/* * rsa.c * ----- * Basic RSA functions based on Cryptech ModExp core. * * The mix of what we're doing in software vs what we're doing on the * FPGA is a moving target. Goal for now is to have the bits we need * to do in C be straightforward to review and as simple as possible * (but no simpler). * * Much of the code in this module is based, at least loosely, on Tom * St Denis's libtomcrypt code. * * Authors: Rob Austein * Copyright (c) 2015, SUNET * * Redistribution and use in source and binary forms, with or * without modification, are permitted provided that the following * conditions are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in * the documentation and/or other materials provided with the * distribution. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF * ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ /* * We use "Tom's Fast Math" library for our bignum implementation. * This particular implementation has a couple of nice features: * * - The code is relatively readable, thus reviewable. * * - The bignum representation doesn't use dynamic memory, which * simplifies things for us. * * The price tag for not using dynamic memory is that libtfm has to be * configured to know about the largest bignum one wants it to be able * to support at compile time. This should not be a serious problem. * * We use a lot of one-element arrays (fp_int[1] instead of plain * fp_int) to avoid having to prefix every use of an fp_int with "&". * Perhaps we should encapsulate this idiom in a typedef. * * Unfortunately, libtfm is bad about const-ification, but we want to * hide that from our users, so our public API uses const as * appropriate and we use inline functions to remove const constraints * in a relatively type-safe manner before calling libtom. */ #include #include #include #include #include #include #include "hal.h" #include "verilog_constants.h" #include #include "asn1_internal.h" /* * Whether to use ModExp core. It works, but at the moment it's so * slow that a full test run can take more than an hour. */ #ifndef HAL_RSA_USE_MODEXP #define HAL_RSA_USE_MODEXP 1 #endif /* * Whether we want debug output. */ static int debug = 0; void hal_rsa_set_debug(const int onoff) { debug = onoff; } /* * Whether we want RSA blinding. */ static int blinding = 1; void hal_rsa_set_blinding(const int onoff) { blinding = onoff; } /* * RSA key implementation. This structure type is private to this * module, anything else that needs to touch one of these just gets a * typed opaque pointer. We do, however, export the size, so that we * can make memory allocation the caller's problem. */ struct hal_rsa_key { hal_rsa_key_type_t type; /* What kind of key this is */ fp_int n[1]; /* The modulus */ fp_int e[1]; /* Public exponent */ fp_int d[1]; /* Private exponent */ fp_int p[1]; /* 1st prime factor */ fp_int q[1]; /* 2nd prime factor */ fp_int u[1]; /* 1/q mod p */ fp_int dP[1]; /* d mod (p - 1) */ fp_int dQ[1]; /* d mod (q - 1) */ }; const size_t hal_rsa_key_t_size = sizeof(hal_rsa_key_t); /* * Initializers. We want to be able to initialize automatic fp_int * variables a sane value (less error prone), but picky compilers * whine about the number of curly braces required. So we define a * macro which isolates that madness in one place. */ #define INIT_FP_INT {{{0}}} /* * Error handling. */ #define lose(_code_) \ do { err = _code_; goto fail; } while (0) #define FP_CHECK(_expr_) \ do { \ switch (_expr_) { \ case FP_OKAY: break; \ case FP_VAL: lose(HAL_ERROR_BAD_ARGUMENTS); \ case FP_MEM: lose(HAL_ERROR_ALLOCATION_FAILURE); \ default: lose(HAL_ERROR_IMPOSSIBLE); \ } \ } while (0) /* * Unpack a bignum into a byte array, with length check. */ static hal_error_t unpack_fp(const fp_int * const bn, uint8_t *buffer, const size_t length) { hal_error_t err = HAL_OK; assert(bn != NULL && buffer != NULL); const size_t bytes = fp_unsigned_bin_size(unconst_fp_int(bn)); if (bytes > length) lose(HAL_ERROR_RESULT_TOO_LONG); memset(buffer, 0, length); fp_to_unsigned_bin(unconst_fp_int(bn), buffer + length - bytes); fail: return err; } #if HAL_RSA_USE_MODEXP /* * Unwrap bignums into byte arrays, feed them into hal_modexp(), and * wrap result back up as a bignum. */ static hal_error_t modexp(const hal_core_t *core, const fp_int * msg, const fp_int * const exp, const fp_int * const mod, fp_int *res) { hal_error_t err = HAL_OK; if ((err = hal_core_check_name(&core, MODEXPS6_NAME)) != HAL_OK) return err; assert(msg != NULL && exp != NULL && mod != NULL && res != NULL); fp_int reduced_msg[1] = INIT_FP_INT; if (fp_cmp_mag(unconst_fp_int(msg), unconst_fp_int(mod)) != FP_LT) { fp_init(reduced_msg); fp_mod(unconst_fp_int(msg), unconst_fp_int(mod), reduced_msg); msg = reduced_msg; } const size_t exp_len = (fp_unsigned_bin_size(unconst_fp_int(exp)) + 3) & ~3; const size_t mod_len = (fp_unsigned_bin_size(unconst_fp_int(mod)) + 3) & ~3; uint8_t msgbuf[mod_len]; uint8_t expbuf[exp_len]; uint8_t modbuf[mod_len]; uint8_t resbuf[mod_len]; if ((err = unpack_fp(msg, msgbuf, sizeof(msgbuf))) != HAL_OK || (err = unpack_fp(exp, expbuf, sizeof(expbuf))) != HAL_OK || (err = unpack_fp(mod, modbuf, sizeof(modbuf))) != HAL_OK || (err = hal_modexp(core, msgbuf, sizeof(msgbuf), expbuf, sizeof(expbuf), modbuf, sizeof(modbuf), resbuf, sizeof(resbuf))) != HAL_OK) goto fail; fp_read_unsigned_bin(res, resbuf, sizeof(resbuf)); fail: memset(msgbuf, 0, sizeof(msgbuf)); memset(expbuf, 0, sizeof(expbuf)); memset(modbuf, 0, sizeof(modbuf)); return err; } /* * Wrapper to let us export our modexp function as a replacement for * TFM's, to avoid dragging in all of the TFM montgomery code when we * use TFM's Miller-Rabin test code. * * This code is here rather than in a separate module because of the * error handling: TFM's error codes aren't really capable of * expressing all the things that could go wrong here. */ int fp_exptmod(fp_int *a, fp_int *b, fp_int *c, fp_int *d) { return modexp(NULL, a, b, c, d) == HAL_OK ? FP_OKAY : FP_VAL; } #else /* HAL_RSA_USE_MODEXP */ /* * Workaround to let us use TFM's software implementation of modular * exponentiation when we want to test other things and don't want to * wait for the slow FPGA implementation. */ static hal_error_t modexp(const fp_int * const msg, const fp_int * const exp, const fp_int * const mod, fp_int *res) { hal_error_t err = HAL_OK; FP_CHECK(fp_exptmod(unconst_fp_int(msg), unconst_fp_int(exp), unconst_fp_int(mod), res)); fail: return err; } #endif /* HAL_RSA_USE_MODEXP */ /* * Create blinding factors. There are various schemes for amortizing * the cost of this over multiple RSA operations, at present we don't * try. Come back to this if it looks like a bottleneck. */ static hal_error_t create_blinding_factors(const hal_core_t *core, const hal_rsa_key_t * const key, fp_int *bf, fp_int *ubf) { assert(key != NULL && bf != NULL && ubf != NULL); uint8_t rnd[fp_unsigned_bin_size(unconst_fp_int(key->n))]; hal_error_t err = HAL_OK; if ((err = hal_get_random(NULL, rnd, sizeof(rnd))) != HAL_OK) goto fail; fp_init(bf); fp_read_unsigned_bin(bf, rnd, sizeof(rnd)); fp_copy(bf, ubf); if ((err = modexp(core, bf, key->e, key->n, bf)) != HAL_OK) goto fail; FP_CHECK(fp_invmod(ubf, unconst_fp_int(key->n), ubf)); fail: memset(rnd, 0, sizeof(rnd)); return err; } /* * RSA decryption via Chinese Remainder Theorem (Garner's formula). */ static hal_error_t rsa_crt(const hal_core_t *core, const hal_rsa_key_t * const key, fp_int *msg, fp_int *sig) { assert(key != NULL && msg != NULL && sig != NULL); hal_error_t err = HAL_OK; fp_int t[1] = INIT_FP_INT; fp_int m1[1] = INIT_FP_INT; fp_int m2[1] = INIT_FP_INT; fp_int bf[1] = INIT_FP_INT; fp_int ubf[1] = INIT_FP_INT; /* * Handle blinding if requested. */ if (blinding) { if ((err = create_blinding_factors(core, key, bf, ubf)) != HAL_OK) goto fail; FP_CHECK(fp_mulmod(msg, bf, unconst_fp_int(key->n), msg)); } /* * m1 = msg ** dP mod p * m2 = msg ** dQ mod q */ if ((err = modexp(core, msg, key->dP, key->p, m1)) != HAL_OK || (err = modexp(core, msg, key->dQ, key->q, m2)) != HAL_OK) goto fail; /* * t = m1 - m2. */ fp_sub(m1, m2, t); /* * Add zero (mod p) if needed to make t positive. If doing this * once or twice doesn't help, something is very wrong. */ if (fp_cmp_d(t, 0) == FP_LT) fp_add(t, unconst_fp_int(key->p), t); if (fp_cmp_d(t, 0) == FP_LT) fp_add(t, unconst_fp_int(key->p), t); if (fp_cmp_d(t, 0) == FP_LT) lose(HAL_ERROR_IMPOSSIBLE); /* * sig = (t * u mod p) * q + m2 */ FP_CHECK(fp_mulmod(t, unconst_fp_int(key->u), unconst_fp_int(key->p), t)); fp_mul(t, unconst_fp_int(key->q), t); fp_add(t, m2, sig); /* * Unblind if necessary. */ if (blinding) FP_CHECK(fp_mulmod(sig, ubf, unconst_fp_int(key->n), sig)); fail: fp_zero(t); fp_zero(m1); fp_zero(m2); return err; } /* * Public API for raw RSA encryption and decryption. * * NB: This does not handle PKCS #1.5 padding, at the moment that's up * to the caller. */ hal_error_t hal_rsa_encrypt(const hal_core_t *core, const hal_rsa_key_t * const key, const uint8_t * const input, const size_t input_len, uint8_t * output, const size_t output_len) { hal_error_t err = HAL_OK; if (key == NULL || input == NULL || output == NULL || input_len > output_len) return HAL_ERROR_BAD_ARGUMENTS; fp_int i[1] = INIT_FP_INT; fp_int o[1] = INIT_FP_INT; fp_read_unsigned_bin(i, unconst_uint8_t(input), input_len); if ((err = modexp(core, i, key->e, key->n, o)) != HAL_OK || (err = unpack_fp(o, output, output_len)) != HAL_OK) goto fail; fail: fp_zero(i); fp_zero(o); return err; } hal_error_t hal_rsa_decrypt(const hal_core_t *core, const hal_rsa_key_t * const key, const uint8_t * const input, const size_t input_len, uint8_t * output, const size_t output_len) { hal_error_t err = HAL_OK; if (key == NULL || input == NULL || output == NULL || input_len > output_len) return HAL_ERROR_BAD_ARGUMENTS; fp_int i[1] = INIT_FP_INT; fp_int o[1] = INIT_FP_INT; fp_read_unsigned_bin(i, unconst_uint8_t(input), input_len); /* * Do CRT if we have all the necessary key components, otherwise * just do brute force ModExp. */ if (fp_iszero(key->p) || fp_iszero(key->q) || fp_iszero(key->u) || fp_iszero(key->dP) || fp_iszero(key->dQ)) err = modexp(core, i, key->d, key->n, o); else err = rsa_crt(core, key, i, o); if (err != HAL_OK || (err = unpack_fp(o, output, output_len)) != HAL_OK) goto fail; fail: fp_zero(i); fp_zero(o); return err; } /* * Clear a key. We might want to do something a bit more energetic * than plain old memset() eventually. */ void hal_rsa_key_clear(hal_rsa_key_t *key) { if (key != NULL) memset(key, 0, sizeof(*key)); } /* * Load a key from raw components. This is a simplistic version: we * don't attempt to generate missing private key components, we just * reject the key if it doesn't have everything we expect. * * In theory, the only things we'd really need for the private key if * we were being nicer about this would be e, p, and q, as we could * calculate everything else from them. */ static hal_error_t load_key(const hal_rsa_key_type_t type, hal_rsa_key_t **key_, void *keybuf, const size_t keybuf_len, const uint8_t * const n, const size_t n_len, const uint8_t * const e, const size_t e_len, const uint8_t * const d, const size_t d_len, const uint8_t * const p, const size_t p_len, const uint8_t * const q, const size_t q_len, const uint8_t * const