/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) * All rights reserved. * * This package is an SSL implementation written * by Eric Young (eay@cryptsoft.com). * The implementation was written so as to conform with Netscapes SSL. * * This library is free for commercial and non-commercial use as long as * the following conditions are aheared to. The following conditions * apply to all code found in this distribution, be it the RC4, RSA, * lhash, DES, etc., code; not just the SSL code. The SSL documentation * included with this distribution is covered by the same copyright terms * except that the holder is Tim Hudson (tjh@cryptsoft.com). * * Copyright remains Eric Young's, and as such any Copyright notices in * the code are not to be removed. * If this package is used in a product, Eric Young should be given attribution * as the author of the parts of the library used. * This can be in the form of a textual message at program startup or * in documentation (online or textual) provided with the package. * * 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 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. * 3. All advertising materials mentioning features or use of this software * must display the following acknowledgement: * "This product includes cryptographic software written by * Eric Young (eay@cryptsoft.com)" * The word 'cryptographic' can be left out if the rouines from the library * being used are not cryptographic related :-). * 4. If you include any Windows specific code (or a derivative thereof) from * the apps directory (application code) you must include an acknowledgement: * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" * * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``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 AUTHOR 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. * * The licence and distribution terms for any publically available version or * derivative of this code cannot be changed. i.e. this code cannot simply be * copied and put under another distribution licence * [including the GNU Public Licence.] */ #include #include #include #include #include #include #include #include #include #include "internal.h" #include "../bn/internal.h" #include "../../internal.h" #include "../delocate.h" static int check_modulus_and_exponent_sizes(const RSA *rsa) { unsigned rsa_bits = BN_num_bits(rsa->n); if (rsa_bits > 16 * 1024) { OPENSSL_PUT_ERROR(RSA, RSA_R_MODULUS_TOO_LARGE); return 0; } // Mitigate DoS attacks by limiting the exponent size. 33 bits was chosen as // the limit based on the recommendations in [1] and [2]. Windows CryptoAPI // doesn't support values larger than 32 bits [3], so it is unlikely that // exponents larger than 32 bits are being used for anything Windows commonly // does. // // [1] https://www.imperialviolet.org/2012/03/16/rsae.html // [2] https://www.imperialviolet.org/2012/03/17/rsados.html // [3] https://msdn.microsoft.com/en-us/library/aa387685(VS.85).aspx static const unsigned kMaxExponentBits = 33; if (BN_num_bits(rsa->e) > kMaxExponentBits) { OPENSSL_PUT_ERROR(RSA, RSA_R_BAD_E_VALUE); return 0; } // Verify |n > e|. Comparing |rsa_bits| to |kMaxExponentBits| is a small // shortcut to comparing |n| and |e| directly. In reality, |kMaxExponentBits| // is much smaller than the minimum RSA key size that any application should // accept. if (rsa_bits <= kMaxExponentBits) { OPENSSL_PUT_ERROR(RSA, RSA_R_KEY_SIZE_TOO_SMALL); return 0; } assert(BN_ucmp(rsa->n, rsa->e) > 0); return 1; } static int ensure_fixed_copy(BIGNUM **out, const BIGNUM *in, int width) { if (*out != NULL) { return 1; } BIGNUM *copy = BN_dup(in); if (copy == NULL || !bn_resize_words(copy, width)) { BN_free(copy); return 0; } *out = copy; CONSTTIME_SECRET(copy->d, sizeof(BN_ULONG) * width); return 1; } // freeze_private_key finishes initializing |rsa|'s private key components. // After this function has returned, |rsa| may not be changed. This is needed // because |RSA| is a public struct and, additionally, OpenSSL 1.1.0 opaquified // it wrong (see https://github.com/openssl/openssl/issues/5158). static int freeze_private_key(RSA *rsa, BN_CTX *ctx) { CRYPTO_MUTEX_lock_read(&rsa->lock); int frozen = rsa->private_key_frozen; CRYPTO_MUTEX_unlock_read(&rsa->lock); if (frozen) { return 1; } int ret = 0; CRYPTO_MUTEX_lock_write(&rsa->lock); if (rsa->private_key_frozen) { ret = 1; goto err; } // Pre-compute various intermediate values, as well as copies of private // exponents with correct widths. Note that other threads may concurrently // read from |rsa->n|, |rsa->e|, etc., so any fixes must be in separate // copies. We use |mont_n->N|, |mont_p->N|, and |mont_q->N| as copies of |n|, // |p|, and |q| with the correct minimal widths. if (rsa->mont_n == NULL) { rsa->mont_n = BN_MONT_CTX_new_for_modulus(rsa->n, ctx); if (rsa->mont_n == NULL) { goto err; } } const BIGNUM *n_fixed = &rsa->mont_n->N; // The only public upper-bound of |rsa->d| is the bit length of |rsa->n|. The // ASN.1 serialization of RSA private keys unfortunately leaks the byte length // of |rsa->d|, but normalize it so we only leak it once, rather than per // operation. if (rsa->d != NULL && !ensure_fixed_copy(&rsa->d_fixed, rsa->d, n_fixed->width)) { goto err; } if (rsa->p != NULL && rsa->q != NULL) { // TODO: p and q are also CONSTTIME_SECRET but not yet marked as such // because the Montgomery code does things like test whether or not values // are zero. So the secret marking probably needs to happen inside that // code. if (rsa->mont_p == NULL) { rsa->mont_p = BN_MONT_CTX_new_consttime(rsa->p, ctx); if (rsa->mont_p == NULL) { goto err; } } const BIGNUM *p_fixed = &rsa->mont_p->N; if (rsa->mont_q == NULL) { rsa->mont_q = BN_MONT_CTX_new_consttime(rsa->q, ctx); if (rsa->mont_q == NULL) { goto err; } } const BIGNUM *q_fixed = &rsa->mont_q->N; if (rsa->dmp1 != NULL && rsa->dmq1 != NULL) { // Key generation relies on this function to compute |iqmp|. if (rsa->iqmp == NULL) { BIGNUM *iqmp = BN_new(); if (iqmp == NULL || !bn_mod_inverse_secret_prime(iqmp, rsa->q, rsa->p, ctx, rsa->mont_p)) { BN_free(iqmp); goto err; } rsa->iqmp = iqmp; } // CRT components are only publicly bounded by their corresponding // moduli's bit lengths. |rsa->iqmp| is unused outside of this one-time // setup, so we do not compute a fixed-width version of it. if (!ensure_fixed_copy(&rsa->dmp1_fixed, rsa->dmp1, p_fixed->width) || !ensure_fixed_copy(&rsa->dmq1_fixed, rsa->dmq1, q_fixed->width)) { goto err; } // Compute |inv_small_mod_large_mont|. Note that it is always modulo the // larger prime, independent of what is stored in |rsa->iqmp|. if (rsa->inv_small_mod_large_mont == NULL) { BIGNUM *inv_small_mod_large_mont = BN_new(); int ok; if (BN_cmp(rsa->p, rsa->q) < 0) { ok = inv_small_mod_large_mont != NULL && bn_mod_inverse_secret_prime(inv_small_mod_large_mont, rsa->p, rsa->q, ctx, rsa->mont_q) && BN_to_montgomery(inv_small_mod_large_mont, inv_small_mod_large_mont, rsa->mont_q, ctx); } else { ok = inv_small_mod_large_mont != NULL && BN_to_montgomery(inv_small_mod_large_mont, rsa->iqmp, rsa->mont_p, ctx); } if (!ok) { BN_free(inv_small_mod_large_mont); goto err; } rsa->inv_small_mod_large_mont = inv_small_mod_large_mont; CONSTTIME_SECRET( rsa->inv_small_mod_large_mont->d, sizeof(BN_ULONG) * rsa->inv_small_mod_large_mont->width); } } } rsa->private_key_frozen = 1; ret = 1; err: CRYPTO_MUTEX_unlock_write(&rsa->lock); return ret; } size_t rsa_default_size(const RSA *rsa) { return BN_num_bytes(rsa->n); } int RSA_encrypt(RSA *rsa, size_t *out_len, uint8_t *out, size_t max_out, const uint8_t *in, size_t in_len, int padding) { if (rsa->n == NULL || rsa->e == NULL) { OPENSSL_PUT_ERROR(RSA, RSA_R_VALUE_MISSING); return 0; } const unsigned rsa_size = RSA_size(rsa); BIGNUM *f, *result; uint8_t *buf = NULL; BN_CTX *ctx = NULL; int i, ret = 0; if (max_out < rsa_size) { OPENSSL_PUT_ERROR(RSA, RSA_R_OUTPUT_BUFFER_TOO_SMALL); return 0; } if (!check_modulus_and_exponent_sizes(rsa)) { return 0; } ctx = BN_CTX_new(); if (ctx == NULL) { goto err; } BN_CTX_start(ctx); f = BN_CTX_get(ctx); result = BN_CTX_get(ctx); buf = OPENSSL_malloc(rsa_size); if (!f || !result || !buf) { OPENSSL_PUT_ERROR(RSA, ERR_R_MALLOC_FAILURE); goto err; } switch (padding) { case RSA_PKCS1_PADDING: i = RSA_padding_add_PKCS1_type_2(buf, rsa_size, in, in_len); break; case RSA_PKCS1_OAEP_PADDING: // Use the default parameters: SHA-1 for both hashes and no label. i = RSA_padding_add_PKCS1_OAEP_mgf1(buf, rsa_size, in, in_len, NULL, 0, NULL, NULL); break; case RSA_NO_PADDING: i = RSA_padding_add_none(buf, rsa_size, in, in_len); break; default: OPENSSL_PUT_ERROR(RSA, RSA_R_UNKNOWN_PADDING_TYPE); goto err; } if (i <= 0) { goto err; } if (BN_bin2bn(buf, rsa_size, f) == NULL) { goto err; } if (BN_ucmp(f, rsa->n) >= 0) { // usually the padding functions would catch this OPENSSL_PUT_ERROR(RSA, RSA_R_DATA_TOO_LARGE_FOR_MODULUS); goto err; } if (!BN_MONT_CTX_set_locked(&rsa->mont_n, &rsa->lock, rsa->n, ctx) || !BN_mod_exp_mont(result, f, rsa->e, &rsa->mont_n->N, ctx, rsa->mont_n)) { goto err; } // put in leading 0 bytes if the number is less than the length of the // modulus if (!BN_bn2bin_padded(out, rsa_size, result)) { OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR); goto err; } *out_len = rsa_size; ret = 1; err: if (ctx != NULL) { BN_CTX_end(ctx); BN_CTX_free(ctx); } OPENSSL_free(buf); return