Added stricter rule on input for RSA private key operation (mathematically correct...

diff --git a/src/rsa/rsa_i15_priv.c b/src/rsa/rsa_i15_priv.c
index e692da4..177cc3a 100644 (file)
--- a/src/rsa/rsa_i15_priv.c
+++ b/src/rsa/rsa_i15_priv.c
@@ -27,24 +27,6 @@
 #define U      (2 + ((BR_MAX_RSA_FACTOR + 14) / 15))
 #define TLEN   (8 * U)
 
-/* obsolete
-static void
-print_int(const char *name, const uint16_t *x)
-{
-       extern int printf(const char *fmt, ...);
-       unsigned char tmp[1000];
-       size_t u, len;
-
-       len = (x[0] - (x[0] >> 4) + 7) >> 3;
-       br_i15_encode(tmp, len, x);
-       printf("%s = ", name);
-       for (u = 0; u < len; u ++) {
-               printf("%02X", tmp[u]);
-       }
-       printf("\n");
-}
-*/
-
 /* see bearssl_rsa.h */
 uint32_t
 br_rsa_i15_private(unsigned char *x, const br_rsa_private_key *sk)
@@ -53,7 +35,7 @@ br_rsa_i15_private(unsigned char *x, const br_rsa_private_key *sk)
        size_t plen, qlen;
        size_t fwlen;
        uint16_t p0i, q0i;
-       size_t xlen;
+       size_t xlen, u;
        uint16_t tmp[1 + TLEN];
        long z;
        uint16_t *mp, *mq, *s1, *s2, *t1, *t2, *t3;
@@ -117,19 +99,56 @@ br_rsa_i15_private(unsigned char *x, const br_rsa_private_key *sk)
        br_i15_decode(mq, q, qlen);
 
        /*
-        * Compute s2 = x^dq mod q.
+        * Decode p.
         */
-       q0i = br_i15_ninv15(mq[1]);
-       s2 = mq + fwlen;
-       br_i15_decode_reduce(s2, x, xlen, mq);
-       r = br_i15_modpow_opt(s2, sk->dq, sk->dqlen, mq, q0i,
-               mq + 2 * fwlen, TLEN - 2 * fwlen);
+       t1 = mq + fwlen;
+       br_i15_decode(t1, p, plen);
 
        /*
-        * Decode p.
+        * Compute the modulus (product of the two factors), to compare
+        * it with the source value. We use br_i15_mulacc(), since it's
+        * already used later on.
+        */
+       t2 = mq + 2 * fwlen;
+       br_i15_zero(t2, mq[0]);
+       br_i15_mulacc(t2, mq, t1);
+
+       /*
+        * We encode the modulus into bytes, to perform the comparison
+        * with bytes. We know that the product length, in bytes, is
+        * exactly xlen.
+        * The comparison actually computes the carry when subtracting
+        * the modulus from the source value; that carry must be 1 for
+        * a value in the correct range. We keep it in r, which is our
+        * accumulator for the error code.
+        */
+       t3 = mq + 4 * fwlen;
+       br_i15_encode(t3, xlen, t2);
+       u = xlen;
+       r = 0;
+       while (u > 0) {
+               uint32_t wn, wx;
+
+               u --;
+               wn = ((unsigned char *)t3)[u];
+               wx = x[u];
+               r = ((wx - (wn + r)) >> 8) & 1;
+       }
+
+       /*
+        * Move the decoded p to another temporary buffer.
         */
        mp = mq + 2 * fwlen;
-       br_i15_decode(mp, p, plen);
+       memmove(mp, t1, fwlen * sizeof *t1);
+
+       /*
+        * Compute s2 = x^dq mod q.
+        */
+       q0i = br_i15_ninv15(mq[1]);
+       s2 = mq + fwlen;
+       br_i15_decode_reduce(s2, x, xlen, mq);
+       r &= br_i15_modpow_opt(s2, sk->dq, sk->dqlen, mq, q0i,
+               mq + 3 * fwlen, TLEN - 3 * fwlen);
 
        /*
         * Compute s1 = x^dq mod q.

diff --git a/src/rsa/rsa_i31_priv.c b/src/rsa/rsa_i31_priv.c
index cb2858b..b1e1244 100644 (file)
--- a/src/rsa/rsa_i31_priv.c
+++ b/src/rsa/rsa_i31_priv.c
@@ -35,7 +35,7 @@ br_rsa_i31_private(unsigned char *x, const br_rsa_private_key *sk)
        size_t plen, qlen;
        size_t fwlen;
        uint32_t p0i, q0i;
-       size_t xlen;
+       size_t xlen, u;
        uint32_t tmp[1 + TLEN];
        long z;
        uint32_t *mp, *mq, *s1, *s2, *t1, *t2, *t3;
@@ -82,7 +82,7 @@ br_rsa_i31_private(unsigned char *x, const br_rsa_private_key *sk)
        }
 
        /*
-        * Compute signature length (in bytes).
+        * Compute modulus length (in bytes).
         */
        xlen = (sk->n_bitlen + 7) >> 3;
 
@@ -93,19 +93,56 @@ br_rsa_i31_private(unsigned char *x, const br_rsa_private_key *sk)
        br_i31_decode(mq, q, qlen);
 
        /*
-        * Compute s2 = x^dq mod q.
+        * Decode p.
         */
-       q0i = br_i31_ninv31(mq[1]);
-       s2 = mq + fwlen;
-       br_i31_decode_reduce(s2, x, xlen, mq);
-       r = br_i31_modpow_opt(s2, sk->dq, sk->dqlen, mq, q0i,
-               mq + 2 * fwlen, TLEN - 2 * fwlen);
+       t1 = mq + fwlen;
+       br_i31_decode(t1, p, plen);
 
        /*
-        * Decode p.
+        * Compute the modulus (product of the two factors), to compare
+        * it with the source value. We use br_i31_mulacc(), since it's
+        * already used later on.
+        */
+       t2 = mq + 2 * fwlen;
+       br_i31_zero(t2, mq[0]);
+       br_i31_mulacc(t2, mq, t1);
+
+       /*
+        * We encode the modulus into bytes, to perform the comparison
+        * with bytes. We know that the product length, in bytes, is
+        * exactly xlen.
+        * The comparison actually computes the carry when subtracting
+        * the modulus from the source value; that carry must be 1 for
+        * a value in the correct range. We keep it in r, which is our
+        * accumulator for the error code.
+        */
+       t3 = mq + 4 * fwlen;
+       br_i31_encode(t3, xlen, t2);
+       u = xlen;
+       r = 0;
+       while (u > 0) {
+               uint32_t wn, wx;
+
+               u --;
+               wn = ((unsigned char *)t3)[u];
+               wx = x[u];
+               r = ((wx - (wn + r)) >> 8) & 1;
+       }
+
+       /*
+        * Move the decoded p to another temporary buffer.
         */
        mp = mq + 2 * fwlen;
-       br_i31_decode(mp, p, plen);
+       memmove(mp, t1, fwlen * sizeof *t1);
+
+       /*
+        * Compute s2 = x^dq mod q.
+        */
+       q0i = br_i31_ninv31(mq[1]);
+       s2 = mq + fwlen;
+       br_i31_decode_reduce(s2, x, xlen, mq);
+       r &= br_i31_modpow_opt(s2, sk->dq, sk->dqlen, mq, q0i,
+               mq + 3 * fwlen, TLEN - 3 * fwlen);
 
        /*
         * Compute s1 = x^dp mod p.

diff --git a/src/rsa/rsa_i32_priv.c b/src/rsa/rsa_i32_priv.c
index 3c08d00..05c22ec 100644 (file)
--- a/src/rsa/rsa_i32_priv.c
+++ b/src/rsa/rsa_i32_priv.c
@@ -35,7 +35,8 @@ br_rsa_i32_private(unsigned char *x, const br_rsa_private_key *sk)
        uint32_t tmp[6 * U];
        uint32_t *mp, *mq, *s1, *s2, *t1, *t2, *t3;
        uint32_t p0i, q0i;
-       size_t xlen;
+       size_t xlen, u;
+       uint32_t r;
 
