[crypto] Add RFC 3526 FFDHE key exchange algorithms

The family of finite fields defined in RFC 7919 is almost identical to
that defined in RFC 3526, with the difference being that the older
standard uses the constant "pi" rather than "e".

Extend the definition of an FFDHE group to include a pointer to the
group constant, add the value of "pi", and define the modp2048,
modp3072, and modp4096 FFDHE groups.

Signed-off-by: Michael Brown <mcb30@ipxe.org>

diff --git a/src/crypto/ffdhe.c b/src/crypto/ffdhe.c
index 41bd90813bbc8ad2258dd132d9b7de85167e308a..d6f9449bef1c19d3fb7588ff8ed177fe771fbda3 100644 (file)
--- a/src/crypto/ffdhe.c
+++ b/src/crypto/ffdhe.c
@@ -39,6 +39,10 @@ FILE_SECBOOT ( PERMITTED );
  * FFDHE_GROUP() declarations.  Doing so would approximately double
  * the space requirements for both read-only data (from 0.5kB to 1kB)
  * and for uninitialised data (from 3.5kB to 7kB).
+ *
+ * RFC 3526 defines an almost identical family of finite fields all
+ * constructed from the constant "pi", which may be used by older TLS
+ * servers.
  */
 
 #include <stdint.h>
@@ -46,8 +50,24 @@ FILE_SECBOOT ( PERMITTED );
 #include <errno.h>
 #include <ipxe/ffdhe.h>
 
-/** Euler's number ("e") */
-static const uint8_t euler[] = {
+/** Maximum length of FFDHE prime modulus */
+#define FFDHE_LEN 4096
+
+/** Maximum length of group constant portion of FFDHE prime modulus */
+#define FFDHE_CONSTANT_LEN \
+       ( FFDHE_LEN - 8 /* high */ - 4 /* lsb32 */ - 8 /* low */ )
+
+/** An FFDHE prime modulus */
+#define ffdhe_modulus_t( len )                                           \
+       struct {                                                          \
+               uint64_t high;                                            \
+               uint8_t constant[ len + FFDHE_CONSTANT_LEN - FFDHE_LEN ]; \
+               uint32_t lsb32;                                           \
+               uint64_t low;                                             \
+       } __attribute__ (( packed ))
+
+/** Euler's constant ("e") */
+static const uint8_t euler[FFDHE_CONSTANT_LEN] = {
        0xad, 0xf8, 0x54, 0x58, 0xa2, 0xbb, 0x4a, 0x9a, 0xaf, 0xdc, 0x56,
        0x20, 0x27, 0x3d, 0x3c, 0xf1, 0xd8, 0xb9, 0xc5, 0x83, 0xce, 0x2d,
        0x36, 0x95, 0xa9, 0xe1, 0x36, 0x41, 0x14, 0x64, 0x33, 0xfb, 0xcc,
@@ -95,20 +115,54 @@ static const uint8_t euler[] = {
        0xf4, 0x41, 0x82, 0xe1, 0xc6, 0x8a, 0x00, 0x7e
 };
 
-/** FFDHE non-Euler length */
-#define FFDHE_PAD_LEN ( 8 /* high */ + 4 /* lsb32 */ + 8 /* low */ )
-
-/** An FFDHE prime modulus */
-#define ffdhe_modulus_t( len )                                         \