ret; } // MAX_BLINDINGS_PER_RSA defines the maximum number of cached BN_BLINDINGs per // RSA*. Then this limit is exceeded, BN_BLINDING objects will be created and // destroyed as needed. #define MAX_BLINDINGS_PER_RSA 1024 // rsa_blinding_get returns a BN_BLINDING to use with |rsa|. It does this by // allocating one of the cached BN_BLINDING objects in |rsa->blindings|. If // none are free, the cache will be extended by a extra element and the new // BN_BLINDING is returned. // // On success, the index of the assigned BN_BLINDING is written to // |*index_used| and must be passed to |rsa_blinding_release| when finished. static BN_BLINDING *rsa_blinding_get(RSA *rsa, unsigned *index_used, BN_CTX *ctx) { assert(ctx != NULL); assert(rsa->mont_n != NULL); BN_BLINDING *ret = NULL; BN_BLINDING **new_blindings; uint8_t *new_blindings_inuse; char overflow = 0; CRYPTO_MUTEX_lock_write(&rsa->lock); unsigned i; for (i = 0; i < rsa->num_blindings; i++) { if (rsa->blindings_inuse[i] == 0) { rsa->blindings_inuse[i] = 1; ret = rsa->blindings[i]; *index_used = i; break; } } if (ret != NULL) { CRYPTO_MUTEX_unlock_write(&rsa->lock); return ret; } overflow = rsa->num_blindings >= MAX_BLINDINGS_PER_RSA; // We didn't find a free BN_BLINDING to use so increase the length of // the arrays by one and use the newly created element. CRYPTO_MUTEX_unlock_write(&rsa->lock); ret = BN_BLINDING_new(); if (ret == NULL) { return NULL; } if (overflow) { // We cannot add any more cached BN_BLINDINGs so we use |ret| // and mark it for destruction in |rsa_blinding_release|. *index_used = MAX_BLINDINGS_PER_RSA; return ret; } CRYPTO_MUTEX_lock_write(&rsa->lock); new_blindings = OPENSSL_malloc(sizeof(BN_BLINDING *) * (rsa->num_blindings + 1)); if (new_blindings == NULL) { goto err1; } OPENSSL_memcpy(new_blindings, rsa->blindings, sizeof(BN_BLINDING *) * rsa->num_blindings); new_blindings[rsa->num_blindings] = ret; new_blindings_inuse = OPENSSL_malloc(rsa->num_blindings + 1); if (new_blindings_inuse == NULL) { goto err2; } OPENSSL_memcpy(new_blindings_inuse, rsa->blindings_inuse, rsa->num_blindings); new_blindings_inuse[rsa->num_blindings] = 1; *index_used = rsa->num_blindings; OPENSSL_free(rsa->blindings); rsa->blindings = new_blindings; OPENSSL_free(rsa->blindings_inuse); rsa->blindings_inuse = new_blindings_inuse; rsa->num_blindings++; CRYPTO_MUTEX_unlock_write(&rsa->lock); return ret; err2: OPENSSL_free(new_blindings); err1: CRYPTO_MUTEX_unlock_write(&rsa->lock); BN_BLINDING_free(ret); return NULL; } // rsa_blinding_release marks the cached BN_BLINDING at the given index as free // for other threads to use. static void rsa_blinding_release(RSA *rsa, BN_BLINDING *blinding, unsigned blinding_index) { if (blinding_index == MAX_BLINDINGS_PER_RSA) { // This blinding wasn't cached. BN_BLINDING_free(blinding); return; } CRYPTO_MUTEX_lock_write(&rsa->lock); rsa->blindings_inuse[blinding_index] = 0; CRYPTO_MUTEX_unlock_write(&rsa->lock); } // signing int rsa_default_sign_raw(RSA *rsa, size_t *out_len, uint8_t *out, size_t max_out, const uint8_t *in, size_t in_len, int padding) { const unsigned rsa_size = RSA_size(rsa); uint8_t *buf = NULL; int i, ret = 0; if (max_out < rsa_size) { OPENSSL_PUT_ERROR(RSA, RSA_R_OUTPUT_BUFFER_TOO_SMALL); return 0; } buf = OPENSSL_malloc(rsa_size); if (buf == NULL) { OPENSSL_PUT_ERROR(RSA, ERR_R_MALLOC_FAILURE); goto err; } switch (padding) { case RSA_PKCS1_PADDING: i = RSA_padding_add_PKCS1_type_1(buf, rsa_size, in, in_len); break; case RSA_NO_PADDING: i = RSA_padding_add_none(buf, rsa_size, in, in_len); break; default: OPENSSL_PUT_ERROR(RSA, RSA_R_UNKNOWN_PADDING_TYPE); goto err; } if (i <= 0) { goto err; } if (!RSA_private_transform(rsa, out, buf, rsa_size)) { goto err; } CONSTTIME_DECLASSIFY(out, rsa_size); *out_len = rsa_size; ret = 1; err: OPENSSL_free(buf); return ret; } int rsa_default_decrypt(RSA *rsa, size_t *out_len, uint8_t *out, size_t max_out, const uint8_t *in, size_t in_len, int padding) { const unsigned rsa_size = RSA_size(rsa); uint8_t *buf = NULL; int ret = 0; if (max_out < rsa_size) { OPENSSL_PUT_ERROR(RSA, RSA_R_OUTPUT_BUFFER_TOO_SMALL); return 0; } if (padding == RSA_NO_PADDING) { buf = out; } else { // Allocate a temporary buffer to hold the padded plaintext. buf = OPENSSL_malloc(rsa_size); if (buf == NULL) { OPENSSL_PUT_ERROR(RSA, ERR_R_MALLOC_FAILURE); goto err; } } if (in_len != rsa_size) { OPENSSL_PUT_ERROR(RSA, RSA_R_DATA_LEN_NOT_EQUAL_TO_MOD_LEN); goto err; } if (!RSA_private_transform(rsa, buf, in, rsa_size)) { goto err; } switch (padding) { case RSA_PKCS1_PADDING: ret = RSA_padding_check_PKCS1_type_2(out, out_len, rsa_size, buf, rsa_size); break; case RSA_PKCS1_OAEP_PADDING: // Use the default parameters: SHA-1 