Support multi-prime RSA (RFC 8017)

* Introduce RSA_generate_multi_prime_key to generate multi-prime
  RSA private key. As well as the following functions:
    RSA_get_multi_prime_extra_count
    RSA_get0_multi_prime_factors
    RSA_get0_multi_prime_crt_params
    RSA_set0_multi_prime_params
    RSA_get_version
* Support EVP operations for multi-prime RSA
* Support ASN.1 operations for multi-prime RSA
* Support multi-prime check in RSA_check_key_ex
* Support multi-prime RSA in apps/genrsa and apps/speed
* Support multi-prime RSA manipulation functions
* Test cases and documentation are added
* CHANGES is updated

Reviewed-by: Tim Hudson <tjh@openssl.org>
Reviewed-by: Bernd Edlinger <bernd.edlinger@hotmail.de>
(Merged from https://github.com/openssl/openssl/pull/4241)

1 files changed, 75 insertions, 6 deletions

diff --git a/crypto/rsa/rsa_chk.c b/crypto/rsa/rsa_chk.c
index 00260fb18e..4cf682258b 100644
--- a/crypto/rsa/rsa_chk.c
+++ b/crypto/rsa/rsa_chk.c
@@ -1,5 +1,5 @@
 /*
- * Copyright 1999-2016 The OpenSSL Project Authors. All Rights Reserved.
+ * Copyright 1999-2017 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
@@ -20,7 +20,8 @@ int RSA_check_key_ex(const RSA *key, BN_GENCB *cb)
 {
     BIGNUM *i, *j, *k, *l, *m;
     BN_CTX *ctx;
-    int ret = 1;
+    int ret = 1, ex_primes = 0, idx;
+    RSA_PRIME_INFO *pinfo;
 
     if (key->p == NULL || key->q == NULL || key->n == NULL
             || key->e == NULL || key->d == NULL) {
@@ -28,6 +29,13 @@ int RSA_check_key_ex(const RSA *key, BN_GENCB *cb)
         return 0;
     }
 
+    /* multi-prime? */
+    if (key->version == RSA_ASN1_VERSION_MULTI
+        && (ex_primes = sk_RSA_PRIME_INFO_num(key->prime_infos)) <= 0) {
+        RSAerr(RSA_F_RSA_CHECK_KEY_EX, RSA_R_INVALID_MULTI_PRIME_KEY);
+        return 0;
+    }
+
     i = BN_new();
     j = BN_new();
     k = BN_new();
@@ -62,17 +70,37 @@ int RSA_check_key_ex(const RSA *key, BN_GENCB *cb)
         RSAerr(RSA_F_RSA_CHECK_KEY_EX, RSA_R_Q_NOT_PRIME);
     }
 
-    /* n = p*q? */
+    /* r_i prime? */
+    for (idx = 0; idx < ex_primes; idx++) {
+        pinfo = sk_RSA_PRIME_INFO_value(key->prime_infos, idx);
+        if (BN_is_prime_ex(pinfo->r, BN_prime_checks, NULL, cb) != 1) {
+            ret = 0;
+            RSAerr(RSA_F_RSA_CHECK_KEY_EX, RSA_R_MP_R_NOT_PRIME);
+        }
+    }
+
+    /* n = p*q * r_3...r_i? */
     if (!BN_mul(i, key->p, key->q, ctx)) {
         ret = -1;
         goto err;
     }
+    for (idx = 0; idx < ex_primes; idx++) {
+        pinfo = sk_RSA_PRIME_INFO_value(key->prime_infos, idx);
+        if (!BN_mul(i, i, pinfo->r, ctx)) {
+            ret = -1;
+            goto err;
+        }
+    }
     if (BN_cmp(i, key->n) != 0) {
         ret = 0;
-        RSAerr(RSA_F_RSA_CHECK_KEY_EX, RSA_R_N_DOES_NOT_EQUAL_P_Q);
+        if (ex_primes)
+            RSAerr(RSA_F_RSA_CHECK_KEY_EX,
+                   RSA_R_N_DOES_NOT_EQUAL_PRODUCT_OF_PRIMES);
+        else
+            RSAerr(RSA_F_RSA_CHECK_KEY_EX, RSA_R_N_DOES_NOT_EQUAL_P_Q);
     }
 
-    /* d*e = 1  mod lcm(p-1,q-1)? */
+    /* d*e = 1  mod \lambda(n)? */
     if (!BN_sub(i, key->p, BN_value_one())) {
         ret = -1;
         goto err;
@@ -82,7 +110,7 @@ int RSA_check_key_ex(const RSA *key, BN_GENCB *cb)
         goto err;
     }
 
-    /* now compute k = lcm(i,j) */
+    /* now compute k = \lambda(n) = LCM(i, j, r_3 - 1...) */
     if (!BN_mul(l, i, j, ctx)) {
         ret = -1;
         goto err;
@@ -91,6 +119,21 @@ int RSA_check_key_ex(const RSA *key, BN_GENCB *cb)
         ret = -1;
         goto err;
     }
+    for (idx = 0; idx < ex_primes; idx++) {
+        pinfo = sk_RSA_PRIME_INFO_value(key->prime_infos, idx);
+        if (!BN_sub(k, pinfo->r, BN_value_one())) {
+            ret = -1;
+            goto err;
+        }
+        if (!BN_mul(l, l, k, ctx)) {
+            ret = -1;
+            goto err;
+        }
+        if (!BN_gcd(m, m, k, ctx)) {
+            ret = -1;
+            goto err;
+        }
+    }
     if (!BN_div(k, NULL, l, m, ctx)) { /* remainder is 0 */
         ret = -1;
         goto err;
@@ -145,6 +188,32 @@ int RSA_check_key_ex(const RSA *key, BN_GENCB *cb)
         }
     }
 
+    for (idx = 0; idx < ex_primes; idx++) {
+        pinfo = sk_RSA_PRIME_INFO_value(key->prime_infos, idx);
+        /* d_i = d mod (r_i - 1)? */
+        if (!BN_sub(i, pinfo->r, BN_value_one())) {
+            ret = -1;
+            goto err;
+        }
+        if (!BN_mod(j, key->d, i, ctx)) {
+            ret = -1;
+            goto err;
+        }
+        if (BN_cmp(j, pinfo->d) != 0) {
+            ret = 0;
+            RSAerr(RSA_F_RSA_CHECK_KEY_EX, RSA_R_MP_EXPONENT_NOT_CONGRUENT_TO_D);
+        }
+        /* t_i = R_i ^ -1 mod r_i ? */
+        if (!BN_mod_inverse(i, pinfo->pp, pinfo->r, ctx)) {
+            ret = -1;
+            goto err;
+        }
+        if (BN_cmp(i, pinfo->t) != 0) {
+            ret = 0;
+            RSAerr(RSA_F_RSA_CHECK_KEY_EX, RSA_R_MP_COEFFICIENT_NOT_INVERSE_OF_R);
+        }
+    }
+
  err:
     BN_free(i);
     BN_free(j);