        /*
         * All our temporary buffers are from the tmp[] array.
@@ -82,16 +83,22 @@ br_rsa_i32_private(unsigned char *x, const br_rsa_private_key *sk)
        br_i32_decode(mq, q, qlen);
 
        /*
-        * obsolete -- we do not compute the length of n, it is now
-        * an input parameter.
-       br_i32_zero(t3, mp[0]);
-       br_i32_mulacc(t3, mp, mq);
-       n_bitlen = br_i32_bit_length(t3 + 1, (t3[0] + 31) >> 5);
-       if (xlen != ((n_bitlen + 7) >> 3)) {
-               return 0;
-       }
+        * Recompute modulus, to compare with the source value.
         */
+       br_i32_zero(t2, mp[0]);
+       br_i32_mulacc(t2, mp, mq);
        xlen = (sk->n_bitlen + 7) >> 3;
+       br_i32_encode(t2 + 2 * U, xlen, t2);
+       u = xlen;
+       r = 0;
+       while (u > 0) {
+               uint32_t wn, wx;
+
+               u --;
+               wn = ((unsigned char *)(t2 + 2 * U))[u];
+               wx = x[u];
+               r = ((wx - (wn + r)) >> 8) & 1;
+       }
 
        /*
         * Compute s1 = x^dp mod p.
@@ -149,5 +156,5 @@ br_rsa_i32_private(unsigned char *x, const br_rsa_private_key *sk)
         * The only error conditions remaining at that point are invalid
         * values for p and q (even integers).
         */
-       return p0i & q0i & 1;
+       return p0i & q0i & r;
 }

diff --git a/src/rsa/rsa_i62_priv.c b/src/rsa/rsa_i62_priv.c
index ffa03c2..f0da600 100644 (file)
--- a/src/rsa/rsa_i62_priv.c
+++ b/src/rsa/rsa_i62_priv.c
@@ -37,7 +37,7 @@ br_rsa_i62_private(unsigned char *x, const br_rsa_private_key *sk)
        size_t plen, qlen;
        size_t fwlen;
        uint32_t p0i, q0i;
-       size_t xlen;
+       size_t xlen, u;
        uint64_t tmp[TLEN];
        long z;
        uint32_t *mp, *mq, *s1, *s2, *t1, *t2, *t3;
@@ -95,19 +95,56 @@ br_rsa_i62_private(unsigned char *x, const br_rsa_private_key *sk)
        br_i31_decode(mq, q, qlen);
 
        /*
-        * Compute s2 = x^dq mod q.
+        * Decode p.
         */
-       q0i = br_i31_ninv31(mq[1]);
-       s2 = (uint32_t *)(tmp + fwlen);
-       br_i31_decode_reduce(s2, x, xlen, mq);
-       r = br_i62_modpow_opt(s2, sk->dq, sk->dqlen, mq, q0i,
-               tmp + 2 * fwlen, TLEN - 2 * fwlen);
+       t1 = (uint32_t *)(tmp + fwlen);
+       br_i31_decode(t1, p, plen);
 
        /*
-        * Decode p.
+        * Compute the modulus (product of the two factors), to compare
+        * it with the source value. We use br_i31_mulacc(), since it's
+        * already used later on.
+        */
+       t2 = (uint32_t *)(tmp + 2 * fwlen);
+       br_i31_zero(t2, mq[0]);
+       br_i31_mulacc(t2, mq, t1);
+
+       /*
+        * We encode the modulus into bytes, to perform the comparison
+        * with bytes. We know that the product length, in bytes, is
+        * exactly xlen.
+        * The comparison actually computes the carry when subtracting
+        * the modulus from the source value; that carry must be 1 for
+        * a value in the correct range. We keep it in r, which is our
+        * accumulator for the error code.
+        */
+       t3 = (uint32_t *)(tmp + 4 * fwlen);
+       br_i31_encode(t3, xlen, t2);
+       u = xlen;
+       r = 0;
+       while (u > 0) {
+               uint32_t wn, wx;
+
+               u --;
+               wn = ((unsigned char *)t3)[u];
+               wx = x[u];
+               r = ((wx - (wn + r)) >> 8) & 1;
+       }
+
+       /*
+        * Move the decoded p to another temporary buffer.
         */
        mp = (uint32_t *)(tmp + 2 * fwlen);
-       br_i31_decode(mp, p, plen);
+       memmove(mp, t1, 2 * fwlen * sizeof *t1);
+
+       /*
+        * Compute s2 = x^dq mod q.
+        */
+       q0i = br_i31_ninv31(mq[1]);
+       s2 = (uint32_t *)(tmp + fwlen);
+       br_i31_decode_reduce(s2, x, xlen, mq);
+       r &= br_i62_modpow_opt(s2, sk->dq, sk->dqlen, mq, q0i,
+               tmp + 3 * fwlen, TLEN - 3 * fwlen);
 
        /*
         * Compute s1 = x^dp mod p.

diff --git a/test/test_crypto.c b/test/test_crypto.c
index a8119be..41f7612 100644 (file)
--- a/test/test_crypto.c
+++ b/test/test_crypto.c
@@ -4720,10 +4720,413 @@ static const br_rsa_private_key RSA_SK = {
        (void *)RSA_IQ, sizeof RSA_IQ
 };
 
