/* * 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, NORDUnet A/S * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions are * met: * - Redistributions of source code must retain the above copyright notice, * this list of conditions and the following disclaimer. * * - 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. * * - Neither the name of the NORDUnet nor the names of its contributors may * be used to endorse or promote products derived from this software * without specific prior written permission. * * 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 * HOLDER 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 "hal.h" #include "hal_internal.h" #include #include "asn1_internal.h" /* * Whether to use ModExp core. It works, but it's painfully slow. */ #ifndef HAL_RSA_SIGN_USE_MODEXP #define HAL_RSA_SIGN_USE_MODEXP 1 #endif #ifndef HAL_RSA_KEYGEN_USE_MODEXP #define HAL_RSA_KEYGEN_USE_MODEXP 0 #endif #if defined(RPC_CLIENT) && RPC_CLIENT != RPC_CLIENT_LOCAL #define hal_get_random(core, buffer, length) hal_rpc_get_random(buffer, length) #endif /* * How big to make the buffers for the modulus coefficient and * Montgomery factor. This will almost certainly want tuning. */ #ifndef HAL_RSA_MAX_OPERAND_LENGTH #define HAL_RSA_MAX_OPERAND_LENGTH MODEXPA7_OPERAND_BYTES #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_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) */ unsigned flags; /* Internal key flags */ uint8_t /* ModExpA7 speedup factors */ nC[HAL_RSA_MAX_OPERAND_LENGTH], nF[HAL_RSA_MAX_OPERAND_LENGTH], pC[HAL_RSA_MAX_OPERAND_LENGTH/2], pF[HAL_RSA_MAX_OPERAND_LENGTH/2], qC[HAL_RSA_MAX_OPERAND_LENGTH/2], qF[HAL_RSA_MAX_OPERAND_LENGTH/2]; }; #define RSA_FLAG_NEEDS_SAVING (1 << 0) #define RSA_FLAG_PRECALC_N_DONE (1 << 1) #define RSA_FLAG_PRECALC_PQ_DONE (1 << 2) 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; if (bn == NULL || buffer == NULL) return HAL_ERROR_IMPOSSIBLE; 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_SIGN_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(hal_core_t *core, const int precalc, const fp_int * const msg, const fp_int * const exp, const fp_int * const mod, fp_int *res, uint8_t *coeff, const size_t coeff_len, uint8_t *mont, const size_t mont_len) { hal_error_t err = HAL_OK; if (msg == NULL || exp == NULL || mod == NULL || res == NULL || coeff == NULL || mont == NULL) return HAL_ERROR_IMPOSSIBLE; const size_t msg_len = (fp_unsigned_bin_size(unconst_fp_int(msg)) + 3) & ~3; 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[msg_len]; uint8_t expbuf[exp_len]; uint8_t modbuf[mod_len]; uint8_t resbuf[mod_len]; hal_modexp_arg_t args = { .core = core, .msg = msgbuf, .msg_len = sizeof(msgbuf), .exp = expbuf, .exp_len = sizeof(expbuf), .mod = modbuf, .mod_len = sizeof(modbuf), .result = resbuf, .result_len = sizeof(resbuf), .coeff = coeff, .coeff_len = coeff_len, .mont = mont, .mont_len = mont_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(precalc, &args)) != 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)); memset(resbuf, 0, sizeof(resbuf)); memset(&args, 0, sizeof(args)); return err; } static hal_error_t