for both hashes and no label. ret = RSA_padding_check_PKCS1_OAEP_mgf1(out, out_len, rsa_size, buf, rsa_size, NULL, 0, NULL, NULL); break; case RSA_NO_PADDING: *out_len = rsa_size; ret = 1; break; default: OPENSSL_PUT_ERROR(RSA, RSA_R_UNKNOWN_PADDING_TYPE); goto err; } CONSTTIME_DECLASSIFY(&ret, sizeof(ret)); if (!ret) { OPENSSL_PUT_ERROR(RSA, RSA_R_PADDING_CHECK_FAILED); } else { CONSTTIME_DECLASSIFY(out, out_len); } err: if (padding != RSA_NO_PADDING) { OPENSSL_free(buf); } return ret; } static int mod_exp(BIGNUM *r0, const BIGNUM *I, RSA *rsa, BN_CTX *ctx); int RSA_verify_raw(RSA *rsa, size_t *out_len, uint8_t *out, size_t max_out, const uint8_t *in, size_t in_len, int padding) { if (rsa->n == NULL || rsa->e == NULL) { OPENSSL_PUT_ERROR(RSA, RSA_R_VALUE_MISSING); return 0; } const unsigned rsa_size = RSA_size(rsa); BIGNUM *f, *result; if (max_out < rsa_size) { OPENSSL_PUT_ERROR(RSA, RSA_R_OUTPUT_BUFFER_TOO_SMALL); return 0; } if (in_len != rsa_size) { OPENSSL_PUT_ERROR(RSA, RSA_R_DATA_LEN_NOT_EQUAL_TO_MOD_LEN); return 0; } if (!check_modulus_and_exponent_sizes(rsa)) { return 0; } BN_CTX *ctx = BN_CTX_new(); if (ctx == NULL) { return 0; } int ret = 0; uint8_t *buf = NULL; BN_CTX_start(ctx); f = BN_CTX_get(ctx); result = BN_CTX_get(ctx); if (f == NULL || result == NULL) { OPENSSL_PUT_ERROR(RSA, ERR_R_MALLOC_FAILURE); goto err; } if (padding == RSA_NO_PADDING) { buf = out; } else { // Allocate a temporary buffer to hold the padded plaintext. buf = OPENSSL_malloc(rsa_size); if (buf == NULL) { OPENSSL_PUT_ERROR(RSA, ERR_R_MALLOC_FAILURE); goto err; } } if (BN_bin2bn(in, in_len, f) == NULL) { goto err; } if (BN_ucmp(f, rsa->n) >= 0) { OPENSSL_PUT_ERROR(RSA, RSA_R_DATA_TOO_LARGE_FOR_MODULUS); goto err; } if (!BN_MONT_CTX_set_locked(&rsa->mont_n, &rsa->lock, rsa->n, ctx) || !BN_mod_exp_mont(result, f, rsa->e, &rsa->mont_n->N, ctx, rsa->mont_n)) { goto err; } if (!BN_bn2bin_padded(buf, rsa_size, result)) { OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR); goto err; } switch (padding) { case RSA_PKCS1_PADDING: ret = RSA_padding_check_PKCS1_type_1(out, out_len, rsa_size, buf, rsa_size); break; case RSA_NO_PADDING: ret = 1; *out_len = rsa_size; break; default: OPENSSL_PUT_ERROR(RSA, RSA_R_UNKNOWN_PADDING_TYPE); goto err; } if (!ret) { OPENSSL_PUT_ERROR(RSA, RSA_R_PADDING_CHECK_FAILED); goto err; } err: BN_CTX_end(ctx); BN_CTX_free(ctx); if (buf != out) { OPENSSL_free(buf); } return ret; } int rsa_default_private_transform(RSA *rsa, uint8_t *out, const uint8_t *in, size_t len) { if (rsa->n == NULL || rsa->d == NULL) { OPENSSL_PUT_ERROR(RSA, RSA_R_VALUE_MISSING); return 0; } BIGNUM *f, *result; BN_CTX *ctx = NULL; unsigned blinding_index = 0; BN_BLINDING *blinding = NULL; int ret = 0; ctx = BN_CTX_new(); if (ctx == NULL) { goto err; } BN_CTX_start(ctx); f = BN_CTX_get(ctx); result = BN_CTX_get(ctx); if (f == NULL || result == NULL) { OPENSSL_PUT_ERROR(RSA, ERR_R_MALLOC_FAILURE); goto err; } if (BN_bin2bn(in, len, f) == NULL) { goto err; } if (BN_ucmp(f, rsa->n) >= 0) { // Usually the padding functions would catch this. OPENSSL_PUT_ERROR(RSA, RSA_R_DATA_TOO_LARGE_FOR_MODULUS); goto err; } if (!freeze_private_key(rsa, ctx)) { OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR); goto err; } const int do_blinding = (rsa->flags & RSA_FLAG_NO_BLINDING) == 0; if (rsa->e == NULL && do_blinding) { // We cannot do blinding or verification without |e|, and continuing without // those countermeasures is dangerous. However, the Java/Android RSA API // requires support for keys where only |d| and |n| (and not |e|) are known. // The callers that require that bad behavior set |RSA_FLAG_NO_BLINDING|. OPENSSL_PUT_ERROR(RSA, RSA_R_NO_PUBLIC_EXPONENT); goto err; } if (do_blinding) { blinding = rsa_blinding_get(rsa, &blinding_index, ctx); if (blinding == NULL) { OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR); goto err; } if (!BN_BLINDING_convert(f, blinding, rsa->e, rsa->mont_n, ctx)) { goto err; } } if (rsa->p != NULL && rsa->q != NULL && rsa->e != NULL && rsa->dmp1 != NULL && rsa->dmq1 != NULL && rsa->iqmp != NULL && // Require that we can reduce |f| by |rsa->p| and |rsa->q| in constant // time, which requires primes be the same size, rounded to the Montgomery // coefficient. (See |mod_montgomery|.) This is not required by RFC 8017, // but it is true for keys generated by us and all common implementations. bn_less_than_montgomery_R(rsa->q, rsa->mont_p) && bn_less_than_montgomery_R(rsa->p, rsa->mont_q)) { if (!mod_exp(result, f, rsa, ctx)) { goto err; } } else if (!BN_mod_exp_mont_consttime(result, f, rsa->d_fixed, rsa->n, ctx, rsa->mont_n)) { goto err; } // Verify the result to protect against fault attacks as described