+/*
+ * A 2048-bit RSA key, generated with OpenSSL.
+ */
+static const unsigned char RSA2048_N[] = {
+       0xEA, 0xB1, 0xB0, 0x87, 0x60, 0xE2, 0x69, 0xF5,
+       0xC9, 0x3F, 0xCB, 0x4F, 0x9E, 0x7D, 0xD0, 0x56,
+       0x54, 0x8F, 0xF5, 0x59, 0x97, 0x04, 0x3F, 0x30,
+       0xE1, 0xFB, 0x7B, 0xF5, 0xA0, 0xEB, 0xA7, 0x7B,
+       0x29, 0x96, 0x7B, 0x32, 0x48, 0x48, 0xA4, 0x99,
+       0x90, 0x92, 0x48, 0xFB, 0xDC, 0xEC, 0x8A, 0x3B,
+       0xE0, 0x57, 0x6E, 0xED, 0x1C, 0x5B, 0x78, 0xCF,
+       0x07, 0x41, 0x96, 0x4C, 0x2F, 0xA2, 0xD1, 0xC8,
+       0xA0, 0x5F, 0xFC, 0x2A, 0x5B, 0x3F, 0xBC, 0xD7,
+       0xE6, 0x91, 0xF1, 0x44, 0xD6, 0xD8, 0x41, 0x66,
+       0x3E, 0x80, 0xEE, 0x98, 0x73, 0xD5, 0x32, 0x60,
+       0x7F, 0xDF, 0xBF, 0xB2, 0x0B, 0xA5, 0xCA, 0x11,
+       0x88, 0x1A, 0x0E, 0xA1, 0x61, 0x4C, 0x5A, 0x70,
+       0xCE, 0x12, 0xC0, 0x61, 0xF5, 0x50, 0x0E, 0xF6,
+       0xC1, 0xC2, 0x88, 0x8B, 0xE5, 0xCE, 0xAE, 0x90,
+       0x65, 0x23, 0xA7, 0xAD, 0xCB, 0x04, 0x17, 0x00,
+       0xA2, 0xDB, 0xB0, 0x21, 0x49, 0xDD, 0x3C, 0x2E,
+       0x8C, 0x47, 0x27, 0xF2, 0x84, 0x51, 0x63, 0xEB,
+       0xF8, 0xAF, 0x63, 0xA7, 0x89, 0xE1, 0xF0, 0x2F,
+       0xF9, 0x9C, 0x0A, 0x8A, 0xBC, 0x57, 0x05, 0xB0,
+       0xEF, 0xA0, 0xDA, 0x67, 0x70, 0xAF, 0x3F, 0xA4,
+       0x92, 0xFC, 0x4A, 0xAC, 0xEF, 0x89, 0x41, 0x58,
+       0x57, 0x63, 0x0F, 0x6A, 0x89, 0x68, 0x45, 0x4C,
+       0x20, 0xF9, 0x7F, 0x50, 0x9D, 0x8C, 0x52, 0xC4,
+       0xC1, 0x33, 0xCD, 0x42, 0x35, 0x12, 0xEC, 0x82,
+       0xF9, 0xC1, 0xB7, 0x60, 0x7B, 0x52, 0x61, 0xD0,
+       0xAE, 0xFD, 0x4B, 0x68, 0xB1, 0x55, 0x0E, 0xAB,
+       0x99, 0x24, 0x52, 0x60, 0x8E, 0xDB, 0x90, 0x34,
+       0x61, 0xE3, 0x95, 0x7C, 0x34, 0x64, 0x06, 0xCB,
+       0x44, 0x17, 0x70, 0x78, 0xC1, 0x1B, 0x87, 0x8F,
+       0xCF, 0xB0, 0x7D, 0x93, 0x59, 0x84, 0x49, 0xF5,
+       0x55, 0xBB, 0x48, 0xCA, 0xD3, 0x76, 0x1E, 0x7F
+};
+static const unsigned char RSA2048_E[] = {
+       0x01, 0x00, 0x01
+};
+static const unsigned char RSA2048_P[] = {
+       0xF9, 0xA7, 0xB5, 0xC4, 0xE8, 0x52, 0xEC, 0xB1,
+       0x33, 0x6A, 0x68, 0x32, 0x63, 0x2D, 0xBA, 0xE5,
+       0x61, 0x14, 0x69, 0x82, 0xC8, 0x31, 0x14, 0xD5,
+       0xC2, 0x6C, 0x1A, 0xBE, 0xA0, 0x68, 0xA6, 0xC5,
+       0xEA, 0x40, 0x59, 0xFB, 0x0A, 0x30, 0x3D, 0xD5,
+       0xDD, 0x94, 0xAE, 0x0C, 0x9F, 0xEE, 0x19, 0x0C,
+       0xA8, 0xF2, 0x85, 0x27, 0x60, 0xAA, 0xD5, 0x7C,
+       0x59, 0x91, 0x1F, 0xAF, 0x5E, 0x00, 0xC8, 0x2D,
+       0xCA, 0xB4, 0x70, 0xA1, 0xF8, 0x8C, 0x0A, 0xB3,
+       0x08, 0x95, 0x03, 0x9E, 0xA4, 0x6B, 0x9D, 0x55,
+       0x47, 0xE0, 0xEC, 0xB3, 0x21, 0x7C, 0xE4, 0x16,
+       0x91, 0xE3, 0xD7, 0x1B, 0x3D, 0x81, 0xF1, 0xED,
+       0x16, 0xF9, 0x05, 0x0E, 0xA6, 0x9F, 0x37, 0x73,
+       0x18, 0x1B, 0x9C, 0x9D, 0x33, 0xAD, 0x25, 0xEF,
+       0x3A, 0xC0, 0x4B, 0x34, 0x24, 0xF5, 0xFD, 0x59,
+       0xF5, 0x65, 0xE6, 0x92, 0x2A, 0x04, 0x06, 0x3D
+};
+static const unsigned char RSA2048_Q[] = {
+       0xF0, 0xA8, 0xA4, 0x20, 0xDD, 0xF3, 0x99, 0xE6,
+       0x1C, 0xB1, 0x21, 0xE8, 0x66, 0x68, 0x48, 0x00,
+       0x04, 0xE3, 0x21, 0xA3, 0xE8, 0xC5, 0xFD, 0x85,
+       0x6D, 0x2C, 0x98, 0xE3, 0x36, 0x39, 0x3E, 0x80,
+       0xB7, 0x36, 0xA5, 0xA9, 0xBB, 0xEB, 0x1E, 0xB8,
+       0xEB, 0x44, 0x65, 0xE8, 0x81, 0x7D, 0xE0, 0x87,
+       0xC1, 0x08, 0x94, 0xDD, 0x92, 0x40, 0xF4, 0x8B,
+       0x3C, 0xB5, 0xC1, 0xAD, 0x9D, 0x4C, 0x14, 0xCD,
+       0xD9, 0x2D, 0xB6, 0xE4, 0x99, 0xB3, 0x71, 0x63,
+       0x64, 0xE1, 0x31, 0x7E, 0x34, 0x95, 0x96, 0x52,
+       0x85, 0x27, 0xBE, 0x40, 0x10, 0x0A, 0x9E, 0x01,
+       0x1C, 0xBB, 0xB2, 0x5B, 0x40, 0x85, 0x65, 0x6E,
+       0xA0, 0x88, 0x73, 0xF6, 0x22, 0xCC, 0x23, 0x26,
+       0x62, 0xAD, 0x92, 0x57, 0x57, 0xF4, 0xD4, 0xDF,
+       0xD9, 0x7C, 0xDE, 0xAD, 0xD2, 0x1F, 0x32, 0x29,
+       0xBA, 0xE7, 0xE2, 0x32, 0xA1, 0xA0, 0xBF, 0x6B
+};
+static const unsigned char RSA2048_DP[] = {
+       0xB2, 0xF9, 0xD7, 0x66, 0xC5, 0x83, 0x05, 0x6A,
+       0x77, 0xC8, 0xB5, 0xD0, 0x41, 0xA7, 0xBC, 0x0F,
+       0xCB, 0x4B, 0xFD, 0xE4, 0x23, 0x2E, 0x84, 0x98,
+       0x46, 0x1C, 0x88, 0x03, 0xD7, 0x2D, 0x8F, 0x39,
