/* * 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) 2015-2018, 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 /* * How big to make the blinding factors cache. * Zero disables the cache entirely. */ #ifndef HAL_RSA_BLINDING_CACHE_SIZE #define HAL_RSA_BLINDING_CACHE_SIZE 2 #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; } #if HAL_RSA_BLINDING_CACHE_SIZE > 0 typedef struct { unsigned lru; fp_int n[1], bf[1], ubf[1]; } bfc_slot_t; static struct { unsigned lru; bfc_slot_t slot[HAL_RSA_BLINDING_CACHE_SIZE]; } bfc; #endif /* * 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. */ static hal_error_t create_blinding_factors(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; hal_rsa_bf_lock(); #if HAL_RSA_BLINDING_CACHE_SIZE > 0 unsigned best_delta = 0; int best_index = 0; for (int i = 0; i < HAL_RSA_BLINDING_CACHE_SIZE; i++) { bfc_slot_t *b = &bfc.slot[i]; const unsigned delta = bfc.lru - b->lru; if (delta > best_delta) { best_delta = delta; best_index = i; } if (fp_cmp_mag(b->n, key->n) == FP_EQ) { if (fp_sqrmod(b->bf, key->n, b->bf) != FP_OKAY || fp_sqrmod(b->ubf, key->n, b->ubf) != FP_OKAY) continue; /* should never happen, but be safe */ fp_copy(b->bf, bf); fp_copy(b->ubf, ubf); err = HAL_OK; goto fail; } } #endif 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(NULL, 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)); #if HAL_RSA_BLINDING_CACHE_SIZE > 0 { bfc_slot_t *b = &bfc.slot[best_index]; fp_copy(key->n, b->n); fp_copy(bf, b->bf); fp_copy(ubf, b->ubf); b->lru = ++bfc.lru; } #endif fail: hal_rsa_bf_unlock(); 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(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: */ 1150' href='#n1150'>1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810