| 1 | /* |
| 2 | * Helper functions for the RSA module |
| 3 | * |
| 4 | * Copyright (C) 2006-2017, ARM Limited, All Rights Reserved |
| 5 | * SPDX-License-Identifier: GPL-2.0 |
| 6 | * |
| 7 | * This program is free software; you can redistribute it and/or modify |
| 8 | * it under the terms of the GNU General Public License as published by |
| 9 | * the Free Software Foundation; either version 2 of the License, or |
| 10 | * (at your option) any later version. |
| 11 | * |
| 12 | * This program is distributed in the hope that it will be useful, |
| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 15 | * GNU General Public License for more details. |
| 16 | * |
| 17 | * You should have received a copy of the GNU General Public License along |
| 18 | * with this program; if not, write to the Free Software Foundation, Inc., |
| 19 | * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. |
| 20 | * |
| 21 | * This file is part of mbed TLS (https://tls.mbed.org) |
| 22 | * |
| 23 | */ |
| 24 | |
| 25 | #if !defined(MBEDTLS_CONFIG_FILE) |
| 26 | #include "mbedtls/config.h" |
| 27 | #else |
| 28 | #include MBEDTLS_CONFIG_FILE |
| 29 | #endif |
| 30 | |
| 31 | #if defined(MBEDTLS_RSA_C) |
| 32 | |
| 33 | #include "mbedtls/rsa.h" |
| 34 | #include "mbedtls/bignum.h" |
| 35 | #include "mbedtls/rsa_internal.h" |
| 36 | |
| 37 | /* |
| 38 | * Compute RSA prime factors from public and private exponents |
| 39 | * |
| 40 | * Summary of algorithm: |
| 41 | * Setting F := lcm(P-1,Q-1), the idea is as follows: |
| 42 | * |
| 43 | * (a) For any 1 <= X < N with gcd(X,N)=1, we have X^F = 1 modulo N, so X^(F/2) |
| 44 | * is a square root of 1 in Z/NZ. Since Z/NZ ~= Z/PZ x Z/QZ by CRT and the |
| 45 | * square roots of 1 in Z/PZ and Z/QZ are +1 and -1, this leaves the four |
| 46 | * possibilities X^(F/2) = (+-1, +-1). If it happens that X^(F/2) = (-1,+1) |
| 47 | * or (+1,-1), then gcd(X^(F/2) + 1, N) will be equal to one of the prime |
| 48 | * factors of N. |
| 49 | * |
| 50 | * (b) If we don't know F/2 but (F/2) * K for some odd (!) K, then the same |
| 51 | * construction still applies since (-)^K is the identity on the set of |
| 52 | * roots of 1 in Z/NZ. |
| 53 | * |
| 54 | * The public and private key primitives (-)^E and (-)^D are mutually inverse |
| 55 | * bijections on Z/NZ if and only if (-)^(DE) is the identity on Z/NZ, i.e. |
| 56 | * if and only if DE - 1 is a multiple of F, say DE - 1 = F * L. |
| 57 | * Splitting L = 2^t * K with K odd, we have |
| 58 | * |
| 59 | * DE - 1 = FL = (F/2) * (2^(t+1)) * K, |
| 60 | * |
| 61 | * so (F / 2) * K is among the numbers |
| 62 | * |
| 63 | * (DE - 1) >> 1, (DE - 1) >> 2, ..., (DE - 1) >> ord |
| 64 | * |
| 65 | * where ord is the order of 2 in (DE - 1). |
| 66 | * We can therefore iterate through these numbers apply the construction |
| 67 | * of (a) and (b) above to attempt to factor N. |
| 68 | * |
| 69 | */ |
| 70 | int mbedtls_rsa_deduce_primes( mbedtls_mpi const *N, |
| 71 | mbedtls_mpi const *E, mbedtls_mpi const *D, |
| 72 | mbedtls_mpi *P, mbedtls_mpi *Q ) |
| 73 | { |
| 74 | int ret = 0; |
| 75 | |
| 76 | uint16_t attempt; /* Number of current attempt */ |
| 77 | uint16_t iter; /* Number of squares computed in the current attempt */ |
| 78 | |
| 79 | uint16_t order; /* Order of 2 in DE - 1 */ |
| 80 | |
| 81 | mbedtls_mpi T; /* Holds largest odd divisor of DE - 1 */ |
| 82 | mbedtls_mpi K; /* Temporary holding the current candidate */ |