modexp2(const int precalc, const fp_int * const msg, hal_core_t *core1, const fp_int * const exp1, const fp_int * const mod1, fp_int * res1, uint8_t *coeff1, const size_t coeff1_len, uint8_t *mont1, const size_t mont1_len, hal_core_t *core2, const fp_int * const exp2, const fp_int * const mod2, fp_int * res2, uint8_t *coeff2, const size_t coeff2_len, uint8_t *mont2, const size_t mont2_len) { hal_error_t err = HAL_OK; if (msg == NULL || exp1 == NULL || mod1 == NULL || res1 == NULL || coeff1 == NULL || mont1 == NULL || exp2 == NULL || mod2 == NULL || res2 == NULL || coeff2 == NULL || mont2 == NULL) return HAL_ERROR_IMPOSSIBLE; const size_t msg_len = (fp_unsigned_bin_size(unconst_fp_int(msg)) + 3) & ~3; const size_t exp1_len = (fp_unsigned_bin_size(unconst_fp_int(exp1)) + 3) & ~3; const size_t mod1_len = (fp_unsigned_bin_size(unconst_fp_int(mod1)) + 3) & ~3; const size_t exp2_len = (fp_unsigned_bin_size(unconst_fp_int(exp2)) + 3) & ~3; const size_t mod2_len = (fp_unsigned_bin_size(unconst_fp_int(mod2)) + 3) & ~3; uint8_t msgbuf[msg_len]; uint8_t expbuf1[exp1_len], modbuf1[mod1_len], resbuf1[mod1_len]; uint8_t expbuf2[exp2_len], modbuf2[mod2_len], resbuf2[mod2_len]; hal_modexp_arg_t args1 = { .core = core1, .msg = msgbuf, .msg_len = sizeof(msgbuf), .exp = expbuf1, .exp_len = sizeof(expbuf1), .mod = modbuf1, .mod_len = sizeof(modbuf1), .result = resbuf1, .result_len = sizeof(resbuf1), .coeff = coeff1, .coeff_len = coeff1_len, .mont = mont1, .mont_len = mont1_len }; hal_modexp_arg_t args2 = { .core = core2, .msg = msgbuf, .msg_len = sizeof(msgbuf), .exp = expbuf2, .exp_len = sizeof(expbuf2), .mod = modbuf2, .mod_len = sizeof(modbuf2), .result = resbuf2, .result_len = sizeof(resbuf2), .coeff = coeff2, .coeff_len = coeff2_len, .mont = mont2, .mont_len = mont2_len }; if ((err = unpack_fp(msg, msgbuf, sizeof(msgbuf))) != HAL_OK || (err = unpack_fp(exp1, expbuf1, sizeof(expbuf1))) != HAL_OK || (err = unpack_fp(mod1, modbuf1, sizeof(modbuf1))) != HAL_OK || (err = unpack_fp(exp2, expbuf2, sizeof(expbuf2))) != HAL_OK || (err = unpack_fp(mod2, modbuf2, sizeof(modbuf2))) != HAL_OK || (err = hal_modexp2(precalc, &args1, &args2)) != HAL_OK) goto fail; fp_read_unsigned_bin(res1, resbuf1, sizeof(resbuf1)); fp_read_unsigned_bin(res2, resbuf2, sizeof(resbuf2)); fail: memset(msgbuf, 0, sizeof(msgbuf)); memset(expbuf1, 0, sizeof(expbuf1)); memset(modbuf1, 0, sizeof(modbuf1)); memset(resbuf1, 0, sizeof(resbuf1)); memset(&args1, 0, sizeof(args1)); memset(expbuf2, 0, sizeof(expbuf2)); memset(modbuf2, 0, sizeof(modbuf2)); memset(resbuf2, 0, sizeof(resbuf2)); memset(&args2, 0, sizeof(args2)); return err; } #else /* HAL_RSA_SIGN_USE_MODEXP */ /* * Use libtfm's software implementation of modular exponentiation. * Now that the ModExpA7 core performs about as well as the software * implementation, there's probably no need to use this, but we're * still tuning things, so leave the hook here for now. */ static hal_error_t modexp(const hal_core_t *core, /* ignored */ const int precalc, /* ignored */ const fp_int * const msg, const fp_int * const exp, const fp_int * const mod, fp_int *res, uint8_t *coeff, const size_t coeff_len, /* ignored */ uint8_t *mont, const size_t mont_len) /* ignored */ { 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; } static hal_error_t modexp2(const int precalc, /* ignored */ const fp_int * const msg, hal_core_t *core1, /* ignored */ const fp_int * const exp1, const fp_int * const mod1, fp_int * res1, uint8_t *coeff1, const size_t coeff1_len, /* ignored */ uint8_t *mont1, const size_t mont1_len, /* ignored */ hal_core_t *core2, /* ignored */ const fp_int * const exp2, const fp_int * const mod2, fp_int * res2, uint8_t *coeff2, const size_t coeff2_len, /* ignored */ uint8_t *mont2, const size_t mont2_len) /* ignored */ { hal_error_t err = HAL_OK; FP_CHECK(fp_exptmod(unconst_fp_int(msg), unconst_fp_int(exp1), unconst_fp_int(mod1), res1)); FP_CHECK(fp_exptmod(unconst_fp_int(msg), unconst_fp_int(exp2), unconst_fp_int(mod2), res2)); fail: return err; } #endif /* HAL_RSA_SIGN_USE_MODEXP */ /* * Wrapper to let us export our modexp function as a replacement for * libtfm's when running libtfm's Miller-Rabin test code. * * At the moment, the libtfm software implementation performs * disproportionately better than our core does for the specific case * of Miller-Rabin tests, for reasons we don't really understand. * So there's not much point in enabling this, except as a test to * confirm this behavior. * * This code is here rather than in a separate module because of the * error handling: libtfm's error codes aren't really capable of * expressing all the things that could go wrong here. */ #if HAL_RSA_SIGN_USE_MODEXP && HAL_RSA_KEYGEN_USE_MODEXP int fp_exptmod(fp_int *a, fp_int *b, fp_int *c, fp_int *d) { const size_t len = (fp_unsigned_bin_size(unconst_fp_int(b)) + 3) & ~3; uint8_t C[len], F[len]; const hal_error_t err = modexp(NULL, 0, a, b, c, d, C, sizeof(C), F, sizeof(F)); memset(C, 0, sizeof(C)); memset(F, 0, sizeof(F)); return err == HAL_OK ? FP_OKAY : FP_VAL; } #endif /* HAL_RSA_SIGN_USE_MODEXP && HAL_RSA_KEYGEN_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(hal_core_t *core, hal_rsa_key_t *key, fp_int *bf, fp_int *ubf) { if (key == NULL || bf == NULL || ubf == NULL) return HAL_ERROR_IMPOSSIBLE; const int precalc = !(key->flags & RSA_FLAG_PRECALC_N_DONE); 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, precalc, bf, key->e, key->n, bf, key->nC, sizeof(key->nC), key->nF, sizeof(key->nF))) != HAL_OK) goto fail; if (precalc) key->flags |= RSA_FLAG_PRECALC_N_DONE | RSA_FLAG_NEEDS_SAVING; 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(hal_core_t *core1, hal_core_t *core2, hal_rsa_key_t *key, fp_int *msg, fp_int *sig) { if (key == NULL || msg == NULL || sig == NULL) return HAL_ERROR_IMPOSSIBLE; const int precalc = !(key->flags & RSA_FLAG_PRECALC_PQ_DONE); 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(core1, 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 = modexp2(precalc, msg, core1, key->dP, key->p, m1, key->pC, sizeof(key->pC), key->pF, sizeof(key->pF), core2, key->dQ, key->q, m2, key->qC, sizeof(key->qC), key->qF, sizeof(key->qF))) != HAL_OK) goto fail; if (precalc) key->flags |= RSA_FLAG_PRECALC_PQ_DONE | RSA_FLAG_NEEDS_SAVING; /* * 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(hal_core_t *core, hal_rsa_key_t *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; const int precalc = !