-       struct {                                                        \
-               uint64_t high;                                          \
-               uint8_t euler[ len - FFDHE_PAD_LEN ];                   \
-               uint32_t lsb32;                                         \
-               uint64_t low;                                           \
-       } __attribute__ (( packed ))
-
-/** Maximum length of big integer values */
-#define FFDHE_LEN ( sizeof ( euler ) + FFDHE_PAD_LEN )
+/** Constant "pi" */
+static const uint8_t pi[FFDHE_CONSTANT_LEN] = {
+       0xc9, 0x0f, 0xda, 0xa2, 0x21, 0x68, 0xc2, 0x34, 0xc4, 0xc6, 0x62,
+       0x8b, 0x80, 0xdc, 0x1c, 0xd1, 0x29, 0x02, 0x4e, 0x08, 0x8a, 0x67,
+       0xcc, 0x74, 0x02, 0x0b, 0xbe, 0xa6, 0x3b, 0x13, 0x9b, 0x22, 0x51,
+       0x4a, 0x08, 0x79, 0x8e, 0x34, 0x04, 0xdd, 0xef, 0x95, 0x19, 0xb3,
+       0xcd, 0x3a, 0x43, 0x1b, 0x30, 0x2b, 0x0a, 0x6d, 0xf2, 0x5f, 0x14,
+       0x37, 0x4f, 0xe1, 0x35, 0x6d, 0x6d, 0x51, 0xc2, 0x45, 0xe4, 0x85,
+       0xb5, 0x76, 0x62, 0x5e, 0x7e, 0xc6, 0xf4, 0x4c, 0x42, 0xe9, 0xa6,
+       0x37, 0xed, 0x6b, 0x0b, 0xff, 0x5c, 0xb6, 0xf4, 0x06, 0xb7, 0xed,
+       0xee, 0x38, 0x6b, 0xfb, 0x5a, 0x89, 0x9f, 0xa5, 0xae, 0x9f, 0x24,
+       0x11, 0x7c, 0x4b, 0x1f, 0xe6, 0x49, 0x28, 0x66, 0x51, 0xec, 0xe4,
+       0x5b, 0x3d, 0xc2, 0x00, 0x7c, 0xb8, 0xa1, 0x63, 0xbf, 0x05, 0x98,
+       0xda, 0x48, 0x36, 0x1c, 0x55, 0xd3, 0x9a, 0x69, 0x16, 0x3f, 0xa8,
+       0xfd, 0x24, 0xcf, 0x5f, 0x83, 0x65, 0x5d, 0x23, 0xdc, 0xa3, 0xad,
+       0x96, 0x1c, 0x62, 0xf3, 0x56, 0x20, 0x85, 0x52, 0xbb, 0x9e, 0xd5,
+       0x29, 0x07, 0x70, 0x96, 0x96, 0x6d, 0x67, 0x0c, 0x35, 0x4e, 0x4a,
+       0xbc, 0x98, 0x04, 0xf1, 0x74, 0x6c, 0x08, 0xca, 0x18, 0x21, 0x7c,
+       0x32, 0x90, 0x5e, 0x46, 0x2e, 0x36, 0xce, 0x3b, 0xe3, 0x9e, 0x77,
+       0x2c, 0x18, 0x0e, 0x86, 0x03, 0x9b, 0x27, 0x83, 0xa2, 0xec, 0x07,
+       0xa2, 0x8f, 0xb5, 0xc5, 0x5d, 0xf0, 0x6f, 0x4c, 0x52, 0xc9, 0xde,
+       0x2b, 0xcb, 0xf6, 0x95, 0x58, 0x17, 0x18, 0x39, 0x95, 0x49, 0x7c,
+       0xea, 0x95, 0x6a, 0xe5, 0x15, 0xd2, 0x26, 0x18, 0x98, 0xfa, 0x05,
+       0x10, 0x15, 0x72, 0x8e, 0x5a, 0x8a, 0xaa, 0xc4, 0x2d, 0xad, 0x33,
+       0x17, 0x0d, 0x04, 0x50, 0x7a, 0x33, 0xa8, 0x55, 0x21, 0xab, 0xdf,
+       0x1c, 0xba, 0x64, 0xec, 0xfb, 0x85, 0x04, 0x58, 0xdb, 0xef, 0x0a,
+       0x8a, 0xea, 0x71, 0x57, 0x5d, 0x06, 0x0c, 0x7d, 0xb3, 0x97, 0x0f,
+       0x85, 0xa6, 0xe1, 0xe4, 0xc7, 0xab, 0xf5, 0xae, 0x8c, 0xdb, 0x09,
+       0x33, 0xd7, 0x1e, 0x8c, 0x94, 0xe0, 0x4a, 0x25, 0x61, 0x9d, 0xce,
