/*
- * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
+ * Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved.
*
* Licensed under the OpenSSL license (the "License"). You may not use
* this file except in compliance with the License. You can obtain a copy
#include <openssl/bn.h>
#include "rsa_locl.h"
-static int rsa_builtin_keygen(RSA *rsa, int bits, BIGNUM *e_value,
+static int rsa_builtin_keygen(RSA *rsa, int bits, int primes, BIGNUM *e_value,
BN_GENCB *cb);
/*
*/
int RSA_generate_key_ex(RSA *rsa, int bits, BIGNUM *e_value, BN_GENCB *cb)
{
- if (rsa->meth->rsa_keygen)
+ if (rsa->meth->rsa_keygen != NULL)
return rsa->meth->rsa_keygen(rsa, bits, e_value, cb);
- return rsa_builtin_keygen(rsa, bits, e_value, cb);
+
+ return RSA_generate_multi_prime_key(rsa, bits, RSA_DEFAULT_PRIME_NUM,
+ e_value, cb);
}
-static int rsa_builtin_keygen(RSA *rsa, int bits, BIGNUM *e_value,
+int RSA_generate_multi_prime_key(RSA *rsa, int bits, int primes,
+ BIGNUM *e_value, BN_GENCB *cb)
+{
+ /* multi-prime is only supported with the builtin key generation */
+ if (rsa->meth->rsa_multi_prime_keygen != NULL) {
+ return rsa->meth->rsa_multi_prime_keygen(rsa, bits, primes,
+ e_value, cb);
+ } else if (rsa->meth->rsa_keygen != NULL) {
+ /*
+ * However, if rsa->meth implements only rsa_keygen, then we
+ * have to honour it in 2-prime case and assume that it wouldn't
+ * know what to do with multi-prime key generated by builtin
+ * subroutine...
+ */
+ if (primes == 2)
+ return rsa->meth->rsa_keygen(rsa, bits, e_value, cb);
+ else
+ return 0;
+ }
+
+ return rsa_builtin_keygen(rsa, bits, primes, e_value, cb);
+}
+
+static int rsa_builtin_keygen(RSA *rsa, int bits, int primes, BIGNUM *e_value,
BN_GENCB *cb)
{
- BIGNUM *r0 = NULL, *r1 = NULL, *r2 = NULL, *r3 = NULL, *tmp;
- int bitsp, bitsq, ok = -1, n = 0;
+ BIGNUM *r0 = NULL, *r1 = NULL, *r2 = NULL, *tmp, *prime;
+ int ok = -1, n = 0, bitsr[RSA_MAX_PRIME_NUM], bitse = 0;
+ int i = 0, quo = 0, rmd = 0, adj = 0, retries = 0;
+ RSA_PRIME_INFO *pinfo = NULL;
+ STACK_OF(RSA_PRIME_INFO) *prime_infos = NULL;
BN_CTX *ctx = NULL;
+ BN_ULONG bitst = 0;
+ unsigned long error = 0;
+
+ if (bits < RSA_MIN_MODULUS_BITS) {
+ ok = 0; /* we set our own err */
+ RSAerr(RSA_F_RSA_BUILTIN_KEYGEN, RSA_R_KEY_SIZE_TOO_SMALL);
+ goto err;
+ }
+
+ if (primes < RSA_DEFAULT_PRIME_NUM || primes > rsa_multip_cap(bits)) {
+ ok = 0; /* we set our own err */
+ RSAerr(RSA_F_RSA_BUILTIN_KEYGEN, RSA_R_KEY_PRIME_NUM_INVALID);
+ goto err;
+ }
ctx = BN_CTX_new();
if (ctx == NULL)
r0 = BN_CTX_get(ctx);
r1 = BN_CTX_get(ctx);
r2 = BN_CTX_get(ctx);
- r3 = BN_CTX_get(ctx);
- if (r3 == NULL)
+ if (r2 == NULL)
goto err;
- bitsp = (bits + 1) / 2;
- bitsq = bits - bitsp;
+ /* divide bits into 'primes' pieces evenly */
+ quo = bits / primes;
+ rmd = bits % primes;
+
+ for (i = 0; i < primes; i++)
+ bitsr[i] = (i < rmd) ? quo + 1 : quo;
/* We need the RSA components non-NULL */