| 83 | |
| 84 | const unsigned char primes[] = { 2, |
| 85 | 3, 5, 7, 11, 13, 17, 19, 23, |
| 86 | 29, 31, 37, 41, 43, 47, 53, 59, |
| 87 | 61, 67, 71, 73, 79, 83, 89, 97, |
| 88 | 101, 103, 107, 109, 113, 127, 131, 137, |
| 89 | 139, 149, 151, 157, 163, 167, 173, 179, |
| 90 | 181, 191, 193, 197, 199, 211, 223, 227, |
| 91 | 229, 233, 239, 241, 251 |
| 92 | }; |
| 93 | |
| 94 | const size_t num_primes = sizeof( primes ) / sizeof( *primes ); |
| 95 | |
| 96 | if( P == NULL || Q == NULL || P->p != NULL || Q->p != NULL ) |
| 97 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); |
| 98 | |
| 99 | if( mbedtls_mpi_cmp_int( N, 0 ) <= 0 || |
| 100 | mbedtls_mpi_cmp_int( D, 1 ) <= 0 || |
| 101 | mbedtls_mpi_cmp_mpi( D, N ) >= 0 || |
| 102 | mbedtls_mpi_cmp_int( E, 1 ) <= 0 || |
| 103 | mbedtls_mpi_cmp_mpi( E, N ) >= 0 ) |
| 104 | { |
| 105 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); |
| 106 | } |
| 107 | |
| 108 | /* |
| 109 | * Initializations and temporary changes |
| 110 | */ |
| 111 | |
| 112 | mbedtls_mpi_init( &K ); |
| 113 | mbedtls_mpi_init( &T ); |
| 114 | |
| 115 | /* T := DE - 1 */ |
| 116 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, D, E ) ); |
| 117 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &T, &T, 1 ) ); |
| 118 | |
| 119 | if( ( order = (uint16_t) mbedtls_mpi_lsb( &T ) ) == 0 ) |
| 120 | { |
| 121 | ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA; |
| 122 | goto cleanup; |
| 123 | } |
| 124 | |
| 125 | /* After this operation, T holds the largest odd divisor of DE - 1. */ |
| 126 | MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &T, order ) ); |
| 127 | |
| 128 | /* |
| 129 | * Actual work |
| 130 | */ |
| 131 | |
| 132 | /* Skip trying 2 if N == 1 mod 8 */ |
| 133 | attempt = 0; |
| 134 | if( N->p[0] % 8 == 1 ) |
| 135 | attempt = 1; |
| 136 | |
| 137 | for( ; attempt < num_primes; ++attempt ) |
| 138 | { |
| 139 | mbedtls_mpi_lset( &K, primes[attempt] ); |
| 140 | |
| 141 | /* Check if gcd(K,N) = 1 */ |
| 142 | MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) ); |
| 143 | if( mbedtls_mpi_cmp_int( P, 1 ) != 0 ) |
| 144 | continue; |
| 145 | |
| 146 | /* Go through K^T + 1, K^(2T) + 1, K^(4T) + 1, ... |
| 147 | * and check whether they have nontrivial GCD with N. */ |
| 148 | MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &K, &K, &T, N, |
| 149 | Q /* temporarily use Q for storing Montgomery |
| 150 | * multiplication helper values */ ) ); |
| 151 | |
| 152 | for( iter = 1; iter <= order; ++iter ) |
| 153 | { |
| 154 | /* If we reach 1 prematurely, there's no point |
| 155 | * in continuing to square K */ |
| 156 | if( mbedtls_mpi_cmp_int( &K, 1 ) == 0 ) |
| 157 | break; |
| 158 | |
| 159 | MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &K, &K, 1 ) ); |
| 160 | MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) ); |
| 161 | |
| 162 | if( mbedtls_mpi_cmp_int( P, 1 ) == 1 && |
| 163 | mbedtls_mpi_cmp_mpi( P, N ) == -1 ) |
| 164 | { |
| 165 | /* |
| 166 | * Have found a nontrivial divisor P of N. |
| 167 | * Set Q := N / P. |
| 168 | */ |
| 169 | |
| 170 | MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( Q, NULL, N, P ) ); |
| 171 | goto cleanup; |
| 172 | } |
| 173 | |
| 174 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) ); |
| 175 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &K ) ); |
| 176 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, N ) ); |
| 177 | } |