+       0xDD, 0x98, 0xAA, 0xA9, 0x3D, 0x01, 0x9E, 0xA2,
+       0xDE, 0x8A, 0x43, 0x48, 0x8B, 0xB2, 0xFE, 0xC4,
+       0x43, 0xAE, 0x31, 0x65, 0x2C, 0x78, 0xEC, 0x39,
+       0x8C, 0x60, 0x6C, 0xCD, 0xA4, 0xDF, 0x7C, 0xA2,
+       0xCF, 0x6A, 0x12, 0x41, 0x1B, 0xD5, 0x11, 0xAA,
+       0x8D, 0xE1, 0x7E, 0x49, 0xD1, 0xE7, 0xD0, 0x50,
+       0x1E, 0x0A, 0x92, 0xC6, 0x4C, 0xA0, 0xA3, 0x47,
+       0xC6, 0xE9, 0x07, 0x01, 0xE1, 0x53, 0x72, 0x23,
+       0x9D, 0x4F, 0x82, 0x9F, 0xA1, 0x36, 0x0D, 0x63,
+       0x76, 0x89, 0xFC, 0xF9, 0xF9, 0xDD, 0x0C, 0x8F,
+       0xF7, 0x97, 0x79, 0x92, 0x75, 0x58, 0xE0, 0x7B,
+       0x08, 0x61, 0x38, 0x2D, 0xDA, 0xEF, 0x2D, 0xA5
+};
+static const unsigned char RSA2048_DQ[] = {
+       0x8B, 0x69, 0x56, 0x33, 0x08, 0x00, 0x8F, 0x3D,
+       0xC3, 0x8F, 0x45, 0x52, 0x48, 0xC8, 0xCE, 0x34,
+       0xDC, 0x9F, 0xEB, 0x23, 0xF5, 0xBB, 0x84, 0x62,
+       0xDF, 0xDC, 0xBE, 0xF0, 0x98, 0xBF, 0xCE, 0x9A,
+       0x68, 0x08, 0x4B, 0x2D, 0xA9, 0x83, 0xC9, 0xF7,
+       0x5B, 0xAA, 0xF2, 0xD2, 0x1E, 0xF9, 0x99, 0xB1,
+       0x6A, 0xBC, 0x9A, 0xE8, 0x44, 0x4A, 0x46, 0x9F,
+       0xC6, 0x5A, 0x90, 0x49, 0x0F, 0xDF, 0x3C, 0x0A,
+       0x07, 0x6E, 0xB9, 0x0D, 0x72, 0x90, 0x85, 0xF6,
+       0x0B, 0x41, 0x7D, 0x17, 0x5C, 0x44, 0xEF, 0xA0,
+       0xFC, 0x2C, 0x0A, 0xC5, 0x37, 0xC5, 0xBE, 0xC4,
+       0x6C, 0x2D, 0xBB, 0x63, 0xAB, 0x5B, 0xDB, 0x67,
+       0x9B, 0xAD, 0x90, 0x67, 0x9C, 0xBE, 0xDE, 0xF9,
+       0xE4, 0x9E, 0x22, 0x31, 0x60, 0xED, 0x9E, 0xC7,
+       0xD2, 0x48, 0xC9, 0x02, 0xAE, 0xBF, 0x8D, 0xA2,
+       0xA8, 0xF8, 0x9D, 0x8B, 0xB1, 0x1F, 0xDA, 0xE3
+};
+static const unsigned char RSA2048_IQ[] = {
+       0xB5, 0x48, 0xD4, 0x48, 0x5A, 0x33, 0xCD, 0x13,
+       0xFE, 0xC6, 0xF7, 0x01, 0x0A, 0x3E, 0x40, 0xA3,
+       0x45, 0x94, 0x6F, 0x85, 0xE4, 0x68, 0x66, 0xEC,
+       0x69, 0x6A, 0x3E, 0xE0, 0x62, 0x3F, 0x0C, 0xEF,
+       0x21, 0xCC, 0xDA, 0xAD, 0x75, 0x98, 0x12, 0xCA,
+       0x9E, 0x31, 0xDD, 0x95, 0x0D, 0xBD, 0x55, 0xEB,
+       0x92, 0xF7, 0x9E, 0xBD, 0xFC, 0x28, 0x35, 0x96,
+       0x31, 0xDC, 0x53, 0x80, 0xA3, 0x57, 0x89, 0x3C,
+       0x4A, 0xEC, 0x40, 0x75, 0x13, 0xAC, 0x4F, 0x36,
+       0x3A, 0x86, 0x9A, 0xA6, 0x58, 0xC9, 0xED, 0xCB,
+       0xD6, 0xBB, 0xB2, 0xD9, 0xAA, 0x04, 0xC4, 0xE8,
+       0x47, 0x3E, 0xBD, 0x14, 0x9B, 0x8F, 0x61, 0x70,
+       0x69, 0x66, 0x23, 0x62, 0x18, 0xE3, 0x52, 0x98,
+       0xE3, 0x22, 0xE9, 0x6F, 0xDA, 0x28, 0x68, 0x08,
+       0xB8, 0xB9, 0x8B, 0x97, 0x8B, 0x77, 0x3F, 0xCA,
+       0x9D, 0x9D, 0xBE, 0xD5, 0x2D, 0x3E, 0xC2, 0x11
+};
+
+static const br_rsa_public_key RSA2048_PK = {
+       (void *)RSA2048_N, sizeof RSA2048_N,
+       (void *)RSA2048_E, sizeof RSA2048_E
+};
+
+static const br_rsa_private_key RSA2048_SK = {
+       2048,
+       (void *)RSA2048_P, sizeof RSA2048_P,
+       (void *)RSA2048_Q, sizeof RSA2048_Q,
+       (void *)RSA2048_DP, sizeof RSA2048_DP,
+       (void *)RSA2048_DQ, sizeof RSA2048_DQ,
+       (void *)RSA2048_IQ, sizeof RSA2048_IQ
+};
+
+/*
+ * A 4096-bit RSA key, generated with OpenSSL.
+ */
+static const unsigned char RSA4096_N[] = {
+       0xAA, 0x17, 0x71, 0xBC, 0x92, 0x3E, 0xB5, 0xBD,
+       0x3E, 0x64, 0xCF, 0x03, 0x9B, 0x24, 0x65, 0x33,
+       0x5F, 0xB4, 0x47, 0x89, 0xE5, 0x63, 0xE4, 0xA0,
+       0x5A, 0x51, 0x95, 0x07, 0x73, 0xEE, 0x00, 0xF6,
+       0x3E, 0x31, 0x0E, 0xDA, 0x15, 0xC3, 0xAA, 0x21,
+       0x6A, 0xCD, 0xFF, 0x46, 0x6B, 0xDF, 0x0A, 0x7F,
+       0x8A, 0xC2, 0x25, 0x19, 0x47, 0x44, 0xD8, 0x52,
+       0xC1, 0x56, 0x25, 0x6A, 0xE0, 0xD2, 0x61, 0x11,
+       0x2C, 0xF7, 0x73, 0x9F, 0x5F, 0x74, 0xAA, 0xDD,
+       0xDE, 0xAF, 0x81, 0xF6, 0x0C, 0x1A, 0x3A, 0xF9,
+       0xC5, 0x47, 0x82, 0x75, 0x1D, 0x41, 0xF0, 0xB2,
+       0xFD, 0xBA, 0xE2, 0xA4, 0xA1, 0xB8, 0x32, 0x48,
+       0x06, 0x0D, 0x29, 0x2F, 0x44, 0x14, 0xF5, 0xAC,
+       0x54, 0x83, 0xC4, 0xB6, 0x85, 0x85, 0x9B, 0x1C,
+       0x05, 0x61, 0x28, 0x62, 0x24, 0xA8, 0xF0, 0xE6,
+       0x80, 0xA7, 0x91, 0xE8, 0xC7, 0x8E, 0x52, 0x17,
+       0xBE, 0xAF, 0xC6, 0x0A, 0xA3, 0xFB, 0xD1, 0x04,
+       0x15, 0x3B, 0x14, 0x35, 0xA5, 0x41, 0xF5, 0x30,
+       0xFE, 0xEF, 0x53, 0xA7, 0x89, 0x91, 0x78, 0x30,