u, const size_t u_len, const uint8_t * const dP, const size_t dP_len, const uint8_t * const dQ, const size_t dQ_len) { if (key_ == NULL || keybuf == NULL || keybuf_len < sizeof(hal_rsa_key_t)) return HAL_ERROR_BAD_ARGUMENTS; memset(keybuf, 0, keybuf_len); hal_rsa_key_t *key = keybuf; key->type = type; #define _(x) do { fp_init(key->x); if (x == NULL) goto fail; fp_read_unsigned_bin(key->x, unconst_uint8_t(x), x##_len); } while (0) switch (type) { case HAL_RSA_PRIVATE: _(d); _(p); _(q); _(u); _(dP); _(dQ); case HAL_RSA_PUBLIC: _(n); _(e); *key_ = key; return HAL_OK; } #undef _ fail: memset(key, 0, sizeof(*key)); return HAL_ERROR_BAD_ARGUMENTS; } /* * Public API to load_key(). */ hal_error_t hal_rsa_key_load_private(hal_rsa_key_t **key_, void *keybuf, const size_t keybuf_len, const uint8_t * const n, const size_t n_len, const uint8_t * const e, const size_t e_len, const uint8_t * const d, const size_t d_len, const uint8_t * const p, const size_t p_len, const uint8_t * const q, const size_t q_len, const uint8_t * const u, const size_t u_len, const uint8_t * const dP, const size_t dP_len, const uint8_t * const dQ, const size_t dQ_len) { return load_key(HAL_RSA_PRIVATE, key_, keybuf, keybuf_len, n, n_len, e, e_len, d, d_len, p, p_len, q, q_len, u, u_len, dP, dP_len, dQ, dQ_len); } hal_error_t hal_rsa_key_load_public(hal_rsa_key_t **key_, void *keybuf, const size_t keybuf_len, const uint8_t * const n, const size_t n_len, const uint8_t * const e, const size_t e_len) { return load_key(HAL_RSA_PUBLIC, key_, keybuf, keybuf_len, n, n_len, e, e_len, NULL, 0, NULL, 0, NULL, 0, NULL, 0, NULL, 0, NULL, 0); } /* * Extract the key type. */ hal_error_t hal_rsa_key_get_type(const hal_rsa_key_t * const key, hal_rsa_key_type_t *key_type) { if (key == NULL || key_type == NULL) return HAL_ERROR_BAD_ARGUMENTS; *key_type = key->type; return HAL_OK; } /* * Extract public key components. */ static hal_error_t extract_component(const hal_rsa_key_t * const key, const size_t offset, uint8_t *res, size_t *res_len, const size_t res_max) { if (key == NULL) return HAL_ERROR_BAD_ARGUMENTS; const fp_int * const bn = (const fp_int *) (((const uint8_t *) key) + offset); const size_t len = fp_unsigned_bin_size(unconst_fp_int(bn)); if (res_len != NULL) *res_len = len; if (res == NULL) return HAL_OK; if (len > res_max) return HAL_ERROR_RESULT_TOO_LONG; memset(res, 0, res_max); fp_to_unsigned_bin(unconst_fp_int(bn), res); return HAL_OK; } hal_error_t hal_rsa_key_get_modulus(const hal_rsa_key_t * const key, uint8_t *res, size_t *res_len, const size_t res_max) { return extract_component(key, offsetof(hal_rsa_key_t, n), res, res_len, res_max); } hal_error_t hal_rsa_key_get_public_exponent(const hal_rsa_key_t * const key, uint8_t *res, size_t *res_len, const size_t res_max) { return extract_component(key, offsetof(hal_rsa_key_t, e), res, res_len, res_max); } /* * Generate a prime factor for an RSA keypair. * * Get random bytes, munge a few bits, and stuff into a bignum. Keep * doing this until we find a result that's (probably) prime and for * which result - 1 is relatively prime with respect to e. */ static hal_error_t find_prime(const unsigned prime_length, const fp_int * const e, fp_int *result) { uint8_t buffer[prime_length]; hal_error_t err; fp_int t[1] = INIT_FP_INT; do { if ((err = hal_get_random(NULL, buffer, sizeof(buffer))) != HAL_OK) return err; buffer[0 ] |= 0xc0; buffer[sizeof(buffer) - 1] |= 0x01; fp_read_unsigned_bin(result, buffer, sizeof(buffer)); } while (!fp_isprime(result) || (fp_sub_d(result, 1, t), fp_gcd(t, unconst_fp_int(e), t), fp_cmp_d(t, 1) != FP_EQ)); fp_zero(t); return HAL_OK; } /* * Generate a new RSA keypair. */ hal_error_t hal_rsa_key_gen(const hal_core_t *core, hal_rsa_key_t **key_, void *keybuf, const