(key->flags & RSA_FLAG_PRECALC_N_DONE); 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); err = modexp(core, precalc, i, key->e, key->n, o, key->nC, sizeof(key->nC), key->nF, sizeof(key->nF)); if (err == HAL_OK && precalc) key->flags |= RSA_FLAG_PRECALC_N_DONE | RSA_FLAG_NEEDS_SAVING; if (err == HAL_OK) err = unpack_fp(o, output, output_len); fp_zero(i); fp_zero(o); return err; } hal_error_t hal_rsa_decrypt(hal_core_t *core1, hal_core_t *core2, hal_rsa_key_t *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 = rsa_crt(core1, core2, key, i, o); else { const int precalc = !(key->flags & RSA_FLAG_PRECALC_N_DONE); err = modexp(core1, precalc, i, key->d, key->n, o, key->nC, sizeof(key->nC), key->nF, sizeof(key->nF)); if (err == HAL_OK && precalc) key->flags |= RSA_FLAG_PRECALC_N_DONE | RSA_FLAG_NEEDS_SAVING; } 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_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_KEY_TYPE_RSA_PRIVATE: _(d); _(p); _(q); _(u); _(dP); _(dQ); case HAL_KEY_TYPE_RSA_PUBLIC: _(n); _(e); *key_ = key; return HAL_OK; default: goto fail; } #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_KEY_TYPE_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_KEY_TYPE_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_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 to * construct our initial candidate. * * Initialize table of remainders when dividing candidate by each * entry in corresponding table of small primes. We'd have to perform * these tests in any case for any succesful candidate, and doing it * up front lets us amortize the cost over the entire search, so we do * this unconditionally before entering the search loop. * * If all of the remainders were non-zero, run the requisite number of * Miller-Rabin tests using the first few entries from that same table * of small primes as the test values. If we get past Miller-Rabin, * the candidate is (probably) prime, to a confidence level which we * can tune by adjusting the number of Miller-Rabin tests. * * For RSA, we also need (result - 1) to be relatively prime with * respect to the public exponent. If a (probable) prime passes that * test, we have a winner. * * If any of the above tests failed, we increment the candidate and * all remainders by two, then loop back to the remainder test. This * is where the table pays off: incrementing remainders is really * cheap, and since most composite numbers fail the small primes test, * making that cheap makes the whole loop run significantly faster. * * General approach suggested by HAC note 4.51. Range of small prime * table and default number of Miller-Rabin tests suggested by Schneier. */ #ifndef HAL_RSA_MILLER_RABIN_TESTS #define HAL_RSA_MILLER_RABIN_TESTS (5) #endif static const uint16_t small_prime[] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999 }; static hal_error_t find_prime(const unsigned prime_length, const fp_int * const e, fp_int *result) { uint16_t remainder[sizeof(small_prime)/sizeof(*small_prime)]; uint8_t