+       0xe3, 0xd2, 0x26, 0x1a, 0xd2, 0xee, 0x6b, 0xf1, 0x2f, 0xfa, 0x06,
+       0xd9, 0x8a, 0x08, 0x64, 0xd8, 0x76, 0x02, 0x73, 0x3e, 0xc8, 0x6a,
+       0x64, 0x52, 0x1f, 0x2b, 0x18, 0x17, 0x7b, 0x20, 0x0c, 0xbb, 0xe1,
+       0x17, 0x57, 0x7a, 0x61, 0x5d, 0x6c, 0x77, 0x09, 0x88, 0xc0, 0xba,
+       0xd9, 0x46, 0xe2, 0x08, 0xe2, 0x4f, 0xa0, 0x74, 0xe5, 0xab, 0x31,
+       0x43, 0xdb, 0x5b, 0xfc, 0xe0, 0xfd, 0x10, 0x8e, 0x4b, 0x82, 0xd1,
+       0x20, 0xa9, 0x21, 0x08, 0x01, 0x1a, 0x72, 0x3c, 0x12, 0xa7, 0x87,
+       0xe6, 0xd7, 0x88, 0x71, 0x9a, 0x10, 0xbd, 0xba, 0x5b, 0x26, 0x99,
+       0xc3, 0x27, 0x18, 0x6a, 0xf4, 0xe2, 0x3c, 0x1a, 0x94, 0x68, 0x34,
+       0xb6, 0x15, 0x0b, 0xda, 0x25, 0x83, 0xe9, 0xca, 0x2a, 0xd4, 0x4c,
+       0xe8, 0xdb, 0xbb, 0xc2, 0xdb, 0x04, 0xde, 0x8e, 0xf9, 0x2e, 0x8e,
+       0xfc, 0x14, 0x1f, 0xbe, 0xca, 0xa6, 0x28, 0x7c, 0x59, 0x47, 0x4e,
+       0x6b, 0xc0, 0x5d, 0x99, 0xb2, 0x96, 0x4f, 0xa0, 0x90, 0xc3, 0xa2,
+       0x23, 0x3b, 0xa1, 0x86, 0x51, 0x5b, 0xe7, 0xed, 0x1f, 0x61, 0x29,
+       0x70, 0xce, 0xe2, 0xd7, 0xaf, 0xb8, 0x1b, 0xdd, 0x76, 0x21, 0x70,
+       0x48, 0x1c, 0xd0, 0x06, 0x91, 0x27, 0xd5, 0xb0, 0x5a, 0xa9, 0x93,
+       0xb4, 0xea, 0x98, 0x8d, 0x8f, 0xdd, 0xc1, 0x86, 0xff, 0xb7, 0xdc,
+       0x90, 0xa6, 0xc0, 0x8f, 0x4d, 0xf4, 0x35, 0xc9
+};
 
 /** Maximum number of elements in big integer values */
 #define FFDHE_SIZE bigint_required_size ( FFDHE_LEN )
@@ -156,7 +210,7 @@ int ffdhe ( struct ffdhe_group *group, const void *public, const void *private,
        /* Construct modulus */
        assert ( sizeof ( *tmp ) == len );
        memset ( tmp, 0xff, sizeof ( *tmp ) );
-       memcpy ( tmp->euler, euler, sizeof ( tmp->euler ) );
+       memcpy ( tmp->constant, group->constant, sizeof ( tmp->constant ) );
        tmp->lsb32 = group->lsb32;
        bigint_init ( modulus, tmp, len );
        DBGC ( group, "FFDHE %s mod: %s\n",
@@ -200,6 +254,9 @@ int ffdhe ( struct ffdhe_group *group, const void *public, const void *private,
 }
 
 /* Supported groups */
-FFDHE_GROUP ( ffdhe2048, ffdhe2048_algorithm, 2048, 225, 0x61285c97 );
-FFDHE_GROUP ( ffdhe3072, ffdhe3072_algorithm, 3072, 275, 0x66c62e37 );
-FFDHE_GROUP ( ffdhe4096, ffdhe4096_algorithm, 4096, 325, 0x5e655f6a );
+FFDHE_GROUP ( ffdhe2048, ffdhe2048_algorithm, euler, 2048, 225, 0x61285c97 );
+FFDHE_GROUP ( ffdhe3072, ffdhe3072_algorithm, euler, 3072, 275, 0x66c62e37 );
+FFDHE_GROUP ( ffdhe4096, ffdhe4096_algorithm, euler, 4096, 325, 0x5e655f6a );
+FFDHE_GROUP ( modp2048, modp2048_algorithm, pi, 2048, 230, 0x8aacaa68 );
+FFDHE_GROUP ( modp3072, modp3072_algorithm, pi, 3072, 279, 0xa93ad2ca );