size_t keybuf_len, const unsigned key_length, const uint8_t * const public_exponent, const size_t public_exponent_len) { hal_rsa_key_t *key = keybuf; hal_error_t err = HAL_OK; fp_int p_1[1] = INIT_FP_INT; fp_int q_1[1] = INIT_FP_INT; if (key_ == NULL || keybuf == NULL || keybuf_len < sizeof(hal_rsa_key_t)) return HAL_ERROR_BAD_ARGUMENTS; memset(keybuf, 0, keybuf_len); key->type = HAL_RSA_PRIVATE; fp_read_unsigned_bin(key->e, (uint8_t *) public_exponent, public_exponent_len); if (key_length < bitsToBytes(1024) || key_length > bitsToBytes(8192)) return HAL_ERROR_UNSUPPORTED_KEY; if (fp_cmp_d(key->e, 0x010001) != FP_EQ) return HAL_ERROR_UNSUPPORTED_KEY; /* * Find a good pair of prime numbers. */ if ((err = find_prime(key_length / 2, key->e, key->p)) != HAL_OK || (err = find_prime(key_length / 2, key->e, key->q)) != HAL_OK) return err; /* * Calculate remaining key components. */ fp_init(p_1); fp_sub_d(key->p, 1, p_1); fp_init(q_1); fp_sub_d(key->q, 1, q_1); fp_mul(key->p, key->q, key->n); /* n = p * q */ fp_lcm(p_1, q_1, key->d); FP_CHECK(fp_invmod(key->e, key->d, key->d)); /* d = (1/e) % lcm(p-1, q-1) */ FP_CHECK(fp_mod(key->d, p_1, key->dP)); /* dP = d % (p-1) */ FP_CHECK(fp_mod(key->d, q_1, key->dQ)); /* dQ = d % (q-1) */ FP_CHECK(fp_invmod(key->q, key->p, key->u)); /* u = (1/q) % p */ *key_ = key; /* Fall through to cleanup */ fail: if (err != HAL_OK) memset(keybuf, 0, keybuf_len); fp_zero(p_1); fp_zero(q_1); return err; } /* * Just enough ASN.1 to read and write PKCS #1.5 RSAPrivateKey syntax * (RFC 2313 section 7.2). * * RSAPrivateKey fields in the required order. */ #define RSAPrivateKey_fields \ _(version); \ _(key->n); \ _(key->e); \ _(key->d); \ _(key->p); \ _(key->q); \ _(key->dP); \ _(key->dQ); \ _(key->u); hal_error_t hal_rsa_key_to_der(const hal_rsa_key_t * const key, uint8_t *der, size_t *der_len, const size_t der_max) { hal_error_t err = HAL_OK; if (key == NULL || der_len == NULL || key->type != HAL_RSA_PRIVATE) return HAL_ERROR_BAD_ARGUMENTS; fp_int version[1] = INIT_FP_INT; /* * Calculate data length. */ size_t vlen = 0; #define _(x) { size_t i; if ((err = hal_asn1_encode_integer(x, NULL, &i, der_max - vlen)) != HAL_OK) return err; vlen += i; } RSAPrivateKey_fields; #undef _ /* * Encode header. */ if ((err = hal_asn1_encode_header(ASN1_SEQUENCE, vlen, der, der_len, der_max)) != HAL_OK) return err; const size_t hlen = *der_len; *der_len += vlen; if (der == NULL) return HAL_OK; /* * Encode data. */ der += hlen; #define _(x) { size_t i; if ((err = hal_asn1_encode_integer(x, der, &i, vlen)) != HAL_OK) return err; der += i; vlen -= i; } RSAPrivateKey_fields; #undef _ return HAL_OK; } size_t hal_rsa_key_to_der_len(const hal_rsa_key_t * const key) { size_t len = 0; return hal_rsa_key_to_der(key, NULL, &len, 0) == HAL_OK ? len : 0; } hal_error_t hal_rsa_key_from_der(hal_rsa_key_t **key_, void *keybuf, const size_t keybuf_len, const uint8_t *der, const size_t der_len) { if (key_ == NULL || keybuf == NULL || keybuf_len < sizeof(hal_rsa_key_t) || der == NULL) return HAL_ERROR_BAD_ARGUMENTS; memset(keybuf, 0, keybuf_len); hal_rsa_key_t *key = keybuf; key->type = HAL_RSA_PRIVATE; hal_error_t err = HAL_OK; size_t hlen, vlen; if ((err = hal_asn1_decode_header(ASN1_SEQUENCE, der, der_len, &hlen, &vlen)) != HAL_OK) return err; der += hlen; fp_int version[1] = INIT_FP_INT; #define _(x) { size_t i; if ((err = hal_asn1_decode_integer(x, der, &i, vlen)) != HAL_OK) return err; der += i; vlen -= i; } RSAPrivateKey_fields; #undef _ if (fp_cmp_d(version, 0) != FP_EQ) return HAL_ERROR_ASN1_PARSE_FAILED; *key_ = key; return HAL_OK; } /* * Local variables: * indent-tabs-mode: nil * End: */ 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 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