buffer[prime_length]; fp_int t[1] = INIT_FP_INT; hal_error_t err; if ((err = hal_get_random(NULL, buffer, sizeof(buffer))) != HAL_OK) return err; buffer[0] &= ~0x01; /* Headroom for search */ buffer[0] |= 0xc0; /* Result large enough */ buffer[sizeof(buffer) - 1] |= 0x01; /* Candidates are odd */ fp_read_unsigned_bin(result, buffer, sizeof(buffer)); memset(buffer, 0, sizeof(buffer)); for (size_t i = 0; i < sizeof(small_prime)/sizeof(*small_prime); i++) { fp_digit d; fp_mod_d(result, small_prime[i], &d); remainder[i] = d; } for (;;) { int possible = 1; for (size_t i = 0; i < sizeof(small_prime)/sizeof(*small_prime); i++) possible &= remainder[i] != 0; for (size_t i = 0; possible && i < HAL_RSA_MILLER_RABIN_TESTS; i++) { fp_set(t, small_prime[i]); fp_prime_miller_rabin(result, t, &possible); } if (possible) { fp_sub_d(result, 1, t); fp_gcd(t, unconst_fp_int(e), t); possible = fp_cmp_d(t, 1) == FP_EQ; } if (possible) break; fp_add_d(result, 2, result); for (size_t i = 0; i < sizeof(small_prime)/sizeof(*small_prime); i++) if ((remainder[i] += 2) >= small_prime[i]) remainder[i] -= small_prime[i]; } memset(remainder, 0, sizeof(remainder)); fp_zero(t); return HAL_OK; } /* * Generate a new RSA keypair. */ hal_error_t hal_rsa_key_gen(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_KEY_TYPE_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->flags |= RSA_FLAG_NEEDS_SAVING; *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; } /* * Whether a key contains new data that need saving (newly generated * key, updated speedup components, whatever). */ int hal_rsa_key_needs_saving(const hal_rsa_key_t * const key) { return key != NULL && (key->flags & RSA_FLAG_NEEDS_SAVING); } /* * Just enough ASN.1 to read and write PKCS #1.5 RSAPrivateKey syntax * (RFC 2313 section 7.2) wrapped in a PKCS #8 PrivateKeyInfo (RFC 5208). * * RSAPrivateKey fields in the required order. * * The "extra" fields are additional key components specific to the * systolic modexpa7 core. We represent these in ASN.1 as OPTIONAL * fields using IMPLICIT PRIVATE tags, since this is neither * standardized nor meaningful to anybody else. Underlying encoding * is INTEGER or OCTET STRING (currently the latter). */ #define RSAPrivateKey_fields \ _(version); \ _(key->n); \ _(key->e); \ _(key->d); \ _(key->p); \ _(key->q); \ _(key->dP); \ _(key->dQ); \ _(key->u); #define RSAPrivateKey_extra_fields \ _(ASN1_PRIVATE + 0, nC, RSA_FLAG_PRECALC_N_DONE); \ _(ASN1_PRIVATE + 1, nF, RSA_FLAG_PRECALC_N_DONE); \ _(ASN1_PRIVATE + 2, pC, RSA_FLAG_PRECALC_PQ_DONE); \ _(ASN1_PRIVATE + 3, pF, RSA_FLAG_PRECALC_PQ_DONE); \ _(ASN1_PRIVATE + 4, qC, RSA_FLAG_PRECALC_PQ_DONE); \ _(ASN1_PRIVATE + 5, qF, RSA_FLAG_PRECALC_PQ_DONE); hal_error_t hal_rsa_private_key_to_der_internal(const hal_rsa_key_t * const key, const int include_extra, uint8_t *der, size_t *der_len, const size_t der_max) { hal_error_t err = HAL_OK; if (key == NULL || key->type != HAL_KEY_TYPE_RSA_PRIVATE) return HAL_ERROR_BAD_ARGUMENTS; fp_int version[1] = INIT_FP_INT; /* * Calculate data length. */ size_t hlen = 0, vlen = 0; #define _(x) \ { \ size_t n = 0; \ err = hal_asn1_encode_integer(x, NULL, &n, der_max - vlen); \ if (err != HAL_OK) \ return err; \ vlen += n; \ } RSAPrivateKey_fields; #undef _ #define _(x,y,z) \ if ((key->flags & z) != 0) { \ size_t n = 0; \ if ((err = hal_asn1_encode_header(x, sizeof(key->y), NULL, \ &n, 0)) != HAL_OK) \ return err; \ vlen += n + sizeof(key->y); \ } if (include_extra) { RSAPrivateKey_extra_fields; } #undef _ if ((err = hal_asn1_encode_header(ASN1_SEQUENCE, vlen, NULL, &hlen, 0)) != HAL_OK) return err; if ((err = hal_asn1_encode_pkcs8_privatekeyinfo(hal_asn1_oid_rsaEncryption, hal_asn1_oid_rsaEncryption_len, NULL, 0, NULL, hlen + vlen, NULL, der_len, der_max)) != HAL_OK) return err; if (der == NULL) return HAL_OK; /* * Encode data. */ if ((err = hal_asn1_encode_header(ASN1_SEQUENCE, vlen, der, &hlen, der_max)) != HAL_OK) return err; uint8_t *d = der + hlen; memset(d, 0, vlen); #define _(x) \ { \ size_t n = 0; \ err = hal_asn1_encode_integer(x, d, &n, vlen); \ if (err != HAL_OK) \ return err; \ d += n; \ vlen -= n; \ } RSAPrivateKey_fields; #undef _ #define _(x,y,z) \ if ((key->flags & z) != 0) { \ size_t n = 0; \ if ((err = hal_asn1_encode_header(x, sizeof(key->y), d, \ &n, vlen)) != HAL_OK) \ return err; \ d += n; \ vlen -= n; \ memcpy(d, key->y, sizeof(key->y)); \ d += sizeof(key->y); \ vlen -= sizeof(key->y); \ } if (include_extra) { RSAPrivateKey_extra_fields; } #undef _ return hal_asn1_encode_pkcs8_privatekeyinfo(hal_asn1_oid_rsaEncryption, hal_asn1_oid_rsaEncryption_len, NULL, 0, der, d - der, der, der_len, der_max); } hal_error_t hal_rsa_private_key_to_der(const hal_rsa_key_t * const key, uint8_t *der, size_t *der_len, const size_t der_max) { return hal_rsa_private_key_to_der_internal(key, 0, der, der_len, der_max); } hal_error_t hal_rsa_private_key_to_der_extra(const hal_rsa_key_t * const key, uint8_t *der, size_t *der_len, const size_t der_max) { return hal_rsa_private_key_to_der_internal(key, 1, der, der_len, der_max); } hal_error_t hal_rsa_private_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_KEY_TYPE_RSA_PRIVATE; size_t hlen, vlen, alg_oid_len, curve_oid_len, privkey_len; const uint8_t *alg_oid, *curve_oid, *privkey; hal_error_t err; if ((err = hal_asn1_decode_pkcs8_privatekeyinfo(&alg_oid, &alg_oid_len, &curve_oid, &curve_oid_len, &privkey, &privkey_len, der, der_len)) != HAL_OK) return err; if (alg_oid_len != hal_asn1_oid_rsaEncryption_len || memcmp(alg_oid, hal_asn1_oid_rsaEncryption, alg_oid_len) != 0 || curve_oid_len != 0) return HAL_ERROR_ASN1_PARSE_FAILED; if ((err = hal_asn1_decode_header(ASN1_SEQUENCE, privkey, privkey_len, &hlen, &vlen)) != HAL_OK) return err; const uint8_t *d = privkey + hlen; fp_int version[1] = INIT_FP_INT; #define _(x) \ { \ size_t n; \ err = hal_asn1_decode_integer(x, d, &n, vlen); \ if (err != HAL_OK) \ return err; \ d += n; \ vlen -= n; \ } RSAPrivateKey_fields; #undef _ #define _(x,y,z) \ if (hal_asn1_peek(x, d, vlen)) { \ size_t hl = 0, vl = 0; \ if ((err = hal_asn1_decode_header(x, d, vlen, &hl, &vl)) != HAL_OK) \ return err; \ if (vl > sizeof(key->y)) { \ hal_log(HAL_LOG_DEBUG, "extra factor %s too big (%lu > %lu)", \ #y, (unsigned long) vl, (unsigned long) sizeof(key->y)); \ return