in the // 1997 paper "On the Importance of Checking Cryptographic Protocols for // Faults" by Dan Boneh, Richard A. DeMillo, and Richard J. Lipton. Some // implementations do this only when the CRT is used, but we do it in all // cases. Section 6 of the aforementioned paper describes an attack that // works when the CRT isn't used. That attack is much less likely to succeed // than the CRT attack, but there have likely been improvements since 1997. // // This check is cheap assuming |e| is small; it almost always is. if (rsa->e != NULL) { BIGNUM *vrfy = BN_CTX_get(ctx); if (vrfy == NULL || !BN_mod_exp_mont(vrfy, result, rsa->e, rsa->n, ctx, rsa->mont_n) || !BN_equal_consttime(vrfy, f)) { OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR); goto err; } } if (do_blinding && !BN_BLINDING_invert(result, blinding, rsa->mont_n, ctx)) { goto err; } // The computation should have left |result| as a maximally-wide number, so // that it and serializing does not leak information about the magnitude of // the result. // // See Falko Strenzke, "Manger's Attack revisited", ICICS 2010. assert(result->width == rsa->mont_n->N.width); if (!BN_bn2bin_padded(out, len, result)) { OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR); goto err; } ret = 1; err: if (ctx != NULL) { BN_CTX_end(ctx); BN_CTX_free(ctx); } if (blinding != NULL) { rsa_blinding_release(rsa, blinding, blinding_index); } return ret; } // mod_montgomery sets |r| to |I| mod |p|. |I| must already be fully reduced // modulo |p| times |q|. It returns one on success and zero on error. static int mod_montgomery(BIGNUM *r, const BIGNUM *I, const BIGNUM *p, const BN_MONT_CTX *mont_p, const BIGNUM *q, BN_CTX *ctx) { // Reducing in constant-time with Montgomery reduction requires I <= p * R. We // have I < p * q, so this follows if q < R. The caller should have checked // this already. if (!bn_less_than_montgomery_R(q, mont_p)) { OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR); return 0; } if (// Reduce mod p with Montgomery reduction. This computes I * R^-1 mod p. !BN_from_montgomery(r, I, mont_p, ctx) || // Multiply by R^2 and do another Montgomery reduction to compute // I * R^-1 * R^2 * R^-1 = I mod p. !BN_to_montgomery(r, r, mont_p, ctx)) { return 0; } // By precomputing R^3 mod p (normally |BN_MONT_CTX| only uses R^2 mod p) and // adjusting the API for |BN_mod_exp_mont_consttime|, we could instead compute // I * R mod p here and save a reduction per prime. But this would require // changing the RSAZ code and may not be worth it. Note that the RSAZ code // uses a different radix, so it uses R' = 2^1044. There we'd actually want // R^2 * R', and would futher benefit from a precomputed R'^2. It currently // converts |mont_p->RR| to R'^2. return 1; } static int mod_exp(BIGNUM *r0, const BIGNUM *I, RSA *rsa, BN_CTX *ctx) { assert(ctx != NULL); assert(rsa->n != NULL); assert(rsa->e != NULL); assert(rsa->d != NULL); assert(rsa->p != NULL); assert(rsa->q != NULL); assert(rsa->dmp1 != NULL); assert(rsa->dmq1 != NULL); assert(rsa->iqmp != NULL); BIGNUM *r1, *m1; int ret = 0; BN_CTX_start(ctx); r1 = BN_CTX_get(ctx); m1 = BN_CTX_get(ctx); if (r1 == NULL || m1 == NULL) { goto err; } if (!freeze_private_key(rsa, ctx)) { goto err; } // Implementing RSA with CRT in constant-time is sensitive to which prime is // larger. Canonicalize fields so that |p| is the larger prime. const BIGNUM *dmp1 = rsa->dmp1_fixed, *dmq1 = rsa->dmq1_fixed; const BN_MONT_CTX *mont_p = rsa->mont_p, *mont_q = rsa->mont_q; if (BN_cmp(rsa->p, rsa->q) < 0) { mont_p = rsa->mont_q; mont_q = rsa->mont_p; dmp1 = rsa->dmq1_fixed; dmq1 = rsa->dmp1_fixed; } // Use the minimal-width versions of |n|, |p|, and |q|. Either works, but if // someone gives us non-minimal values, these will be slightly more efficient // on the non-Montgomery operations. const BIGNUM *n = &rsa->mont_n->N; const BIGNUM *p = &mont_p->N; const BIGNUM *q = &mont_q->N; // This is a pre-condition for |mod_montgomery|. It was already checked by the // caller. assert(BN_ucmp(I, n) < 0); if (// |m1| is the result modulo |q|. !mod_montgomery(r1, I, q, mont_q, p, ctx) || !BN_mod_exp_mont_consttime(m1, r1, dmq1, q, ctx, mont_q) || // |r0| is the result modulo |p|. !mod_montgomery(r1, I, p, mont_p, q, ctx) || !BN_mod_exp_mont_consttime(r0, r1, dmp1, p, ctx, mont_p) || // Compute r0 = r0 - m1 mod p. |p| is the larger prime, so |m1| is already // fully reduced mod |p|. !bn_mod_sub_consttime(r0, r0, m1, p, ctx) || // r0 = r0 * iqmp mod p. We use Montgomery multiplication to compute this // in constant time. |inv_small_mod_large_mont| is in Montgomery form and // r0 is not, so the result is taken out of Montgomery