+       0xBE, 0x3A, 0xB1, 0x4B, 0x2E, 0x4A, 0x0E, 0x25,
+       0x1D, 0xCF, 0x51, 0x54, 0x52, 0xF1, 0x88, 0x85,
+       0x36, 0x23, 0xDE, 0xBA, 0x66, 0x25, 0x60, 0x8D,
+       0x45, 0xD7, 0xD8, 0x10, 0x41, 0x64, 0xC7, 0x4B,
+       0xCE, 0x72, 0x13, 0xD7, 0x20, 0xF8, 0x2A, 0x74,
+       0xA5, 0x05, 0xF4, 0x5A, 0x90, 0xF4, 0x9C, 0xE7,
+       0xC9, 0xCF, 0x1E, 0xD5, 0x9C, 0xAC, 0xE5, 0x00,
+       0x83, 0x73, 0x9F, 0xE7, 0xC6, 0x93, 0xC0, 0x06,
+       0xA7, 0xB8, 0xF8, 0x46, 0x90, 0xC8, 0x78, 0x27,
+       0x2E, 0xCC, 0xC0, 0x2A, 0x20, 0xC5, 0xFC, 0x63,
+       0x22, 0xA1, 0xD6, 0x16, 0xAD, 0x9C, 0xD6, 0xFC,
+       0x7A, 0x6E, 0x9C, 0x98, 0x51, 0xEE, 0x6B, 0x6D,
+       0x8F, 0xEF, 0xCE, 0x7C, 0x5D, 0x16, 0xB0, 0xCE,
+       0x9C, 0xEE, 0x92, 0xCF, 0xB7, 0xEB, 0x41, 0x36,
+       0x3A, 0x6C, 0xF2, 0x0D, 0x26, 0x11, 0x2F, 0x6C,
+       0x27, 0x62, 0xA2, 0xCC, 0x63, 0x53, 0xBD, 0xFC,
+       0x9F, 0xBE, 0x9B, 0xBD, 0xE5, 0xA7, 0xDA, 0xD4,
+       0xF8, 0xED, 0x5E, 0x59, 0x2D, 0xAC, 0xCD, 0x13,
+       0xEB, 0xE5, 0x9E, 0x39, 0x82, 0x8B, 0xFD, 0xA8,
+       0xFB, 0xCB, 0x86, 0x27, 0xC7, 0x4B, 0x4C, 0xD0,
+       0xBA, 0x12, 0xD0, 0x76, 0x1A, 0xDB, 0x30, 0xC5,
+       0xB3, 0x2C, 0x4C, 0xC5, 0x32, 0x03, 0x05, 0x67,
+       0x8D, 0xD0, 0x14, 0x37, 0x59, 0x2B, 0xE3, 0x1C,
+       0x25, 0x3E, 0xA5, 0xE4, 0xF1, 0x0D, 0x34, 0xBB,
+       0xD5, 0xF6, 0x76, 0x45, 0x5B, 0x0F, 0x1E, 0x07,
+       0x0A, 0xBA, 0x9D, 0x71, 0x87, 0xDE, 0x45, 0x50,
+       0xE5, 0x0F, 0x32, 0xBB, 0x5C, 0x32, 0x2D, 0x40,
+       0xCD, 0x19, 0x95, 0x4E, 0xC5, 0x54, 0x3A, 0x9A,
+       0x46, 0x9B, 0x85, 0xFE, 0x53, 0xB7, 0xD8, 0x65,
+       0x6D, 0x68, 0x0C, 0xBB, 0xE3, 0x3D, 0x8E, 0x64,
+       0xBE, 0x27, 0x15, 0xAB, 0x12, 0x20, 0xD9, 0x84,
+       0xF5, 0x02, 0xE4, 0xBB, 0xDD, 0xAB, 0x59, 0x51,
+       0xF4, 0xE1, 0x79, 0xBE, 0xB8, 0xA3, 0x8E, 0xD1,
+       0x1C, 0xB0, 0xFA, 0x48, 0x76, 0xC2, 0x9D, 0x7A,
+       0x01, 0xA5, 0xAF, 0x8C, 0xBA, 0xAA, 0x4C, 0x06,
+       0x2B, 0x0A, 0x62, 0xF0, 0x79, 0x5B, 0x42, 0xFC,
+       0xF8, 0xBF, 0xD4, 0xDD, 0x62, 0x32, 0xE3, 0xCE,
+       0xF1, 0x2C, 0xE6, 0xED, 0xA8, 0x8A, 0x41, 0xA3,
+       0xC1, 0x1E, 0x07, 0xB6, 0x43, 0x10, 0x80, 0xB7,
+       0xF3, 0xD0, 0x53, 0x2A, 0x9A, 0x98, 0xA7, 0x4F,
+       0x9E, 0xA3, 0x3E, 0x1B, 0xDA, 0x93, 0x15, 0xF2,
+       0xF4, 0x20, 0xA5, 0xA8, 0x4F, 0x8A, 0xBA, 0xED,
+       0xB1, 0x17, 0x6C, 0x0F, 0xD9, 0x8F, 0x38, 0x11,
+       0xF3, 0xD9, 0x5E, 0x88, 0xA1, 0xA1, 0x82, 0x8B,
+       0x30, 0xD7, 0xC6, 0xCE, 0x4E, 0x30, 0x55, 0x57
+};
+static const unsigned char RSA4096_E[] = {
+       0x01, 0x00, 0x01
+};
+static const unsigned char RSA4096_P[] = {
+       0xD3, 0x7A, 0x22, 0xD8, 0x9B, 0xBF, 0x42, 0xB4,
+       0x53, 0x04, 0x10, 0x6A, 0x84, 0xFD, 0x7C, 0x1D,
+       0xF6, 0xF4, 0x10, 0x65, 0xAA, 0xE5, 0xE1, 0x4E,
+       0xB4, 0x37, 0xF7, 0xAC, 0xF7, 0xD3, 0xB2, 0x3B,
+       0xFE, 0xE7, 0x63, 0x42, 0xE9, 0xF0, 0x3C, 0xE0,
+       0x42, 0xB4, 0xBB, 0x09, 0xD0, 0xB2, 0x7C, 0x70,
+       0xA4, 0x11, 0x97, 0x90, 0x01, 0xD0, 0x0E, 0x7B,
+       0xAF, 0x7D, 0x30, 0x4E, 0x6B, 0x3A, 0xCC, 0x50,
+       0x4E, 0xAF, 0x2F, 0xC3, 0xC2, 0x4F, 0x7E, 0xC5,
+       0xB3, 0x76, 0x33, 0xFB, 0xA7, 0xB1, 0x96, 0xA5,
+       0x46, 0x41, 0xC6, 0xDA, 0x5A, 0xFD, 0x17, 0x0A,
+       0x6A, 0x86, 0x54, 0x83, 0xE1, 0x57, 0xE7, 0xAF,
+       0x8C, 0x42, 0xE5, 0x39, 0xF2, 0xC7, 0xFC, 0x4A,
+       0x3D, 0x3C, 0x94, 0x89, 0xC2, 0xC6, 0x2D, 0x0A,
+       0x5F, 0xD0, 0x21, 0x23, 0x5C, 0xC9, 0xC8, 0x44,
+       0x8A, 0x96, 0x72, 0x4D, 0x96, 0xC6, 0x17, 0x0C,
+       0x36, 0x43, 0x7F, 0xD8, 0xA0, 0x7A, 0x31, 0x7E,
+       0xCE, 0x13, 0xE3, 0x13, 0x2E, 0xE0, 0x91, 0xC2,
+       0x61, 0x13, 0x16, 0x8D, 0x99, 0xCB, 0xA9, 0x2C,
+       0x4D, 0x9D, 0xDD, 0x1D, 0x03, 0xE7, 0xA7, 0x50,
+       0xF4, 0x16, 0x43, 0xB1, 0x7F, 0x99, 0x61, 0x3F,
+       0xA5, 0x59, 0x91, 0x16, 0xC3, 0x06, 0x63, 0x59,
+       0xE9, 0xDA, 0xB5, 0x06, 0x2E, 0x0C, 0xD9, 0xAB,
+       0x93, 0x89, 0x12, 0x82, 0xFB, 0x90, 0xD9, 0x30,
+       0x60, 0xF7, 0x35, 0x2D, 0x18, 0x78, 0xEB, 0x2B,
+       0xA1, 0x06, 0x67, 0x37, 0xDE, 0x72, 0x20, 0xD2,
+       0x80, 0xE5, 0x2C, 0xD7, 0x5E, 0xC7, 0x67, 0x2D,