if (!rsa->n && ((rsa->n = BN_new()) == NULL))
if (!rsa->iqmp && ((rsa->iqmp = BN_secure_new()) == NULL))
goto err;
- BN_copy(rsa->e, e_value);
-
- /* generate p and q */
- for (;;) {
- if (!BN_generate_prime_ex(rsa->p, bitsp, 0, NULL, NULL, cb))
- goto err;
- if (!BN_sub(r2, rsa->p, BN_value_one()))
- goto err;
- if (!BN_gcd(r1, r2, rsa->e, ctx))
- goto err;
- if (BN_is_one(r1))
- break;
- if (!BN_GENCB_call(cb, 2, n++))
+ /* initialize multi-prime components */
+ if (primes > RSA_DEFAULT_PRIME_NUM) {
+ rsa->version = RSA_ASN1_VERSION_MULTI;
+ prime_infos = sk_RSA_PRIME_INFO_new_reserve(NULL, primes - 2);
+ if (prime_infos == NULL)
goto err;
+ if (rsa->prime_infos != NULL) {
+ /* could this happen? */
+ sk_RSA_PRIME_INFO_pop_free(rsa->prime_infos, rsa_multip_info_free);
+ }
+ rsa->prime_infos = prime_infos;
+
+ /* prime_info from 2 to |primes| -1 */
+ for (i = 2; i < primes; i++) {
+ pinfo = rsa_multip_info_new();
+ if (pinfo == NULL)
+ goto err;
+ (void)sk_RSA_PRIME_INFO_push(prime_infos, pinfo);
+ }
}
- if (!BN_GENCB_call(cb, 3, 0))
+
+ if (BN_copy(rsa->e, e_value) == NULL)
goto err;
- for (;;) {
+
+ /* generate p, q and other primes (if any) */
+ for (i = 0; i < primes; i++) {
+ adj = 0;
+ retries = 0;
+
+ if (i == 0) {
+ prime = rsa->p;
+ } else if (i == 1) {
+ prime = rsa->q;
+ } else {
+ pinfo = sk_RSA_PRIME_INFO_value(prime_infos, i - 2);
+ prime = pinfo->r;
+ }
+
+ for (;;) {
+ redo:
+ if (!BN_generate_prime_ex(prime, bitsr[i] + adj, 0, NULL, NULL, cb))
+ goto err;
+ /*
+ * prime should not be equal to p, q, r_3...
+ * (those primes prior to this one)
+ */
+ {
+ int j;
+
+ for (j = 0; j < i; j++) {
+ BIGNUM *prev_prime;
+
+ if (j == 0)
+ prev_prime = rsa->p;
+ else if (j == 1)
+ prev_prime = rsa->q;
+ else
+ prev_prime = sk_RSA_PRIME_INFO_value(prime_infos,
+ j - 2)->r;
+
+ if (!BN_cmp(prime, prev_prime)) {
+ goto redo;
+ }
+ }
+ }
+ if (!BN_sub(r2, prime, BN_value_one()))
+ goto err;
+ ERR_set_mark();
+ BN_set_flags(r2, BN_FLG_CONSTTIME);
+ if (BN_mod_inverse(r1, r2, rsa->e, ctx) != NULL) {
+ /* GCD == 1 since inverse exists */
+ break;
+ }
+ error = ERR_peek_last_error();
+ if (ERR_GET_LIB(error) == ERR_LIB_BN
+ && ERR_GET_REASON(error) == BN_R_NO_INVERSE) {
+ /* GCD != 1 */
+ ERR_pop_to_mark();
+ } else {
+ goto err;
+ }
+ if (!BN_GENCB_call(cb, 2, n++))
+ goto err;
+ }
+
+ bitse += bitsr[i];
+
+ /* calculate n immediately to see if it's sufficient */
+ if (i == 1) {
+ /* we get at least 2 primes */
+ if (!BN_mul(r1, rsa->p, rsa->q, ctx))
+ goto err;
+ } else if (i != 0) {
+ /* modulus n = p * q * r_3 * r_4 ... */
+ if (!BN_mul(r1, rsa->n, prime, ctx))
+ goto err;
+ } else {
+ /* i == 0, do nothing */
+ if (!BN_GENCB_call(cb, 3, i))
+ goto err;
+ continue;
+ }
/*
- * When generating ridiculously small keys, we can get stuck
- * continually regenerating the same prime values. Check for this and
- * bail if it happens 3 times.