form. !BN_mod_mul_montgomery(r0, r0, rsa->inv_small_mod_large_mont, mont_p, ctx) || // r0 = r0 * q + m1 gives the final result. Reducing modulo q gives m1, so // it is correct mod p. Reducing modulo p gives (r0-m1)*iqmp*q + m1 = r0, // so it is correct mod q. Finally, the result is bounded by [m1, n + m1), // and the result is at least |m1|, so this must be the unique answer in // [0, n). !bn_mul_consttime(r0, r0, q, ctx) || !bn_uadd_consttime(r0, r0, m1) || // The result should be bounded by |n|, but fixed-width operations may // bound the width slightly higher, so fix it. !bn_resize_words(r0, n->width)) { goto err; } ret = 1; err: BN_CTX_end(ctx); return ret; } static int ensure_bignum(BIGNUM **out) { if (*out == NULL) { *out = BN_new(); } return *out != NULL; } // kBoringSSLRSASqrtTwo is the BIGNUM representation of ⌊2¹⁵³⁵×√2⌋. This is // chosen to give enough precision for 3072-bit RSA, the largest key size FIPS // specifies. Key sizes beyond this will round up. // // To verify this number, check that n² < 2³⁰⁷¹ < (n+1)², where n is value // represented here. Note the components are listed in little-endian order. Here // is some sample Python code to check: // // >>> TOBN = lambda a, b: a << 32 | b // >>> l = [ ] // >>> n = sum(a * 2**(64*i) for i, a in enumerate(l)) // >>> n**2 < 2**3071 < (n+1)**2 // True const BN_ULONG kBoringSSLRSASqrtTwo[] = { TOBN(0xdea06241, 0xf7aa81c2), TOBN(0xf6a1be3f, 0xca221307), TOBN(0x332a5e9f, 0x7bda1ebf), TOBN(0x0104dc01, 0xfe32352f), TOBN(0xb8cf341b, 0x6f8236c7), TOBN(0x4264dabc, 0xd528b651), TOBN(0xf4d3a02c, 0xebc93e0c), TOBN(0x81394ab6, 0xd8fd0efd), TOBN(0xeaa4a089, 0x9040ca4a), TOBN(0xf52f120f, 0x836e582e), TOBN(0xcb2a6343, 0x31f3c84d), TOBN(0xc6d5a8a3, 0x8bb7e9dc), TOBN(0x460abc72, 0x2f7c4e33), TOBN(0xcab1bc91, 0x1688458a), TOBN(0x53059c60, 0x11bc337b), TOBN(0xd2202e87, 0x42af1f4e), TOBN(0x78048736, 0x3dfa2768), TOBN(0x0f74a85e, 0x439c7b4a), TOBN(0xa8b1fe6f, 0xdc83db39), TOBN(0x4afc8304, 0x3ab8a2c3), TOBN(0xed17ac85, 0x83339915), TOBN(0x1d6f60ba, 0x893ba84c), TOBN(0x597d89b3, 0x754abe9f), TOBN(0xb504f333, 0xf9de6484), }; const size_t kBoringSSLRSASqrtTwoLen = OPENSSL_ARRAY_SIZE(kBoringSSLRSASqrtTwo); // generate_prime sets |out| to a prime with length |bits| such that |out|-1 is // relatively prime to |e|. If |p| is non-NULL, |out| will also not be close to // |p|. |sqrt2| must be ⌊2^(bits-1)×√2⌋ (or a slightly overestimate for large // sizes), and |pow2_bits_100| must be 2^(bits-100). // // This function fails with probability around 2^-21. static int generate_prime(BIGNUM *out, int bits, const BIGNUM *e, const BIGNUM *p, const BIGNUM *sqrt2, const BIGNUM *pow2_bits_100, BN_CTX *ctx, BN_GENCB *cb) { if (bits < 128 || (bits % BN_BITS2) != 0) { OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR); return 0; } assert(BN_is_pow2(pow2_bits_100)); assert(BN_is_bit_set(pow2_bits_100, bits - 100)); // See FIPS 186-4 appendix B.3.3, steps 4 and 5. Note |bits| here is nlen/2. // Use the limit from steps 4.7 and 5.8 for most values of |e|. When |e| is 3, // the 186-4 limit is too low, so we use a higher one. Note this case is not // reachable from |RSA_generate_key_fips|. // // |limit| determines the failure probability. We must find a prime that is // not 1 mod |e|. By the prime number theorem, we'll find one with probability // p = (e-1)/e * 2/(ln(2)*bits). Note the second term is doubled because we // discard even numbers. // // The failure probability is thus (1-p)^limit. To convert that to a power of // two, we take logs. -log_2((1-p)^limit) = -limit * ln(1-p) / ln(2). // // >>> def f(bits, e, limit): // ... p = (e-1.0)/e * 2.0/(math.log(2)*bits) // ... return -limit * math.log(1 - p) / math.log(2) // ... // >>> f(1024, 65537, 5*1024) // 20.842750558272634 // >>> f(1536, 65537, 5*1536) // 20.83294549602474 // >>> f(2048, 65537, 5*2048) // 20.828047576234948 // >>> f(1024, 3, 8*1024) // 22.222147925962307 // >>> f(1536, 3, 8*1536) // 22.21518251065506 // >>> f(2048, 3, 8*2048) // 22.211701985875937 if (bits >= INT_MAX/32) { OPENSSL_PUT_ERROR(RSA, RSA_R_MODULUS_TOO_LARGE); return 0; } int limit = BN_is_word(e, 3) ? bits * 8 : bits * 5; int ret = 0, tries = 0, rand_tries = 0; BN_CTX_start(ctx); BIGNUM *tmp = BN_CTX_get(ctx); if (tmp == NULL) { goto err; } for (;;) { // Generate a random number of length |bits| where the bottom bit is set // (steps 4.2, 4.3, 5.2 and 5.3) and the top bit is set (implied by the // bound checked below in steps 4.4 and 5.5). if (!BN_rand(out, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD) || !BN_GENCB_call(cb, BN_GENCB_GENERATED, rand_tries++)) { goto err; } if (p != NULL) { // If |p| and |out| are too close, try again (step 5.4). if (!bn_abs_sub_consttime(tmp, out, p, ctx)) { goto