+FFDHE_GROUP ( modp4096, modp4096_algorithm, pi, 4096, 328, 0x34063199 );

diff --git a/src/include/ipxe/ffdhe.h b/src/include/ipxe/ffdhe.h
index 6f6d9e878492bef422e3339d83561c46f2c88dd3..349680fdfddd94c1dafd21ba1755eea892f35330 100644 (file)
--- a/src/include/ipxe/ffdhe.h
+++ b/src/include/ipxe/ffdhe.h
@@ -19,6 +19,8 @@ FILE_SECBOOT ( PERMITTED );
 struct ffdhe_group {
        /** Group name */
        const char *name;
+       /** Group constant */
+       const uint8_t *constant;
        /** Length of raw scalar values */
        size_t len;
        /** Number of elements in scalar values */
@@ -35,9 +37,10 @@ extern int ffdhe ( struct ffdhe_group *group, const void *public,
                   const void *private, void *shared );
 
 /** Define a finite field DHE group */
-#define FFDHE_GROUP( _name, _exchange, _bits, _expbits, _lsb )           \
+#define FFDHE_GROUP( _name, _exchange, _constant, _bits, _expbits, _lsb ) \
        static struct ffdhe_group _name ## _group = {                     \
                .name = #_name,                                           \
+               .constant = (_constant),                                  \
                .len = ( _bits / 8 ),                                     \
                .size = bigint_required_size ( _bits / 8 ),               \
                .explen = ( ( _expbits + 7 ) / 8 ),                       \
@@ -66,5 +69,8 @@ extern int ffdhe ( struct ffdhe_group *group, const void *public,
 extern struct exchange_algorithm ffdhe2048_algorithm;
 extern struct exchange_algorithm ffdhe3072_algorithm;
 extern struct exchange_algorithm ffdhe4096_algorithm;
+extern struct exchange_algorithm modp2048_algorithm;
+extern struct exchange_algorithm modp3072_algorithm;
+extern struct exchange_algorithm modp4096_algorithm;
 
 #endif /* _IPXE_FFDHE_H */

diff --git a/src/tests/ffdhe_test.c b/src/tests/ffdhe_test.c
index 9b6fea2817843189b1dfe3dad2090238415fa385..d12819db01e8ebbb9d7d8c6c99b7841e21f68e04 100644 (file)
--- a/src/tests/ffdhe_test.c
+++ b/src/tests/ffdhe_test.c
@@ -410,6 +410,378 @@ EXCHANGE_TEST ( ffdhe4096_random, &ffdhe4096_algorithm,
                 0x88, 0x17, 0xa7, 0x05, 0x4f, 0x43, 0xe4, 0xd2, 0xbf, 0x6b,
                 0x77, 0x08 ) );
 
+/* MODP2048, randomly generated keys */
+EXCHANGE_TEST ( modp2048_random, &modp2048_algorithm,
+       PRIVATE ( 0x01, 0xa4, 0x4e, 0xf0, 0x5a, 0xd9, 0x79, 0xcd, 0xbd, 0xae,
+                 0xd9, 0x77, 0x9f, 0x51, 0xdc, 0xa3, 0x74, 0x53, 0x39, 0xf4,
+                 0xa5, 0x3d, 0xeb, 0x03, 0xf6, 0xd2, 0xfd, 0x12, 0x6c ),