| 178 | |
| 179 | /* |
| 180 | * If we get here, then either we prematurely aborted the loop because |
| 181 | * we reached 1, or K holds primes[attempt]^(DE - 1) mod N, which must |
| 182 | * be 1 if D,E,N were consistent. |
| 183 | * Check if that's the case and abort if not, to avoid very long, |
| 184 | * yet eventually failing, computations if N,D,E were not sane. |
| 185 | */ |
| 186 | if( mbedtls_mpi_cmp_int( &K, 1 ) != 0 ) |
| 187 | { |
| 188 | break; |
| 189 | } |
| 190 | } |
| 191 | |
| 192 | ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA; |
| 193 | |
| 194 | cleanup: |
| 195 | |
| 196 | mbedtls_mpi_free( &K ); |
| 197 | mbedtls_mpi_free( &T ); |
| 198 | return( ret ); |
| 199 | } |
| 200 | |
| 201 | /* |
| 202 | * Given P, Q and the public exponent E, deduce D. |
| 203 | * This is essentially a modular inversion. |
| 204 | */ |
| 205 | int mbedtls_rsa_deduce_private_exponent( mbedtls_mpi const *P, |
| 206 | mbedtls_mpi const *Q, |
| 207 | mbedtls_mpi const *E, |
| 208 | mbedtls_mpi *D ) |
| 209 | { |
| 210 | int ret = 0; |
| 211 | mbedtls_mpi K, L; |
| 212 | |
| 213 | if( D == NULL || mbedtls_mpi_cmp_int( D, 0 ) != 0 ) |
| 214 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); |
| 215 | |
| 216 | if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 || |
| 217 | mbedtls_mpi_cmp_int( Q, 1 ) <= 0 || |
| 218 | mbedtls_mpi_cmp_int( E, 0 ) == 0 ) |
| 219 | { |
| 220 | return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA ); |
| 221 | } |
| 222 | |
| 223 | mbedtls_mpi_init( &K ); |
| 224 | mbedtls_mpi_init( &L ); |
| 225 | |
| 226 | /* Temporarily put K := P-1 and L := Q-1 */ |
| 227 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) ); |
| 228 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) ); |
| 229 | |
| 230 | /* Temporarily put D := gcd(P-1, Q-1) */ |
| 231 | MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( D, &K, &L ) ); |
| 232 | |
| 233 | /* K := LCM(P-1, Q-1) */ |
| 234 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &L ) ); |
| 235 | MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &K, NULL, &K, D ) ); |
| 236 | |
| 237 | /* Compute modular inverse of E in LCM(P-1, Q-1) */ |
| 238 | MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( D, E, &K ) ); |
| 239 | |
| 240 | cleanup: |
| 241 | |
| 242 | mbedtls_mpi_free( &K ); |
| 243 | mbedtls_mpi_free( &L ); |
| 244 | |
| 245 | return( ret ); |
| 246 | } |
| 247 | |
| 248 | /* |
| 249 | * Check that RSA CRT parameters are in accordance with core parameters. |
| 250 | */ |
| 251 | int mbedtls_rsa_validate_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q, |
| 252 | const mbedtls_mpi *D, const mbedtls_mpi *DP, |
| 253 | const mbedtls_mpi *DQ, const mbedtls_mpi *QP ) |
| 254 | { |
| 255 | int ret = 0; |
| 256 | |
| 257 | mbedtls_mpi K, L; |
| 258 | mbedtls_mpi_init( &K ); |
| 259 | mbedtls_mpi_init( &L ); |
| 260 | |
| 261 | /* Check that DP - D == 0 mod P - 1 */ |
| 262 | if( DP != NULL ) |
| 263 | { |
| 264 | if( P == NULL ) |
| 265 | { |
| 266 | ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA; |
| 267 | goto cleanup; |
| 268 | } |
| 269 | |
| 270 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) ); |
| 271 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DP, D ) ); |
| 272 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) ); |
| 273 | |
| 274 | if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 ) |
| 275 | { |
