsa_check_prime_factor_range(const BIGNUM *p, int nbits, BN_CTX *ctx)
  89 {
  90     int ret = 0;
  91     BIGNUM *low;
  92     int shift;
  93
  94     nbits >>= 1;
  95     shift = nbits - BN_num_bits(&bn_inv_sqrt_2);
  96
  97     /* Upper bound check */
  98     if (BN_num_bits(p) != nbits)
  99         return 0;
 100
 101     BN_CTX_start(ctx);
 102     low = BN_CTX_get(ctx);
 103     if (low == NULL)
 104         goto err;
 105
 106     /* set low = (√2)(2^(nbits/2 - 1) */
 107     if (!BN_copy(low, &bn_inv_sqrt_2))
 108         goto err;
 109
 110     if (shift >= 0) {
 111         /*
 112          * We don't have all the bits. bn_inv_sqrt_2 contains a rounded up
 113          * value, so there is a very low probability that we'll reject a valid
 114          * value.
 115          */
 116         if (!BN_lshift(low, low, shift))
 117             goto err;
 118     } else if (!BN_rshift(low, low, -shift)) {
 119         goto err;
 120     }
 121     if (BN_cmp(p, low) <= 0)
 122         goto err;
 123     ret = 1;
 124 err:
 125     BN_CTX_end(ctx);
 126     return ret;
 127 }
 128
 129 /*
 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
 133  *
 134  * See SP800-56Br1 6.4.1.2.3 Step 5 (a to d) & (e to h).
 135  */
 136 int rsa_check_prime_factor(BIGNUM *p, BIGNUM *e, int nbits, BN_CTX *ctx)
 137 {
 138     int ret = 0;
 139     BIGNUM *p1 = NULL, *gcd = NULL;
 140
 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             || rsa_check_prime_factor_range(p, nbits, ctx) != 1)
 145         return 0;
 146
 147     BN_CTX_start(ctx);
 148     p1 = BN_CTX_get(ctx);
 149     gcd = BN_CTX_get(ctx);
 150     if (gcd != NULL) {
 151         BN_set_flags(p1, BN_FLG_CONSTTIME);
 152         BN_set_flags(gcd, BN_FLG_CONSTTIME);
 153         ret = 1;
 154     } else {
 155         ret = 0;
 156     }
 157     ret = ret
 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)
 162           && BN_is_one(gcd);
 163
 164     BN_clear(p1);
 165     BN_CTX_end(ctx);
 166     return ret;
 167 }
 168
 169 /*
 170  * See SP800-56Br1 6.4.1.2.3 Part 6(a-b) Check the private exponent d
 171  * satisfies:
 172  *     (Step 6a) 2^(nBit/2) < d < LCM(p–1, q–1).
 173  *     (Step 6b) 1 = (d*e) mod LCM(p–1, q–1)
 174  */
 175 int rsa_check_private_exponent(const RSA *rsa, int nbits, BN_CTX *ctx)
 176 {
 177     int ret;
 178     BIGNUM *r, *p1, *q1, *lcm, *p1q1, *gcd;
 179
 180     /* (Step 6a) 2^(nbits/2) < d */
 181     if (BN_num_bits(rsa->d) <= (nbits >> 1))
 182         return 0;
 183
 184     BN_CTX_start(ctx);
 185     r = BN_CTX_get(ctx);
 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);
 191     if (gcd != NULL) {
 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);
 198         ret = 1;
 199     } else {
 200         ret = 0;
 201     }
 202     ret = (ret
 203           /* LCM(p - 1, q - 1) */
 204           && (rsa_get_lcm(ctx, rsa->p, rsa->q, lcm, gcd, p1, q1, p1q1) == 1)
 205           /* (Step 6a) d < LCM(p - 1, q - 1) */
 206           && (BN_cmp(rsa->d, lcm) < 0)
 207           /* (Step 6b) 1 = (e . d) mod LCM(p - 1, q - 1) */
 208           && BN_mod_mul(r, rsa->e, rsa->d, lcm, ctx)
 209           && BN_is_one(r));
 210
 211     BN_clear(r);
 212     BN_clear(p1);
 213     BN_clear(q1);
 214     BN_clear(lcm);
 215     BN_clear(gcd);
 216     BN_CTX_end(ctx);
 217     return ret;
 218 }
 219
 220 #ifndef FIPS_MODULE
 221 static int bn_is_three(const BIGNUM *bn)
 222 {
 223     BIGNUM *num = BN_dup(bn);