+       0x40, 0xE7, 0x7A, 0xCF, 0x4A, 0x69, 0x9D, 0xA7,
+       0x90, 0x9F, 0x3B, 0xDF, 0x07, 0x97, 0x64, 0x69,
+       0x06, 0x4F, 0xBA, 0xF4, 0xE5, 0xBD, 0x71, 0x60,
+       0x36, 0xB7, 0xA3, 0xDE, 0x76, 0xC5, 0x38, 0xD7,
+       0x1D, 0x9A, 0xFC, 0x36, 0x3D, 0x3B, 0xDC, 0xCF
+};
+static const unsigned char RSA4096_Q[] = {
+       0xCD, 0xE6, 0xC6, 0xA6, 0x42, 0x4C, 0x45, 0x65,
+       0x8B, 0x85, 0x76, 0xFC, 0x21, 0xB6, 0x57, 0x79,
+       0x3C, 0xE4, 0xE3, 0x85, 0x55, 0x2F, 0x59, 0xD3,
+       0x3F, 0x74, 0xAF, 0x9F, 0x11, 0x04, 0x10, 0x8B,
+       0xF9, 0x5F, 0x4D, 0x25, 0xEE, 0x20, 0xF9, 0x69,
+       0x3B, 0x02, 0xB6, 0x43, 0x0D, 0x0C, 0xED, 0x30,
+       0x31, 0x57, 0xE7, 0x9A, 0x57, 0x24, 0x6B, 0x4A,
+       0x5E, 0xA2, 0xBF, 0xD4, 0x47, 0x7D, 0xFA, 0x78,
+       0x51, 0x86, 0x80, 0x68, 0x85, 0x7C, 0x7B, 0x08,
+       0x4A, 0x35, 0x24, 0x4F, 0x8B, 0x24, 0x49, 0xF8,
+       0x16, 0x06, 0x9C, 0x57, 0x4E, 0x94, 0x4C, 0xBD,
+       0x6E, 0x53, 0x52, 0xC9, 0xC1, 0x64, 0x43, 0x22,
+       0x1E, 0xDD, 0xEB, 0xAC, 0x90, 0x58, 0xCA, 0xBA,
+       0x9C, 0xAC, 0xCF, 0xDD, 0x08, 0x6D, 0xB7, 0x31,
+       0xDB, 0x0D, 0x83, 0xE6, 0x50, 0xA6, 0x69, 0xB1,
+       0x1C, 0x68, 0x92, 0xB4, 0xB5, 0x76, 0xDE, 0xBD,
+       0x4F, 0xA5, 0x30, 0xED, 0x23, 0xFF, 0xE5, 0x80,
+       0x21, 0xAB, 0xED, 0xE6, 0xDC, 0x32, 0x3D, 0xF7,
+       0x45, 0xB8, 0x19, 0x3D, 0x8E, 0x15, 0x7C, 0xE5,
+       0x0D, 0xC8, 0x9B, 0x7D, 0x1F, 0x7C, 0x14, 0x14,
+       0x41, 0x09, 0xA7, 0xEB, 0xFB, 0xD9, 0x5F, 0x9A,
+       0x94, 0xB6, 0xD5, 0xA0, 0x2C, 0xAF, 0xB5, 0xEF,
+       0x5C, 0x5A, 0x8E, 0x34, 0xA1, 0x8F, 0xEB, 0x38,
+       0x0F, 0x31, 0x6E, 0x45, 0x21, 0x7A, 0xAA, 0xAF,
+       0x6C, 0xB1, 0x8E, 0xB2, 0xB9, 0xD4, 0x1E, 0xEF,
+       0x66, 0xD8, 0x4E, 0x3D, 0xF2, 0x0C, 0xF1, 0xBA,
+       0xFB, 0xA9, 0x27, 0xD2, 0x45, 0x54, 0x83, 0x4B,
+       0x10, 0xC4, 0x9A, 0x32, 0x9C, 0xC7, 0x9A, 0xCF,
+       0x4E, 0xBF, 0x07, 0xFC, 0x27, 0xB7, 0x96, 0x1D,
+       0xDE, 0x9D, 0xE4, 0x84, 0x68, 0x00, 0x9A, 0x9F,
+       0x3D, 0xE6, 0xC7, 0x26, 0x11, 0x48, 0x79, 0xFA,
+       0x09, 0x76, 0xC8, 0x25, 0x3A, 0xE4, 0x70, 0xF9
+};
+static const unsigned char RSA4096_DP[] = {
+       0x5C, 0xE3, 0x3E, 0xBF, 0x09, 0xD9, 0xFE, 0x80,
+       0x9A, 0x1E, 0x24, 0xDF, 0xC4, 0xBE, 0x5A, 0x70,
+       0x06, 0xF2, 0xB8, 0xE9, 0x0F, 0x21, 0x9D, 0xCF,
+       0x26, 0x15, 0x97, 0x32, 0x60, 0x40, 0x99, 0xFF,
+       0x04, 0x3D, 0xBA, 0x39, 0xBF, 0xEB, 0x87, 0xB1,
+       0xB1, 0x5B, 0x14, 0xF4, 0x80, 0xB8, 0x85, 0x34,
+       0x2C, 0xBC, 0x95, 0x67, 0xE9, 0x83, 0xEB, 0x78,
+       0xA4, 0x62, 0x46, 0x7F, 0x8B, 0x55, 0xEE, 0x3C,
+       0x2F, 0xF3, 0x7E, 0xF5, 0x6B, 0x39, 0xE3, 0xA3,
+       0x0E, 0xEA, 0x92, 0x76, 0xAC, 0xF7, 0xB2, 0x05,
+       0xB2, 0x50, 0x5D, 0xF9, 0xB7, 0x11, 0x87, 0xB7,
+       0x49, 0x86, 0xEB, 0x44, 0x6A, 0x0C, 0x64, 0x75,
+       0x95, 0x14, 0x24, 0xFF, 0x49, 0x06, 0x52, 0x68,
+       0x81, 0x71, 0x44, 0x85, 0x26, 0x0A, 0x49, 0xEA,
+       0x4E, 0x9F, 0x6A, 0x8E, 0xCF, 0xC8, 0xC9, 0xB0,
+       0x61, 0x77, 0x27, 0x89, 0xB0, 0xFA, 0x1D, 0x51,
+       0x7D, 0xDC, 0x34, 0x21, 0x80, 0x8B, 0x6B, 0x86,
+       0x19, 0x1A, 0x5F, 0x19, 0x23, 0xF3, 0xFB, 0xD1,
+       0xF7, 0x35, 0x9D, 0x28, 0x61, 0x2F, 0x35, 0x85,
+       0x82, 0x2A, 0x1E, 0xDF, 0x09, 0xC2, 0x0C, 0x99,
+       0xE0, 0x3C, 0x8F, 0x4B, 0x3D, 0x92, 0xAF, 0x46,
+       0x77, 0x68, 0x59, 0xF4, 0x37, 0x81, 0x6C, 0xCE,
+       0x27, 0x8B, 0xAB, 0x0B, 0xA5, 0xDA, 0x7B, 0x19,
+       0x83, 0xDA, 0x27, 0x49, 0x65, 0x1A, 0x00, 0x6B,
+       0xE1, 0x8B, 0x73, 0xCD, 0xF4, 0xFB, 0xD7, 0xBF,
+       0xF8, 0x20, 0x89, 0xE1, 0xDE, 0x51, 0x1E, 0xDD,
+       0x97, 0x44, 0x12, 0x68, 0x1E, 0xF7, 0x52, 0xF8,
+       0x6B, 0x93, 0xC1, 0x3B, 0x9F, 0xA1, 0xB8, 0x5F,
+       0xCB, 0x84, 0x45, 0x95, 0xF7, 0x0D, 0xA6, 0x4B,
+       0x03, 0x3C, 0xAE, 0x0F, 0xB7, 0x81, 0x78, 0x75,
+       0x1C, 0x53, 0x99, 0x24, 0xB3, 0xE2, 0x78, 0xCE,
+       0xF3, 0xF0, 0x09, 0x6C, 0x01, 0x85, 0x73, 0xBD
+};
+static const unsigned char RSA4096_DQ[] = {
+       0xCD, 0x88, 0xAC, 0x8B, 0x92, 0x6A, 0xA8, 0x6B,
+       0x71, 0x16, 0xCD, 0x6B, 0x6A, 0x0B, 0xA6, 0xCD,