| 276 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; |
| 277 | goto cleanup; |
| 278 | } |
| 279 | } |
| 280 | |
| 281 | /* Check that DQ - D == 0 mod Q - 1 */ |
| 282 | if( DQ != NULL ) |
| 283 | { |
| 284 | if( Q == NULL ) |
| 285 | { |
| 286 | ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA; |
| 287 | goto cleanup; |
| 288 | } |
| 289 | |
| 290 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1 ) ); |
| 291 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DQ, D ) ); |
| 292 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) ); |
| 293 | |
| 294 | if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 ) |
| 295 | { |
| 296 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; |
| 297 | goto cleanup; |
| 298 | } |
| 299 | } |
| 300 | |
| 301 | /* Check that QP * Q - 1 == 0 mod P */ |
| 302 | if( QP != NULL ) |
| 303 | { |
| 304 | if( P == NULL || Q == NULL ) |
| 305 | { |
| 306 | ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA; |
| 307 | goto cleanup; |
| 308 | } |
| 309 | |
| 310 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, QP, Q ) ); |
| 311 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) ); |
| 312 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, P ) ); |
| 313 | if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 ) |
| 314 | { |
| 315 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; |
| 316 | goto cleanup; |
| 317 | } |
| 318 | } |
| 319 | |
| 320 | cleanup: |
| 321 | |
| 322 | /* Wrap MPI error codes by RSA check failure error code */ |
| 323 | if( ret != 0 && |
| 324 | ret != MBEDTLS_ERR_RSA_KEY_CHECK_FAILED && |
| 325 | ret != MBEDTLS_ERR_RSA_BAD_INPUT_DATA ) |
| 326 | { |
| 327 | ret += MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; |
| 328 | } |
| 329 | |
| 330 | mbedtls_mpi_free( &K ); |
| 331 | mbedtls_mpi_free( &L ); |
| 332 | |
| 333 | return( ret ); |
| 334 | } |
| 335 | |
| 336 | /* |
| 337 | * Check that core RSA parameters are sane. |
| 338 | */ |
| 339 | int mbedtls_rsa_validate_params( const mbedtls_mpi *N, const mbedtls_mpi *P, |
| 340 | const mbedtls_mpi *Q, const mbedtls_mpi *D, |
| 341 | const mbedtls_mpi *E, |
| 342 | int (*f_rng)(void *, unsigned char *, size_t), |
| 343 | void *p_rng ) |
| 344 | { |
| 345 | int ret = 0; |
| 346 | mbedtls_mpi K, L; |
| 347 | |
| 348 | mbedtls_mpi_init( &K ); |
| 349 | mbedtls_mpi_init( &L ); |
| 350 | |
| 351 | /* |
| 352 | * Step 1: If PRNG provided, check that P and Q are prime |
| 353 | */ |
| 354 | |
| 355 | #if defined(MBEDTLS_GENPRIME) |
| 356 | if( f_rng != NULL && P != NULL && |
| 357 | ( ret = mbedtls_mpi_is_prime( P, f_rng, p_rng ) ) != 0 ) |
| 358 | { |
| 359 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; |
| 360 | goto cleanup; |
| 361 | } |
| 362 | |
| 363 | if( f_rng != NULL && Q != NULL && |
| 364 | ( ret = mbedtls_mpi_is_prime( Q, f_rng, p_rng ) ) != 0 ) |
| 365 | { |
| 366 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; |
| 367 | goto cleanup; |
| 368 | } |
| 369 | #else |
| 370 | ((void) f_rng); |
| 371 | ((void) p_rng); |
| 372 | #endif /* MBEDTLS_GENPRIME */ |
| 373 | |
| 374 | /* |
| 375 | * Step 2: Check that 1 < N = P * Q |
| 376 | */ |
| 377 | |
| 378 | if( P != NULL && Q != NULL && N != NULL ) |
| 379 | { |
| 380 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, P, Q ) ); |
| 381 | if( mbedtls_mpi_cmp_int( N, 1 ) <= 0 || |
| 382 | mbedtls_mpi_cmp_mpi( &K, N ) != 0 ) |
| 383 | { |
| 384 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; |