+ * if |r1|, product of factors so far, is not as long as expected
+ * (by checking the first 4 bits are less than 0x9 or greater than
+ * 0xF). If so, re-generate the last prime.
+ *
+ * NOTE: This actually can't happen in two-prime case, because of
+ * the way factors are generated.
+ *
+ * Besides, another consideration is, for multi-prime case, even the
+ * length modulus is as long as expected, the modulus could start at
+ * 0x8, which could be utilized to distinguish a multi-prime private
+ * key by using the modulus in a certificate. This is also covered
+ * by checking the length should not be less than 0x9.
*/
- unsigned int degenerate = 0;
- do {
- if (!BN_generate_prime_ex(rsa->q, bitsq, 0, NULL, NULL, cb))
- goto err;
- } while ((BN_cmp(rsa->p, rsa->q) == 0) && (++degenerate < 3));
- if (degenerate == 3) {
- ok = 0; /* we set our own err */
- RSAerr(RSA_F_RSA_BUILTIN_KEYGEN, RSA_R_KEY_SIZE_TOO_SMALL);
+ if (!BN_rshift(r2, r1, bitse - 4))
goto err;
+ bitst = BN_get_word(r2);
+
+ if (bitst < 0x9 || bitst > 0xF) {
+ /*
+ * For keys with more than 4 primes, we attempt longer factor to
+ * meet length requirement.
+ *
+ * Otherwise, we just re-generate the prime with the same length.
+ *
+ * This strategy has the following goals:
+ *
+ * 1. 1024-bit factors are effcient when using 3072 and 4096-bit key
+ * 2. stay the same logic with normal 2-prime key
+ */
+ bitse -= bitsr[i];
+ if (!BN_GENCB_call(cb, 2, n++))
+ goto err;
+ if (primes > 4) {
+ if (bitst < 0x9)
+ adj++;
+ else
+ adj--;
+ } else if (retries == 4) {
+ /*
+ * re-generate all primes from scratch, mainly used
+ * in 4 prime case to avoid long loop. Max retry times
+ * is set to 4.
+ */
+ i = -1;
+ bitse = 0;
+ continue;
+ }
+ retries++;
+ goto redo;
}
- if (!BN_sub(r2, rsa->q, BN_value_one()))
+ /* save product of primes for further use, for multi-prime only */
+ if (i > 1 && BN_copy(pinfo->pp, rsa->n) == NULL)
goto err;
- if (!BN_gcd(r1, r2, rsa->e, ctx))
+ if (BN_copy(rsa->n, r1) == NULL)
goto err;
- if (BN_is_one(r1))
- break;
- if (!BN_GENCB_call(cb, 2, n++))
+ if (!BN_GENCB_call(cb, 3, i))
goto err;
}
- if (!BN_GENCB_call(cb, 3, 1))
- goto err;
+
if (BN_cmp(rsa->p, rsa->q) < 0) {
tmp = rsa->p;
rsa->p = rsa->q;
rsa->q = tmp;
}
- /* calculate n */
- if (!BN_mul(rsa->n, rsa->p, rsa->q, ctx))
- goto err;
-
/* calculate d */
+
+ /* p - 1 */
if (!BN_sub(r1, rsa->p, BN_value_one()))
- goto err; /* p-1 */
+ goto err;
+ /* q - 1 */
if (!BN_sub(r2, rsa->q, BN_value_one()))
- goto err; /* q-1 */
+ goto err;
+ /* (p - 1)(q - 1) */
if (!BN_mul(r0, r1, r2, ctx))
- goto err; /* (p-1)(q-1) */
+ goto err;
+ /* multi-prime */
+ for (i = 2; i < primes; i++) {
+ pinfo = sk_RSA_PRIME_INFO_value(prime_infos, i - 2);
+ /* save r_i - 1 to pinfo->d temporarily */