 224     int ret = (num != NULL && BN_sub_word(num, 3) && BN_is_zero(num));
 225
 226     BN_free(num);
 227     return ret;
 228 }
 229 #endif /* FIPS_MODULE */
 230
 231 /* Check exponent is odd, and has a bitlen ranging from [17..256] */
 232 int rsa_check_public_exponent(const BIGNUM *e)
 233 {
 234     int bitlen;
 235
 236     /* For legacy purposes RSA_3 is allowed in non fips mode */
 237 #ifndef FIPS_MODULE
 238     if (bn_is_three(e))
 239         return 1;
 240 #endif /* FIPS_MODULE */
 241
 242     bitlen = BN_num_bits(e);
 243     return (BN_is_odd(e) && bitlen > 16 && bitlen < 257);
 244 }
 245
 246 /*
 247  * SP800-56Br1 6.4.1.2.1 (Step 5i): |p - q| > 2^(nbits/2 - 100)
 248  * i.e- numbits(p-q-1) > (nbits/2 -100)
 249  */
 250 int rsa_check_pminusq_diff(BIGNUM *diff, const BIGNUM *p, const BIGNUM *q,
 251                            int nbits)
 252 {
 253     int bitlen = (nbits >> 1) - 100;
 254
 255     if (!BN_sub(diff, p, q))
 256         return -1;
 257     BN_set_negative(diff, 0);
 258
 259     if (BN_is_zero(diff))
 260         return 0;
 261
 262     if (!BN_sub_word(diff, 1))
 263         return -1;
 264     return (BN_num_bits(diff) > bitlen);
 265 }
 266
 267 /*
 268  * return LCM(p-1, q-1)
 269  *
 270  * Caller should ensure that lcm, gcd, p1, q1, p1q1 are flagged with
 271  * BN_FLG_CONSTTIME.
 272  */
 273 int rsa_get_lcm(BN_CTX *ctx, const BIGNUM *p, const BIGNUM *q,
 274                 BIGNUM *lcm, BIGNUM *gcd, BIGNUM *p1, BIGNUM *q1,
 275                 BIGNUM *p1q1)
 276 {
 277     return BN_sub(p1, p, BN_value_one())    /* p-1 */
 278            && BN_sub(q1, q, BN_value_one()) /* q-1 */
 279            && BN_mul(p1q1, p1, q1, ctx)     /* (p-1)(q-1) */
 280            && BN_gcd(gcd, p1, q1, ctx)
 281            && BN_div(lcm, NULL, p1q1, gcd, ctx); /* LCM((p-1, q-1)) */
 282 }
 283
 284 /*
 285  * SP800-56Br1 6.4.2.2 Partial Public Key Validation for RSA refers to
 286  * SP800-89 5.3.3 (Explicit) Partial Public Key Validation for RSA
 287  * caveat is that the modulus must be as specified in SP800-56Br1
 288  */
 289 int rsa_sp800_56b_check_public(const RSA *rsa)
 290 {
 291     int ret = 0, status;
 292 #ifdef FIPS_MODULE
 293     int nbits;
 294 #endif
 295     BN_CTX *ctx = NULL;
 296     BIGNUM *gcd = NULL;
 297
 298     if (rsa->n == NULL || rsa->e == NULL)
 299         return 0;
 300
 301 #ifdef FIPS_MODULE
 302     /*
 303      * (Step a): modulus must be 2048 or 3072 (caveat from SP800-56Br1)
 304      * NOTE: changed to allow keys >= 2048
 305      */
 306     nbits = BN_num_bits(rsa->n);
 307     if (!rsa_sp800_56b_validate_strength(nbits, -1)) {
 308         RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC, RSA_R_INVALID_KEY_LENGTH);
 309         return 0;
 310     }
 311 #endif
 312     if (!BN_is_odd(rsa->n)) {
 313         RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC, RSA_R_INVALID_MODULUS);
 314         return 0;
 315     }
 316     /* (Steps b-c): 2^16 < e < 2^256, n and e must be odd */
 317     if (!rsa_check_public_exponent(rsa->e)) {
 318         RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC,
 319                RSA_R_PUB_EXPONENT_OUT_OF_RANGE);
 320         return 0;
 321     }
 322
 323     ctx = BN_CTX_new_ex(rsa->libctx);
 324     gcd = BN_new();
 325     if (ctx == NULL || gcd == NULL)
 326         goto err;
 327
 328     /* (Steps d-f):
 329      * The modulus is composite, but not a power of a prime.
 330      * The modulus has no factors smaller than 752.