err; } if (BN_cmp(tmp, pow2_bits_100) <= 0) { continue; } } // If out < 2^(bits-1)×√2, try again (steps 4.4 and 5.5). This is equivalent // to out <= ⌊2^(bits-1)×√2⌋, or out <= sqrt2 for FIPS key sizes. // // For larger keys, the comparison is approximate, leaning towards // retrying. That is, we reject a negligible fraction of primes that are // within the FIPS bound, but we will never accept a prime outside the // bound, ensuring the resulting RSA key is the right size. if (BN_cmp(out, sqrt2) <= 0) { continue; } // RSA key generation's bottleneck is discarding composites. If it fails // trial division, do not bother computing a GCD or performing Rabin-Miller. if (!bn_odd_number_is_obviously_composite(out)) { // Check gcd(out-1, e) is one (steps 4.5 and 5.6). int relatively_prime; if (!BN_sub(tmp, out, BN_value_one()) || !bn_is_relatively_prime(&relatively_prime, tmp, e, ctx)) { goto err; } if (relatively_prime) { // Test |out| for primality (steps 4.5.1 and 5.6.1). int is_probable_prime; if (!BN_primality_test(&is_probable_prime, out, BN_prime_checks, ctx, 0, cb)) { goto err; } if (is_probable_prime) { ret = 1; goto err; } } } // If we've tried too many times to find a prime, abort (steps 4.7 and // 5.8). tries++; if (tries >= limit) { OPENSSL_PUT_ERROR(RSA, RSA_R_TOO_MANY_ITERATIONS); goto err; } if (!BN_GENCB_call(cb, 2, tries)) { goto err; } } err: BN_CTX_end(ctx); return ret; } // rsa_generate_key_impl generates an RSA key using a generalized version of // FIPS 186-4 appendix B.3. |RSA_generate_key_fips| performs additional checks // for FIPS-compliant key generation. // // This function returns one on success and zero on failure. It has a failure // probability of about 2^-20. static int rsa_generate_key_impl(RSA *rsa, int bits, const BIGNUM *e_value, BN_GENCB *cb) { // See FIPS 186-4 appendix B.3. This function implements a generalized version // of the FIPS algorithm. |RSA_generate_key_fips| performs additional checks // for FIPS-compliant key generation. // Always generate RSA keys which are a multiple of 128 bits. Round |bits| // down as needed. bits &= ~127; // Reject excessively small keys. if (bits < 256) { OPENSSL_PUT_ERROR(RSA, RSA_R_KEY_SIZE_TOO_SMALL); return 0; } // Reject excessively large public exponents. Windows CryptoAPI and Go don't // support values larger than 32 bits, so match their limits for generating // keys. (|check_modulus_and_exponent_sizes| uses a slightly more conservative // value, but we don't need to support generating such keys.) // https://github.com/golang/go/issues/3161 // https://msdn.microsoft.com/en-us/library/aa387685(VS.85).aspx if (BN_num_bits(e_value) > 32) { OPENSSL_PUT_ERROR(RSA, RSA_R_BAD_E_VALUE); return 0; } int ret = 0; int prime_bits = bits / 2; BN_CTX *ctx = BN_CTX_new(); if (ctx == NULL) { goto bn_err; } BN_CTX_start(ctx); BIGNUM *totient = BN_CTX_get(ctx); BIGNUM *pm1 = BN_CTX_get(ctx); BIGNUM *qm1 = BN_CTX_get(ctx); BIGNUM *sqrt2 = BN_CTX_get(ctx); BIGNUM *pow2_prime_bits_100 = BN_CTX_get(ctx); BIGNUM *pow2_prime_bits = BN_CTX_get(ctx); if (totient == NULL || pm1 == NULL || qm1 == NULL || sqrt2 == NULL || pow2_prime_bits_100 == NULL || pow2_prime_bits == NULL || !BN_set_bit(pow2_prime_bits_100, prime_bits - 100) || !BN_set_bit(pow2_prime_bits, prime_bits)) { goto bn_err; } // We need the RSA components non-NULL. if (!ensure_bignum(&rsa->n) || !ensure_bignum(&rsa->d) || !ensure_bignum(&rsa->e) || !ensure_bignum(&rsa->p) || !ensure_bignum(&rsa->q) || !ensure_bignum(&rsa->dmp1) || !ensure_bignum(&rsa->dmq1)) { goto bn_err; } if (!BN_copy(rsa->e, e_value)) { goto bn_err; } // Compute sqrt2 >= ⌊2^(prime_bits-1)×√2⌋. if (!bn_set_words(sqrt2, kBoringSSLRSASqrtTwo, kBoringSSLRSASqrtTwoLen)) { goto bn_err; } int sqrt2_bits = kBoringSSLRSASqrtTwoLen * BN_BITS2; assert(sqrt2_bits == (int)BN_num_bits(sqrt2)); if (sqrt2_bits > prime_bits) { // For key sizes up to 3072 (prime_bits = 1536), this is exactly // ⌊2^(prime_bits-1)×√2⌋. if (!BN_rshift(sqrt2, sqrt2, sqrt2_bits - prime_bits)) { goto bn_err; } } else if (prime_bits > sqrt2_bits) { // For key sizes beyond 3072, this is approximate. We err towards retrying // to ensure our key is the right size and round up. if (!BN_add_word(sqrt2, 1) || !BN_lshift(sqrt2, sqrt2, prime_bits - sqrt2_bits)) { goto bn_err; } } assert(prime_bits == (int)BN_num_bits(sqrt2)); do { // Generate p and q, each of size |prime_bits|, using the steps outlined in // appendix FIPS 186-4 appendix B.3.3. // // Each call to |generate_prime| fails with probability p = 2^-21. The // probability that either call fails is 1 - (1-p)^2, which is around 2^-20. if (!generate_prime(rsa->p, prime_bits, rsa->e, NULL, sqrt2, pow2_prime_bits_100, ctx, cb) || !BN_GENCB_call(cb, 