+ if (!BN_sub(pinfo->d, pinfo->r, BN_value_one()))
+ goto err;
+ if (!BN_mul(r0, r0, pinfo->d, ctx))
+ goto err;
+ }
+
{
- BIGNUM *local_r0 = NULL, *pr0;
- if (!(rsa->flags & RSA_FLAG_NO_CONSTTIME)) {
- pr0 = local_r0 = BN_new();
- if (local_r0 == NULL)
- goto err;
- BN_with_flags(pr0, r0, BN_FLG_CONSTTIME);
- } else {
- pr0 = r0;
- }
+ BIGNUM *pr0 = BN_new();
+
+ if (pr0 == NULL)
+ goto err;
+
+ BN_with_flags(pr0, r0, BN_FLG_CONSTTIME);
if (!BN_mod_inverse(rsa->d, rsa->e, pr0, ctx)) {
- BN_free(local_r0);
+ BN_free(pr0);
goto err; /* d */
}
- /* We MUST free local_r0 before any further use of r0 */
- BN_free(local_r0);
+ /* We MUST free pr0 before any further use of r0 */
+ BN_free(pr0);
}
{
- BIGNUM *local_d = NULL, *d;
- /* set up d for correct BN_FLG_CONSTTIME flag */
- if (!(rsa->flags & RSA_FLAG_NO_CONSTTIME)) {
- d = local_d = BN_new();
- if (local_d == NULL)
- goto err;
- BN_with_flags(d, rsa->d, BN_FLG_CONSTTIME);
- } else {
- d = rsa->d;
- }
+ BIGNUM *d = BN_new();
+
+ if (d == NULL)
+ goto err;
- if ( /* calculate d mod (p-1) */
- !BN_mod(rsa->dmp1, d, r1, ctx)
- /* calculate d mod (q-1) */
+ BN_with_flags(d, rsa->d, BN_FLG_CONSTTIME);
+
+ /* calculate d mod (p-1) and d mod (q - 1) */
+ if (!BN_mod(rsa->dmp1, d, r1, ctx)
|| !BN_mod(rsa->dmq1, d, r2, ctx)) {
- BN_free(local_d);
+ BN_free(d);
goto err;
}
- /* We MUST free local_d before any further use of rsa->d */
- BN_free(local_d);
+
+ /* calculate CRT exponents */
+ for (i = 2; i < primes; i++) {
+ pinfo = sk_RSA_PRIME_INFO_value(prime_infos, i - 2);
+ /* pinfo->d == r_i - 1 */
+ if (!BN_mod(pinfo->d, d, pinfo->d, ctx)) {
+ BN_free(d);
+ goto err;
+ }
+ }
+
+ /* We MUST free d before any further use of rsa->d */
+ BN_free(d);
}
{
- BIGNUM *local_p = NULL, *p;
+ BIGNUM *p = BN_new();
+
+ if (p == NULL)
+ goto err;
+ BN_with_flags(p, rsa->p, BN_FLG_CONSTTIME);
/* calculate inverse of q mod p */
- if (!(rsa->flags & RSA_FLAG_NO_CONSTTIME)) {
- p = local_p = BN_new();
- if (local_p == NULL)
- goto err;
- BN_with_flags(p, rsa->p, BN_FLG_CONSTTIME);
- } else {
- p = rsa->p;
- }
if (!BN_mod_inverse(rsa->iqmp, rsa->q, p, ctx)) {
- BN_free(local_p);
+ BN_free(p);
goto err;
}
- /* We MUST free local_p before any further use of rsa->p */
- BN_free(local_p);
+
+ /* calculate CRT coefficient for other primes */
+ for (i = 2; i < primes; i++) {
+ pinfo = sk_RSA_PRIME_INFO_value(prime_infos, i - 2);
+ BN_with_flags(p, pinfo->r, BN_FLG_CONSTTIME);
+ if (!BN_mod_inverse(pinfo->t, pinfo->pp, p, ctx)) {
+ BN_free(p);
+ goto err;
+ }
+ }
+
+ /* We MUST free p before any further use of rsa->p */
+ BN_free(p);
}
ok = 1;
if (ctx != NULL)
BN_CTX_end(ctx);
BN_CTX_free(ctx);
-
return ok;
}
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