HAL_ERROR_ASN1_PARSE_FAILED; \ } \ memcpy(key->y, d + hl, vl); \ key->flags |= z; \ d += hl + vl; \ vlen -= hl + vl; \ } RSAPrivateKey_extra_fields; #undef _ if (d != privkey + privkey_len) { hal_log(HAL_LOG_DEBUG, "not at end of buffer (0x%lx != 0x%lx)", (unsigned long) d, (unsigned long) privkey + privkey_len); return HAL_ERROR_ASN1_PARSE_FAILED; } if (!fp_iszero(version)) { hal_log(HAL_LOG_DEBUG, "nonzero version"); return HAL_ERROR_ASN1_PARSE_FAILED; } *key_ = key; return HAL_OK; } /* * ASN.1 public keys in SubjectPublicKeyInfo form, see RFCs 2313, 4055, and 5280. */ hal_error_t hal_rsa_public_key_to_der(const hal_rsa_key_t * const key, uint8_t *der, size_t *der_len, const size_t der_max) { if (key == NULL || (key->type != HAL_KEY_TYPE_RSA_PRIVATE && key->type != HAL_KEY_TYPE_RSA_PUBLIC)) return HAL_ERROR_BAD_ARGUMENTS; size_t hlen, n_len, e_len; hal_error_t err; if ((err = hal_asn1_encode_integer(key->n, NULL, &n_len, 0)) != HAL_OK || (err = hal_asn1_encode_integer(key->e, NULL, &e_len, 0)) != HAL_OK) return err; const size_t vlen = n_len + e_len; if ((err = hal_asn1_encode_header(ASN1_SEQUENCE, vlen, der, &hlen, der_max)) != HAL_OK) return err; if (der != NULL) { uint8_t * const n_out = der + hlen; uint8_t * const e_out = n_out + n_len; if ((err = hal_asn1_encode_integer(key->n, n_out, NULL, der + der_max - n_out)) != HAL_OK || (err = hal_asn1_encode_integer(key->e, e_out, NULL, der + der_max - e_out)) != HAL_OK) return err; } return hal_asn1_encode_spki(hal_asn1_oid_rsaEncryption, hal_asn1_oid_rsaEncryption_len, NULL, 0, der, hlen + vlen, der, der_len, der_max); } size_t hal_rsa_public_key_to_der_len(const hal_rsa_key_t * const key) { size_t len = 0; return hal_rsa_public_key_to_der(key, NULL, &len, 0) == HAL_OK ? len : 0; } hal_error_t hal_rsa_public_key_from_der(hal_rsa_key_t **key_, void *keybuf, const size_t keybuf_len, const uint8_t * const der, const size_t der_len) { hal_rsa_key_t *key = keybuf; if (key_ == NULL || key == NULL || keybuf_len < sizeof(*key) || der == NULL) return HAL_ERROR_BAD_ARGUMENTS; memset(keybuf, 0, keybuf_len); key->type = HAL_KEY_TYPE_RSA_PUBLIC; const uint8_t *alg_oid = NULL, *null = NULL, *pubkey = NULL; size_t alg_oid_len, null_len, pubkey_len; hal_error_t err; if ((err = hal_asn1_decode_spki(&alg_oid, &alg_oid_len, &null, &null_len, &pubkey, &pubkey_len, der, der_len)) != HAL_OK) return err; if (null != NULL || null_len != 0 || alg_oid == NULL || alg_oid_len != hal_asn1_oid_rsaEncryption_len || memcmp(alg_oid, hal_asn1_oid_rsaEncryption, alg_oid_len) != 0) return HAL_ERROR_ASN1_PARSE_FAILED; size_t len, hlen, vlen; if ((err = hal_asn1_decode_header(ASN1_SEQUENCE, pubkey, pubkey_len, &hlen, &vlen)) != HAL_OK) return err; const uint8_t * const pubkey_end = pubkey + hlen + vlen; const uint8_t *d = pubkey + hlen; if ((err = hal_asn1_decode_integer(key->n, d, &len, pubkey_end - d)) != HAL_OK) return err; d += len; if ((err = hal_asn1_decode_integer(key->e, d, &len, pubkey_end - d)) != HAL_OK) return err; d += len; if (d != pubkey_end) return HAL_ERROR_ASN1_PARSE_FAILED; *key_ = key; return HAL_OK; } /* * Local variables: * indent-tabs-mode: nil * End: */