+       PARTNER ( 0xf6, 0x91, 0xc8, 0x2c, 0x69, 0x6d, 0x44, 0x78, 0xa5, 0x8b,
+                 0x5b, 0x39, 0xea, 0xd2, 0x9d, 0x0f, 0xfe, 0xc8, 0x21, 0xe0,
+                 0xbb, 0x61, 0xc2, 0x0b, 0xee, 0x70, 0x04, 0xbe, 0x48, 0xf8,
+                 0xb6, 0x5d, 0x80, 0xe0, 0x8e, 0x2e, 0x92, 0x18, 0x4e, 0xd2,
+                 0xd9, 0x26, 0x33, 0x25, 0x40, 0x63, 0xbe, 0x1d, 0x9f, 0x48,
+                 0xf2, 0x05, 0x56, 0x7d, 0xd3, 0x21, 0x40, 0x52, 0x37, 0x77,
+                 0x37, 0x93, 0x8c, 0x2b, 0x9b, 0x55, 0xb7, 0x23, 0xb9, 0xa1,
+                 0x9e, 0x31, 0x67, 0xfa, 0x93, 0x27, 0xf6, 0x83, 0x60, 0x8e,
+                 0x5f, 0x86, 0xba, 0xe1, 0x06, 0x5b, 0x43, 0xa5, 0x6a, 0x75,
+                 0xfa, 0x84, 0x48, 0xcc, 0x0b, 0x92, 0x9d, 0x4d, 0x56, 0xea,
+                 0x6e, 0x1c, 0x95, 0x23, 0x8f, 0x2c, 0x9e, 0x94, 0x5c, 0x75,
+                 0xde, 0x51, 0xcc, 0xd0, 0x9a, 0xbd, 0xed, 0xc0, 0x72, 0x39,
+                 0x0d, 0xaf, 0xc2, 0x22, 0x02, 0x1e, 0x5f, 0x05, 0x94, 0x4a,
+                 0xc8, 0x99, 0xe5, 0xc3, 0x31, 0x23, 0x5f, 0xe8, 0xfe, 0xd0,
+                 0x01, 0xd8, 0xef, 0x17, 0x7f, 0x7a, 0x34, 0x97, 0x68, 0x57,
+                 0x7e, 0x6c, 0x35, 0xba, 0xae, 0x09, 0x5b, 0xe2, 0x3a, 0xe5,
+                 0x2c, 0xe6, 0xf4, 0xfa, 0x3b, 0x36, 0x30, 0xe9, 0x71, 0x4c,
+                 0x8e, 0x74, 0xe7, 0xa3, 0x1b, 0xdf, 0x3f, 0xfc, 0x94, 0x4b,
+                 0x19, 0x7a, 0xe4, 0x91, 0x27, 0x5f, 0x62, 0x07, 0xb0, 0xdf,
+                 0x2b, 0x56, 0x83, 0x62, 0xe7, 0x18, 0xce, 0x6a, 0xe0, 0x48,
+                 0x2f, 0xf0, 0x45, 0xdf, 0x4a, 0xc6, 0xd9, 0x00, 0xfa, 0xef,
+                 0x1a, 0xc2, 0x1d, 0x4f, 0xf4, 0xd9, 0x7b, 0x84, 0xf1, 0xe1,
+                 0xb5, 0x6d, 0x00, 0xc2, 0xf9, 0xbc, 0xc4, 0xc2, 0xf1, 0xa2,
+                 0x96, 0x1b, 0xc3, 0x3a, 0x41, 0x9a, 0x11, 0xa8, 0xe5, 0x42,
+                 0xfd, 0xad, 0x96, 0x71, 0xcd, 0x20, 0x59, 0x8b, 0xdd, 0xe4,
+                 0xe7, 0xf9, 0xd9, 0x49, 0x4f, 0x9a ),
+       PUBLIC (  0xc0, 0x41, 0xb3, 0xa9, 0x4b, 0x9e, 0x84, 0x8d, 0x3d, 0xaf,
+                 0x70, 0xec, 0x20, 0xd8, 0x79, 0xa1, 0xbf, 0x08, 0x1a, 0xd6,
+                 0xeb, 0x34, 0xc9, 0xa8, 0x27, 0x77, 0x72, 0x0b, 0xb0, 0x3b,
+                 0xa8, 0xf6, 0xfb, 0xf2, 0x37, 0x1b, 0xec, 0xb7, 0x77, 0x26,
+                 0x84, 0xe2, 0xa8, 0xee, 0x85, 0x57, 0x3a, 0x9b, 0xf9, 0x3a,
+                 0x1e, 0x2a, 0xbf, 0xd6, 0xf5, 0x21, 0xcc, 0x4b, 0x93, 0xca,
+                 0x48, 0xa1, 0x68, 0xfa, 0x7c, 0xce, 0x13, 0xbe, 0x6f, 0x44,
+                 0x40, 0x38, 0x34, 0xf2, 0x0e, 0x98, 0x00, 0xd8, 0x17, 0x5a,