+       0xF3, 0x27, 0x58, 0xA6, 0xE4, 0x1D, 0xDC, 0x40,
+       0xAF, 0x7B, 0x3F, 0x44, 0x3D, 0xAC, 0x1D, 0x08,
+       0x5C, 0xE9, 0xF1, 0x0D, 0x07, 0xE4, 0x0A, 0x94,
+       0x2C, 0xBF, 0xCC, 0x48, 0xAA, 0x62, 0x58, 0xF2,
+       0x5E, 0x8F, 0x2D, 0x36, 0x37, 0xFE, 0xB6, 0xCB,
+       0x0A, 0x24, 0xD3, 0xF0, 0x87, 0x5D, 0x0E, 0x05,
+       0xC4, 0xFB, 0xCA, 0x7A, 0x8B, 0xA5, 0x72, 0xFB,
+       0x17, 0x78, 0x6C, 0xC2, 0xAA, 0x56, 0x93, 0x2F,
+       0xFE, 0x6C, 0xA2, 0xEB, 0xD4, 0x18, 0xDD, 0x71,
+       0xCB, 0x0B, 0x89, 0xFC, 0xB3, 0xFB, 0xED, 0xB7,
+       0xC5, 0xB0, 0x29, 0x6D, 0x9C, 0xB9, 0xC5, 0xC4,
+       0xFA, 0x58, 0xD7, 0x36, 0x01, 0x0F, 0xE4, 0x6A,
+       0xF4, 0x0B, 0x4D, 0xBB, 0x3E, 0x8E, 0x9F, 0xBA,
+       0x98, 0x6D, 0x1A, 0xE5, 0x20, 0xAF, 0x84, 0x30,
+       0xDD, 0xAC, 0x3C, 0x66, 0xBC, 0x24, 0xD9, 0x67,
+       0x4A, 0x35, 0x61, 0xC9, 0xAD, 0xCC, 0xC9, 0x66,
+       0x68, 0x46, 0x19, 0x8C, 0x04, 0xA5, 0x16, 0x83,
+       0x5F, 0x7A, 0xFD, 0x1B, 0xAD, 0xAE, 0x22, 0x2D,
+       0x05, 0xAF, 0x29, 0xDC, 0xBB, 0x0E, 0x86, 0x0C,
+       0xBC, 0x9E, 0xB6, 0x28, 0xA9, 0xF2, 0xCC, 0x5E,
+       0x1F, 0x86, 0x95, 0xA5, 0x9C, 0x11, 0x19, 0xF0,
+       0x5F, 0xDA, 0x2C, 0x04, 0xFE, 0x22, 0x80, 0xF7,
+       0x94, 0x3C, 0xBA, 0x01, 0x56, 0xD6, 0x93, 0xFA,
+       0xCE, 0x62, 0xE5, 0xD7, 0x98, 0x23, 0xAB, 0xB9,
+       0xC7, 0x35, 0x57, 0xF6, 0xE2, 0x16, 0x36, 0xE9,
+       0x5B, 0xD7, 0xA5, 0x45, 0x18, 0x93, 0x77, 0xC9,
+       0xB1, 0x05, 0xA8, 0x66, 0xE1, 0x0E, 0xB5, 0xDF,
+       0x23, 0x35, 0xE1, 0xC2, 0xFA, 0x3E, 0x80, 0x1A,
+       0xAD, 0xA4, 0x0C, 0xEF, 0xC7, 0x18, 0xDE, 0x09,
+       0xE6, 0x20, 0x98, 0x31, 0xF1, 0xD3, 0xCF, 0xA1
+};
+static const unsigned char RSA4096_IQ[] = {
+       0x76, 0xD7, 0x75, 0xDF, 0xA3, 0x0C, 0x9D, 0x64,
+       0x6E, 0x00, 0x82, 0x2E, 0x5C, 0x5E, 0x43, 0xC4,
+       0xD2, 0x28, 0xB0, 0xB1, 0xA8, 0xD8, 0x26, 0x91,
+       0xA0, 0xF5, 0xC8, 0x69, 0xFF, 0x24, 0x33, 0xAB,
+       0x67, 0xC7, 0xA3, 0xAE, 0xBB, 0x17, 0x27, 0x5B,
+       0x5A, 0xCD, 0x67, 0xA3, 0x70, 0x91, 0x9E, 0xD5,
+       0xF1, 0x97, 0x00, 0x0A, 0x30, 0x64, 0x3D, 0x9B,
+       0xBF, 0xB5, 0x8C, 0xAC, 0xC7, 0x20, 0x0A, 0xD2,
+       0x76, 0x36, 0x36, 0x5D, 0xE4, 0xAC, 0x5D, 0xBC,
+       0x44, 0x32, 0xB0, 0x76, 0x33, 0x40, 0xDD, 0x29,
+       0x22, 0xE0, 0xFF, 0x55, 0x4C, 0xCE, 0x3F, 0x43,
+       0x34, 0x95, 0x94, 0x7C, 0x22, 0x0D, 0xAB, 0x20,
+       0x38, 0x70, 0xC3, 0x4A, 0x19, 0xCF, 0x81, 0xCE,
+       0x79, 0x28, 0x6C, 0xC2, 0xA3, 0xB3, 0x48, 0x20,
+       0x2D, 0x3E, 0x74, 0x45, 0x2C, 0xAA, 0x9F, 0xA5,
+       0xC2, 0xE3, 0x2D, 0x41, 0x95, 0xBD, 0x78, 0xAB,
+       0x6A, 0xA8, 0x7A, 0x45, 0x52, 0xE2, 0x66, 0xE7,
+       0x6C, 0x38, 0x03, 0xA5, 0xDA, 0xAD, 0x94, 0x3C,
+       0x6A, 0xA1, 0xA2, 0xD5, 0xCD, 0xDE, 0x05, 0xCC,
+       0x6E, 0x3D, 0x8A, 0xF6, 0x9A, 0xA5, 0x0F, 0xA9,
+       0x18, 0xC4, 0xF9, 0x9C, 0x2F, 0xB3, 0xF1, 0x30,
+       0x38, 0x60, 0x69, 0x09, 0x67, 0x2C, 0xE9, 0x42,
+       0x68, 0x3C, 0x70, 0x32, 0x1A, 0x44, 0x32, 0x02,
+       0x82, 0x9F, 0x60, 0xE8, 0xA4, 0x42, 0x74, 0xA2,
+       0xA2, 0x5A, 0x99, 0xDC, 0xC8, 0xCA, 0x15, 0x4D,
+       0xFF, 0xF1, 0x8A, 0x23, 0xD8, 0xD3, 0xB1, 0x9A,
+       0xB4, 0x0B, 0xBB, 0xE8, 0x38, 0x74, 0x0C, 0x52,
+       0xC7, 0x8B, 0x63, 0x4C, 0xEA, 0x7D, 0x5F, 0x58,
+       0x34, 0x53, 0x3E, 0x23, 0x10, 0xBB, 0x60, 0x6B,
+       0x52, 0x9D, 0x89, 0x9F, 0xF0, 0x5F, 0xCE, 0xB3,
+       0x9C, 0x0E, 0x75, 0x0F, 0x87, 0xF6, 0x66, 0xA5,
+       0x4C, 0x94, 0x84, 0xFE, 0x94, 0xB9, 0x04, 0xB7
+};
+
+static const br_rsa_public_key RSA4096_PK = {
+       (void *)RSA4096_N, sizeof RSA4096_N,
+       (void *)RSA4096_E, sizeof RSA4096_E
+};
+
+static const br_rsa_private_key RSA4096_SK = {
+       4096,
+       (void *)RSA4096_P, sizeof RSA4096_P,
+       (void *)RSA4096_Q, sizeof RSA4096_Q,
+       (void *)RSA4096_DP, sizeof RSA4096_DP,
+       (void *)RSA4096_DQ, sizeof RSA4096_DQ,
+       (void *)RSA4096_IQ, sizeof RSA4096_IQ
+};
+
 static void
 test_RSA_core(const char *name, br_rsa_public fpub, br_rsa_private fpriv)
 {
-       unsigned char t1[128], t2[128], t3[128];
+       unsigned char t1[512], t2[512], t3[512];
+       size_t len;
 