| 385 | goto cleanup; |
| 386 | } |
| 387 | } |
| 388 | |
| 389 | /* |
| 390 | * Step 3: Check and 1 < D, E < N if present. |
| 391 | */ |
| 392 | |
| 393 | if( N != NULL && D != NULL && E != NULL ) |
| 394 | { |
| 395 | if ( mbedtls_mpi_cmp_int( D, 1 ) <= 0 || |
| 396 | mbedtls_mpi_cmp_int( E, 1 ) <= 0 || |
| 397 | mbedtls_mpi_cmp_mpi( D, N ) >= 0 || |
| 398 | mbedtls_mpi_cmp_mpi( E, N ) >= 0 ) |
| 399 | { |
| 400 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; |
| 401 | goto cleanup; |
| 402 | } |
| 403 | } |
| 404 | |
| 405 | /* |
| 406 | * Step 4: Check that D, E are inverse modulo P-1 and Q-1 |
| 407 | */ |
| 408 | |
| 409 | if( P != NULL && Q != NULL && D != NULL && E != NULL ) |
| 410 | { |
| 411 | if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 || |
| 412 | mbedtls_mpi_cmp_int( Q, 1 ) <= 0 ) |
| 413 | { |
| 414 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; |
| 415 | goto cleanup; |
| 416 | } |
| 417 | |
| 418 | /* Compute DE-1 mod P-1 */ |
| 419 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) ); |
| 420 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) ); |
| 421 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, P, 1 ) ); |
| 422 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) ); |
| 423 | if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 ) |
| 424 | { |
| 425 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; |
| 426 | goto cleanup; |
| 427 | } |
| 428 | |
| 429 | /* Compute DE-1 mod Q-1 */ |
| 430 | MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) ); |
| 431 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) ); |
| 432 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) ); |
| 433 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) ); |
| 434 | if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 ) |
| 435 | { |
| 436 | ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; |
| 437 | goto cleanup; |
| 438 | } |
| 439 | } |
| 440 | |
| 441 | cleanup: |
| 442 | |
| 443 | mbedtls_mpi_free( &K ); |
| 444 | mbedtls_mpi_free( &L ); |
| 445 | |
| 446 | /* Wrap MPI error codes by RSA check failure error code */ |
| 447 | if( ret != 0 && ret != MBEDTLS_ERR_RSA_KEY_CHECK_FAILED ) |
| 448 | { |
| 449 | ret += MBEDTLS_ERR_RSA_KEY_CHECK_FAILED; |
| 450 | } |
| 451 | |
| 452 | return( ret ); |
| 453 | } |
| 454 | |
| 455 | int mbedtls_rsa_deduce_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q, |
| 456 | const mbedtls_mpi *D, mbedtls_mpi *DP, |
| 457 | mbedtls_mpi *DQ, mbedtls_mpi *QP ) |
| 458 | { |
| 459 | int ret = 0; |
| 460 | mbedtls_mpi K; |
| 461 | mbedtls_mpi_init( &K ); |
| 462 | |
| 463 | /* DP = D mod P-1 */ |
| 464 | if( DP != NULL ) |
| 465 | { |
| 466 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) ); |
| 467 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DP, D, &K ) ); |
| 468 | } |
| 469 | |
| 470 | /* DQ = D mod Q-1 */ |
| 471 | if( DQ != NULL ) |
| 472 | { |
| 473 | MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1 ) ); |
| 474 | MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DQ, D, &K ) ); |
| 475 | } |
| 476 | |
| 477 | /* QP = Q^{-1} mod P */ |
| 478 | if( QP != NULL ) |
| 479 | { |
| 480 | MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( QP, Q, P ) ); |
| 481 | } |
| 482 | |
| 483 | cleanup: |
| 484 | mbedtls_mpi_free( &K ); |
| 485 | |
| 486 | return( ret ); |
| 487 | } |
| 488 | |
| 489 | #endif /* MBEDTLS_RSA_C */ |