+                 0x33, 0xb2, 0x2e, 0xa1, 0x27, 0x84, 0x4f, 0x6b, 0x99, 0xdf,
+                 0x87, 0x62, 0xe7, 0x59, 0xef, 0xb7, 0x97, 0x59, 0x7b, 0x31,
+                 0x16, 0xdb, 0x2f, 0x69, 0x7e, 0x88, 0xb4, 0x0c, 0x63, 0xf6,
+                 0x11, 0x5b, 0xa5, 0x7c, 0x5a, 0x8a, 0xf5, 0x14, 0xa6, 0x2d,
+                 0x2f, 0x30, 0x19, 0x66, 0x77, 0x04, 0x42, 0x51, 0x12, 0xe3,
+                 0x69, 0x4d, 0xd9, 0x4d, 0x39, 0x80, 0x07, 0xde, 0xcc, 0x11,
+                 0xb2, 0x72, 0xe1, 0xb0, 0xfb, 0x2f, 0x00, 0x55, 0xa3, 0xa9,
+                 0xc1, 0xda, 0xf8, 0x7b, 0x57, 0x70, 0x7b, 0x28, 0xd5, 0xb5,
+                 0xa3, 0xda, 0x46, 0x91, 0x4f, 0x85, 0xb2, 0x3d, 0xd6, 0x8b,
+                 0x77, 0x43, 0xe7, 0xd6, 0xf6, 0xfc, 0xa6, 0x17, 0xfc, 0xce,
+                 0x9f, 0xbc, 0x2b, 0x38, 0xc1, 0xc9, 0x41, 0xa1, 0x62, 0x09,
+                 0x9b, 0x14, 0xed, 0x89, 0xbf, 0x87, 0x7d, 0x6b, 0x64, 0x1b,
+                 0x8e, 0x5b, 0x68, 0x59, 0xe3, 0x0c, 0x01, 0xa1, 0x6e, 0xe5,
+                 0x4a, 0xeb, 0xc9, 0x88, 0x54, 0x1e, 0x3a, 0x0a, 0x2f, 0xf0,
+                 0xf5, 0x38, 0x55, 0x8d, 0x30, 0xf1, 0x68, 0x3e, 0xea, 0x5a,
+                 0x57, 0x3b, 0x01, 0x56, 0xc2, 0x1b, 0x27, 0x2a, 0x91, 0x17,
+                 0x1f, 0x55, 0x5e, 0xb7, 0xbf, 0xd1, 0xfe, 0xcb, 0xa6, 0x74,
+                 0xc1, 0x17, 0xd4, 0x01, 0x1f, 0x26 ),
+       SHARED ( 0xf1, 0x4b, 0x16, 0x0e, 0xd4, 0x6e, 0x66, 0x00, 0x2f, 0xc9,
+                0x44, 0xd0, 0xf9, 0x6e, 0x0a, 0xa9, 0x74, 0x4f, 0xc0, 0x9c,
+                0x11, 0xcb, 0x07, 0x0e, 0x73, 0x4c, 0x5d, 0x93, 0xfd, 0x63,
+                0x26, 0x7c, 0x6e, 0x2f, 0xfb, 0x20, 0xa4, 0x92, 0xa9, 0xd2,
+                0x6e, 0x27, 0xf4, 0x27, 0x09, 0x48, 0xc6, 0xd3, 0x1e, 0x75,
+                0xef, 0xff, 0xff, 0x2d, 0x8c, 0x8e, 0xed, 0x0c, 0x48, 0x2f,
+                0xfb, 0x77, 0x28, 0x9b, 0x8d, 0x51, 0x94, 0x7d, 0x15, 0xc7,
+                0xc6, 0x5a, 0xf5, 0x50, 0x34, 0x00, 0x73, 0x8b, 0x0f, 0x9f,
+                0x98, 0x58, 0x9c, 0x08, 0x9c, 0x37, 0x3d, 0xfa, 0xd6, 0x5f,
+                0x87, 0x08, 0xea, 0x30, 0x05, 0x83, 0x4c, 0xaa, 0xbb, 0x13,
+                0xb4, 0x7e, 0xf8, 0xba, 0xac, 0xe8, 0xbb, 0x2b, 0x3b, 0xbe,
+                0x87, 0x62, 0xb7, 0xab, 0x52, 0x1e, 0x1d, 0xa1, 0xdc, 0x9b,
+                0xa9, 0xe8, 0xe6, 0xb1, 0x67, 0xca, 0x50, 0x7a, 0x22, 0xbd,
+                0x98, 0x4a, 0x6f, 0xce, 0x21, 0x9c, 0x7c, 0x26, 0x3a, 0x93,
+                0x04, 0x32, 0xd0, 0xd9, 0xe5, 0xfc, 0x16, 0xb1, 0xd7, 0x14,
+                0x47, 0x1e, 0xba, 0x0a, 0x22, 0xc2, 0x52, 0x11, 0x54, 0x7d,