        printf("Test %s: ", name);
        fflush(stdout);
@@ -4731,19 +5134,104 @@ test_RSA_core(const char *name, br_rsa_public fpub, br_rsa_private fpriv)
        /*
         * A KAT test (computed with OpenSSL).
         */
-       hextobin(t1, "45A3DC6A106BCD3BD0E48FB579643AA3FF801E5903E80AA9B43A695A8E7F454E93FA208B69995FF7A6D5617C2FEB8E546375A664977A48931842AAE796B5A0D64393DCA35F3490FC157F5BD83B9D58C2F7926E6AE648A2BD96CAB8FCCD3D35BB11424AD47D973FF6D69CA774841AEC45DFAE99CCF79893E7047FDE6CB00AA76D");
+       len = hextobin(t1, "45A3DC6A106BCD3BD0E48FB579643AA3FF801E5903E80AA9B43A695A8E7F454E93FA208B69995FF7A6D5617C2FEB8E546375A664977A48931842AAE796B5A0D64393DCA35F3490FC157F5BD83B9D58C2F7926E6AE648A2BD96CAB8FCCD3D35BB11424AD47D973FF6D69CA774841AEC45DFAE99CCF79893E7047FDE6CB00AA76D");
        hextobin(t2, "0001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF003021300906052B0E03021A05000414A94A8FE5CCB19BA61C4C0873D391E987982FBBD3");
-       memcpy(t3, t1, sizeof t1);
-       if (!fpub(t3, sizeof t3, &RSA_PK)) {
-               fprintf(stderr, "RSA public operation failed\n");
+       memcpy(t3, t1, len);
+       if (!fpub(t3, len, &RSA_PK)) {
+               fprintf(stderr, "RSA public operation failed (1)\n");
                exit(EXIT_FAILURE);
        }
-       check_equals("KAT RSA pub", t2, t3, sizeof t2);
+       check_equals("KAT RSA pub", t2, t3, len);
        if (!fpriv(t3, &RSA_SK)) {
-               fprintf(stderr, "RSA private operation failed\n");
+               fprintf(stderr, "RSA private operation failed (1)\n");
+               exit(EXIT_FAILURE);
+       }
+       check_equals("KAT RSA priv (1)", t1, t3, len);
+
+       /*
+        * Another KAT test, with a (fake) hash value slightly different
+        * (last byte is 0xD9 instead of 0xD3).
+        */
+       len = hextobin(t1, "32C2DB8B2C73BBCA9960CB3F11FEDEE7B699359EF2EEC3A632E56B7FF3DE2F371E5179BAB03F17E0BB20D2891ACAB679F95DA9B43A01DAAD192FADD25D8ACCF1498EC80F5BBCAC88EA59D60E3BC9D3CE27743981DE42385FFFFF04DD2D716E1A46C04A28ECAF6CD200DAB81083A830D61538D69BB39A183107BD50302AA6BC28");
+       hextobin(t2, "0001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF003021300906052B0E03021A05000414A94A8FE5CCB19BA61C4C0873D391E987982FBBD9");
+       memcpy(t3, t1, len);
+       if (!fpub(t3, len, &RSA_PK)) {
+               fprintf(stderr, "RSA public operation failed (2)\n");
+               exit(EXIT_FAILURE);
+       }
+       check_equals("KAT RSA pub", t2, t3, len);
+       if (!fpriv(t3, &RSA_SK)) {
+               fprintf(stderr, "RSA private operation failed (2)\n");
+               exit(EXIT_FAILURE);
+       }
+       check_equals("KAT RSA priv (2)", t1, t3, len);
+
+       /*
+        * Third KAT vector is invalid, because the encrypted value is
+        * out of range: instead of x, value is x+n (where n is the
+        * modulus). Mathematically, this still works, but implementations
+        * are supposed to reject such cases.
+        */
+       len = hextobin(t1, "F27781B9B3B358583A24F9BA6B34EE98B67A5AE8D8D4FA567BA773EB6B85EF88848680640A1E2F5FD117876E5FB928B64C6EFC7E03632A3F4C941E15657C0C705F3BB8D0B03A0249143674DB1FE6E5406D690BF2DA76EA7FF3AC6FCE12C7801252FAD52D332BE4AB41F9F8CF1728CDF98AB8E8C20E0C350E4F707A6402C01E0B");
+       hextobin(t2, "BFB6A62E873F9C8DA0C42E7B59360FB0FFE12549E5E636B048C2086B77A7C051663506A959DF177F15F6B4E544EE723C531152C9C9614F923364704307F13F7F15ACF0C1547D55C029DC9ECCE41D117245F4D270FC34B21FF3AD6AEFE58633281540902F547F79F3461F44D33CCB2D094231ADCC76BE25511B4513BB70491DBC");
+       memcpy(t3, t1, len);
+       if (fpub(t3, len, &RSA_PK)) {
+               size_t u;
+               fprintf(stderr, "RSA public operation should have failed"
+                       " (value out of range)\n");
+               fprintf(stderr, "x = ");
+               for (u = 0; u < len; u ++) {
+                       fprintf(stderr, "%02X", t3[u]);
+               }
+               fprintf(stderr, "\n");
+               exit(EXIT_FAILURE);
+       }
+       memcpy(t3, t2, len);
+       if (fpriv(t3, &RSA_SK)) {
+               size_t u;
+               fprintf(stderr, "RSA private operation should have failed"
+                       " (value out of range)\n");
+               fprintf(stderr, "x = ");
+               for (u = 0; u < len; u ++) {
+                       fprintf(stderr, "%02X", t3[u]);
+               }
+               fprintf(stderr, "\n");
+               exit(EXIT_FAILURE);
+       }
+
+       /*
+        * RSA-2048 test vector.
+        */
+       len = hextobin(t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
+       hextobin(t2, "0001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF003031300D060960864801650304020105000420A5A0A792A09438811584A68E240C6C89F1FB1C53C0C86E270B942635F4F6B24A");
+       memcpy(t3, t1, len);
+       if (!fpub(t3, len, &RSA2048_PK)) {
+               fprintf(stderr, "RSA public operation failed (2048)\n");
+               exit(EXIT_FAILURE);
+       }
+       check_equals("KAT RSA pub", t2, t3, len);
+       if (!fpriv(t3, &RSA2048_SK)) {
+               fprintf(stderr, "RSA private operation failed (2048)\n");
+               exit(EXIT_FAILURE);
+       }
+       check_equals("KAT RSA priv (2048)", t1, t3, len);
+
+       /*
+        * RSA-4096 test vector.
+        */
+       len = hextobin(t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
+       hextobin(t2, "0001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF003031300D0609608648016503040201050004205B60DD5AD5B3C62E0DA25FD0D8CB26325E1CE32CC9ED234B288235BCCF6ED2C8");
+       memcpy(t3, t1, len);
+       if (!fpub(t3, len, &RSA4096_PK)) {
+               fprintf(stderr, "RSA public operation failed (4096)\n");
+               exit(EXIT_FAILURE);
+       }
+       check_equals("KAT RSA pub", t2, t3, len);
+       if (!fpriv(t3, &RSA4096_SK)) {
+               fprintf(stderr, "RSA private operation failed (4096)\n");
                exit(EXIT_FAILURE);
        }
-       check_equals("KAT RSA priv", t1, t3, sizeof t1);
+       check_equals("KAT RSA priv (4096)", t1, t3, len);
 
        printf("done.\n");
        fflush(stdout);