 331      */
 332     if (!BN_gcd(gcd, rsa->n, bn_get0_small_factors(), ctx) || !BN_is_one(gcd)) {
 333         RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC, RSA_R_INVALID_MODULUS);
 334         goto err;
 335     }
 336
 337     ret = bn_miller_rabin_is_prime(rsa->n, 0, ctx, NULL, 1, &status);
 338     if (ret != 1 || status != BN_PRIMETEST_COMPOSITE_NOT_POWER_OF_PRIME) {
 339         RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC, RSA_R_INVALID_MODULUS);
 340         ret = 0;
 341         goto err;
 342     }
 343
 344     ret = 1;
 345 err:
 346     BN_free(gcd);
 347     BN_CTX_free(ctx);
 348     return ret;
 349 }
 350
 351 /*
 352  * Perform validation of the RSA private key to check that 0 < D < N.
 353  */
 354 int rsa_sp800_56b_check_private(const RSA *rsa)
 355 {
 356     if (rsa->d == NULL || rsa->n == NULL)
 357         return 0;
 358     return BN_cmp(rsa->d, BN_value_one()) >= 0 && BN_cmp(rsa->d, rsa->n) < 0;
 359 }
 360
 361 /*
 362  * RSA key pair validation.
 363  *
 364  * SP800-56Br1.
 365  *    6.4.1.2 "RSAKPV1 Family: RSA Key - Pair Validation with a Fixed Exponent"
 366  *    6.4.1.3 "RSAKPV2 Family: RSA Key - Pair Validation with a Random Exponent"
 367  *
 368  * It uses:
 369  *     6.4.1.2.3 "rsakpv1 - crt"
 370  *     6.4.1.3.3 "rsakpv2 - crt"
 371  */
 372 int rsa_sp800_56b_check_keypair(const RSA *rsa, const BIGNUM *efixed,
 373                                 int strength, int nbits)
 374 {
 375     int ret = 0;
 376     BN_CTX *ctx = NULL;
 377     BIGNUM *r = NULL;
 378
 379     if (rsa->p == NULL
 380             || rsa->q == NULL
 381             || rsa->e == NULL
 382             || rsa->d == NULL
 383             || rsa->n == NULL) {
 384         RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR, RSA_R_INVALID_REQUEST);
 385         return 0;
 386     }
 387     /* (Step 1): Check Ranges */
 388     if (!rsa_sp800_56b_validate_strength(nbits, strength))
 389         return 0;
 390
 391     /* If the exponent is known */
 392     if (efixed != NULL) {
 393         /* (2): Check fixed exponent matches public exponent. */
 394         if (BN_cmp(efixed, rsa->e) != 0) {
 395             RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR, RSA_R_INVALID_REQUEST);
 396             return 0;
 397         }
 398     }
 399     /* (Step 1.c): e is odd integer 65537 <= e < 2^256 */
 400     if (!rsa_check_public_exponent(rsa->e)) {
 401         /* exponent out of range */
 402         RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR,
 403                RSA_R_PUB_EXPONENT_OUT_OF_RANGE);
 404         return 0;
 405     }
 406     /* (Step 3.b): check the modulus */
 407     if (nbits != BN_num_bits(rsa->n)) {
 408         RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR, RSA_R_INVALID_KEYPAIR);
 409         return 0;
 410     }
 411
 412     ctx = BN_CTX_new_ex(rsa->libctx);
 413     if (ctx == NULL)
 414         return 0;
 415
 416     BN_CTX_start(ctx);
 417     r = BN_CTX_get(ctx);
 418     if (r == NULL || !BN_mul(r, rsa->p, rsa->q, ctx))
 419         goto err;
 420     /* (Step 4.c): Check n = pq */
 421     if (BN_cmp(rsa->n, r) != 0) {
 422         RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR, RSA_R_INVALID_REQUEST);
 423         goto err;
 424     }
 425
 426     /* (Step 5): check prime factors p & q */
 427     ret = rsa_check_prime_factor(rsa->p, rsa->e, nbits, ctx)
 428           && rsa_check_prime_factor(rsa->q, rsa->e, nbits, ctx)
 429           && (rsa_check_pminusq_diff(r, rsa->p, rsa->q, nbits) > 0)
 430           /* (Step 6): Check the private exponent d */
 431           && rsa_check_private_exponent(rsa, nbits, ctx)
 432           /* 6.4.1.2.3 (Step 7): Check the CRT components */
 433           && rsa_check_crt_components(rsa, ctx);
 434     if (ret != 1)
 435         RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR, RSA_R_INVALID_KEYPAIR);
 436
 437 err:
 438     BN_clear(r);
 439     BN_CTX_end(ctx);
 440     BN_CTX_free(ctx);
 441     return ret;
 442 }