+                0x31, 0x3a, 0x86, 0x8b, 0x53, 0x8d, 0x67, 0x49, 0x1c, 0xa2,
+                0x5e, 0x41, 0xc9, 0xd5, 0x6e, 0x81, 0xd8, 0x11, 0x67, 0xba,
+                0xfd, 0xe0, 0xd4, 0x6f, 0x14, 0x22, 0x11, 0x8c, 0x26, 0x80,
+                0x13, 0xe3, 0xe8, 0x69, 0xfc, 0x05, 0x0c, 0xae, 0x30, 0x57,
+                0x85, 0xbd, 0x4e, 0x4a, 0x8e, 0x35, 0xe0, 0xa5, 0x3a, 0xc8,
+                0x24, 0xfe, 0x61, 0x22, 0x9d, 0x3e, 0x7d, 0xc5, 0x14, 0x77,
+                0x15, 0xbe, 0xc2, 0x1f, 0xf0, 0xa4, 0xeb, 0x23, 0xc6, 0xb7,
+                0xc7, 0x44, 0x84, 0xee, 0xb6, 0x9f, 0xad, 0x48, 0x8b, 0xe7,
+                0x7c, 0xef, 0xa0, 0xe0, 0xbd, 0x0d, 0xd4, 0xaf, 0x71, 0x5f,
+                0x46, 0xb1, 0xfa, 0x17, 0x9a, 0x2d ) );
+
+/* MODP3072, randomly generated keys */
+EXCHANGE_TEST ( modp3072_random, &modp3072_algorithm,
+       PRIVATE (  0x01, 0xb0, 0x1e, 0x7d, 0x2e, 0x45, 0x78, 0x9d, 0x93, 0x13,
+                  0x8c, 0x66, 0xf0, 0x0d, 0x70, 0xa4, 0x93, 0xa4, 0xb2, 0x96,
+                  0x25, 0xae, 0x39, 0x57, 0x8d, 0x26, 0xd2, 0xe7, 0x2e, 0xe4,
+                  0x4b, 0xd2, 0xff, 0x53, 0x82 ),
+       PARTNER ( 0x4d, 0x7a, 0x53, 0x2a, 0x99, 0x4e, 0xa9, 0x0c, 0xce, 0x39,
+                 0xda, 0x80, 0xed, 0x33, 0xaf, 0xe1, 0xc3, 0x12, 0x56, 0x98,
+                 0xb5, 0x9f, 0xd4, 0x8f, 0xf4, 0x47, 0xaf, 0x8a, 0xcd, 0xaa,
+                 0x9f, 0x3e, 0xc9, 0xa3, 0x0c, 0x33, 0x87, 0xc0, 0x0e, 0x63,
+                 0x22, 0xcb, 0xb0, 0x2d, 0x2f, 0x14, 0x10, 0x35, 0xff, 0x3b,
+                 0x8a, 0x9a, 0xb9, 0xa8, 0xe8, 0x81, 0xe1, 0xf4, 0xff, 0xcf,
+                 0xb4, 0x38, 0xae, 0x8c, 0xf2, 0x83, 0xa2, 0xbb, 0x02, 0x34,
+                 0x77, 0x54, 0xf1, 0xd5, 0xf0, 0x5b, 0x86, 0xfa, 0xe9, 0x9c,
+                 0xdd, 0xb4, 0x7d, 0xea, 0xfe, 0x1e, 0xc6, 0x92, 0x53, 0xbb,
+                 0xb8, 0xb9, 0x7c, 0x4f, 0x70, 0x78, 0x1e, 0xcc, 0xf6, 0x26,
+                 0xad, 0xea, 0xf6, 0x98, 0xc7, 0x36, 0xda, 0xb9, 0x6f, 0x5e,
+                 0xe8, 0x55, 0x89, 0x82, 0x20, 0xaf, 0x45, 0x62, 0xa2, 0x74,
+                 0x9c, 0x0b, 0xe6, 0x33, 0x81, 0x2b, 0xd9, 0xef, 0xcf, 0xd0,
+                 0x88, 0x67, 0xd0, 0x86, 0xf7, 0xaf, 0x4c, 0xc8, 0xdb, 0x9b,
+                 0x0f, 0xf1, 0x39, 0x1a, 0x57, 0xdf, 0x91, 0x41, 0x25, 0x8c,
+                 0x59, 0x62, 0x2e, 0xf7, 0x00, 0x1b, 0x45, 0x90, 0x4c, 0xa7,
+                 0x53, 0x8e, 0x98, 0xe5, 0xef, 0xe5, 0xd9, 0x3b, 0xd0, 0x64,
+                 0xf7, 0xbe, 0xce, 0x86, 0x14, 0xeb, 0x6d, 0xb6, 0x95, 0x18,
+                 0x9b, 0x4a, 0xfd, 0x30, 0x2e, 0x80, 0x4d, 0x12, 0x16, 0x2d,