3, 0) || !generate_prime(rsa->q, prime_bits, rsa->e, rsa->p, sqrt2, pow2_prime_bits_100, ctx, cb) || !BN_GENCB_call(cb, 3, 1)) { goto bn_err; } if (BN_cmp(rsa->p, rsa->q) < 0) { BIGNUM *tmp = rsa->p; rsa->p = rsa->q; rsa->q = tmp; } // Calculate d = e^(-1) (mod lcm(p-1, q-1)), per FIPS 186-4. This differs // from typical RSA implementations which use (p-1)*(q-1). // // Note this means the size of d might reveal information about p-1 and // q-1. However, we do operations with Chinese Remainder Theorem, so we only // use d (mod p-1) and d (mod q-1) as exponents. Using a minimal totient // does not affect those two values. int no_inverse; if (!bn_usub_consttime(pm1, rsa->p, BN_value_one()) || !bn_usub_consttime(qm1, rsa->q, BN_value_one()) || !bn_lcm_consttime(totient, pm1, qm1, ctx) || !bn_mod_inverse_consttime(rsa->d, &no_inverse, rsa->e, totient, ctx)) { goto bn_err; } // Retry if |rsa->d| <= 2^|prime_bits|. See appendix B.3.1's guidance on // values for d. } while (BN_cmp(rsa->d, pow2_prime_bits) <= 0); if (// Calculate n. !bn_mul_consttime(rsa->n, rsa->p, rsa->q, ctx) || // Calculate d mod (p-1). !bn_div_consttime(NULL, rsa->dmp1, rsa->d, pm1, ctx) || // Calculate d mod (q-1) !bn_div_consttime(NULL, rsa->dmq1, rsa->d, qm1, ctx)) { goto bn_err; } bn_set_minimal_width(rsa->n); // Sanity-check that |rsa->n| has the specified size. This is implied by // |generate_prime|'s bounds. if (BN_num_bits(rsa->n) != (unsigned)bits) { OPENSSL_PUT_ERROR(RSA, ERR_R_INTERNAL_ERROR); goto err; } // Call |freeze_private_key| to compute the inverse of q mod p, by way of // |rsa->mont_p|. if (!freeze_private_key(rsa, ctx)) { goto bn_err; } // The key generation process is complex and thus error-prone. It could be // disastrous to generate and then use a bad key so double-check that the key // makes sense. if (!RSA_check_key(rsa)) { OPENSSL_PUT_ERROR(RSA, RSA_R_INTERNAL_ERROR); goto err; } ret = 1; bn_err: if (!ret) { OPENSSL_PUT_ERROR(RSA, ERR_LIB_BN); } err: if (ctx != NULL) { BN_CTX_end(ctx); BN_CTX_free(ctx); } return ret; } static void replace_bignum(BIGNUM **out, BIGNUM **in) { BN_free(*out); *out = *in; *in = NULL; } static void replace_bn_mont_ctx(BN_MONT_CTX **out, BN_MONT_CTX **in) { BN_MONT_CTX_free(*out); *out = *in; *in = NULL; } int RSA_generate_key_ex(RSA *rsa, int bits, const BIGNUM *e_value, BN_GENCB *cb) { // |rsa_generate_key_impl|'s 2^-20 failure probability is too high at scale, // so we run the FIPS algorithm four times, bringing it down to 2^-80. We // should just adjust the retry limit, but FIPS 186-4 prescribes that value // and thus results in unnecessary complexity. for (int i = 0; i < 4; i++) { ERR_clear_error(); // Generate into scratch space, to avoid leaving partial work on failure. RSA *tmp = RSA_new(); if (tmp == NULL) { return 0; } if (rsa_generate_key_impl(tmp, bits, e_value, cb)) { replace_bignum(&rsa->n, &tmp->n); replace_bignum(&rsa->e, &tmp->e); replace_bignum(&rsa->d, &tmp->d); replace_bignum(&rsa->p, &tmp->p); replace_bignum(&rsa->q, &tmp->q); replace_bignum(&rsa->dmp1, &tmp->dmp1); replace_bignum(&rsa->dmq1, &tmp->dmq1); replace_bignum(&rsa->iqmp, &tmp->iqmp); replace_bn_mont_ctx(&rsa->mont_n, &tmp->mont_n); replace_bn_mont_ctx(&rsa->mont_p, &tmp->mont_p); replace_bn_mont_ctx(&rsa->mont_q, &tmp->mont_q); replace_bignum(&rsa->d_fixed, &tmp->d_fixed); replace_bignum(&rsa->dmp1_fixed, &tmp->dmp1_fixed); replace_bignum(&rsa->dmq1_fixed, &tmp->dmq1_fixed); replace_bignum(&rsa->inv_small_mod_large_mont, &tmp->inv_small_mod_large_mont); rsa->private_key_frozen = tmp->private_key_frozen; RSA_free(tmp); return 1; } uint32_t err = ERR_peek_error(); RSA_free(tmp); tmp = NULL; // Only retry on |RSA_R_TOO_MANY_ITERATIONS|. This is so a caller-induced // failure in |BN_GENCB_call| is still fatal. if (ERR_GET_LIB(err) != ERR_LIB_RSA || ERR_GET_REASON(err) != RSA_R_TOO_MANY_ITERATIONS) { return 0; } } return 0; } int RSA_generate_key_fips(RSA *rsa, int bits, BN_GENCB *cb) { // FIPS 186-4 allows 2048-bit and 3072-bit RSA keys (1024-bit and 1536-bit // primes, respectively) with the prime generation method we use. if (bits != 2048 && bits != 3072) { OPENSSL_PUT_ERROR(RSA, RSA_R_BAD_RSA_PARAMETERS); return 0; } BIGNUM *e = BN_new(); int ret = e != NULL && BN_set_word(e, RSA_F4) && RSA_generate_key_ex(rsa, bits, e, cb) && RSA_check_fips(rsa); BN_free(e); return ret; } DEFINE_METHOD_FUNCTION(RSA_METHOD, RSA_default_method) { // All of the methods are NULL to make it easier for the compiler/linker to // drop unused functions. The wrapper functions will select the appropriate // |rsa_default_*| implementation. OPENSSL_memset(out, 0, sizeof(RSA_METHOD)); out->common.is_static = 1; }