+                 0x55, 0x99, 0xf9, 0xb4, 0x80, 0xad, 0xaa, 0x5e, 0x6e, 0xbe,
+                 0x21, 0x87, 0x2a, 0x47, 0x22, 0x5e, 0x3a, 0xf5, 0x2b, 0x15,
+                 0xab, 0x30, 0x11, 0xf1, 0x5d, 0x17, 0xd8, 0xc3, 0x47, 0x58,
+                 0xf9, 0xe1, 0x71, 0x11, 0xaa, 0x4d, 0xb4, 0x1d, 0x6c, 0x52,
+                 0x0e, 0x58, 0x4a, 0x69, 0x44, 0xea, 0xe1, 0xe8, 0xf3, 0x11,
+                 0x36, 0xb5, 0xd4, 0x67, 0x2c, 0x99, 0x4c, 0xb1, 0xcf, 0x5a,
+                 0xee, 0x36, 0x44, 0xcc, 0x40, 0x5c, 0xff, 0x8c, 0xee, 0x7b,
+                 0xcc, 0xb7, 0x46, 0x55, 0xfe, 0xe8, 0x97, 0xed, 0x23, 0xa7,
+                 0x38, 0xeb, 0xfa, 0x60, 0xbb, 0xea, 0xc3, 0xc4, 0x82, 0x3c,
+                 0x70, 0xd9, 0x2d, 0x45, 0x81, 0x77, 0xf4, 0xe1, 0x24, 0xf5,
+                 0x08, 0x49, 0xce, 0x3f, 0x80, 0x17, 0xe1, 0xdd, 0xf4, 0xf0,
+                 0x9d, 0xc9, 0x10, 0x64, 0x1f, 0x84, 0x44, 0x70, 0xb3, 0xb8,
+                 0x64, 0xa3, 0x55, 0x70, 0x23, 0x2b, 0x70, 0x06, 0x3b, 0x35,
+                 0xd0, 0x83, 0xe1, 0xc2, 0x38, 0xb4, 0x4c, 0xf1, 0x09, 0x19,
+                 0xf5, 0x8a, 0x20, 0xa4, 0xca, 0x9d, 0xbd, 0x65, 0x7c, 0xab,
+                 0xbb, 0x0a, 0xd9, 0xd8, 0x73, 0xf8, 0x5f, 0xf8, 0x96, 0x99,
+                 0xb6, 0x04, 0x81, 0xc9, 0x00, 0x2d, 0x20, 0xda, 0xe1, 0x6a,
+                 0x67, 0x3f, 0x34, 0x2a, 0xdd, 0x6d, 0xda, 0x0e, 0x95, 0xe7,
+                 0x99, 0x28, 0x73, 0x7c, 0x11, 0x8d, 0x10, 0xaa, 0xae, 0x1f,
+                 0xab, 0x6e, 0x52, 0xc2 ),
+       PUBLIC (  0x6d, 0xf3, 0x1c, 0x33, 0xbc, 0x2a, 0x2b, 0x34, 0xa0, 0x76,
+                 0x48, 0x6f, 0xf3, 0xfb, 0xa5, 0x30, 0x0b, 0x5a, 0x1a, 0xb4,
+                 0x50, 0x06, 0x7a, 0x40, 0x3a, 0x4e, 0x47, 0xe3, 0x9e, 0x28,
+                 0x21, 0x69, 0x9b, 0xa1, 0x43, 0x40, 0xda, 0xfa, 0x5c, 0x37,
+                 0xc2, 0x2f, 0x04, 0x25, 0xb1, 0xca, 0x70, 0xe1, 0x08, 0xea,
+                 0xda, 0xd8, 0x0e, 0x79, 0x88, 0x06, 0x22, 0x99, 0x09, 0x65,
+                 0xcd, 0x1b, 0xf1, 0x7d, 0x2c, 0x72, 0x0c, 0x03, 0x63, 0x14,
+                 0xdd, 0x64, 0xff, 0x99, 0xb8, 0x7c, 0xc2, 0x31, 0x0f, 0x6e,
+                 0x0f, 0x6e, 0x2a, 0xfb, 0x63, 0x96, 0x92, 0xa4, 0x94, 0x9e,
+                 0x6f, 0x0f, 0xea, 0x46, 0x8e, 0x0d, 0x2f, 0x01, 0x4b, 0x42,
+                 0xcf, 0x8c, 0x55, 0xc4, 0xcb, 0xb7, 0x1c, 0x38, 0xb3, 0x9b,
+                 0x55, 0x75, 0x40, 0xf6, 0x67, 0x2f, 0x7f, 0xef, 0xf0, 0x13,
+                 0x85, 0x4d, 0x0c, 0x95, 0xd3, 0x57, 0x2c, 0xcf, 0x75, 0x37,
+                 0x66, 0x5f, 0xa9, 0x2d, 0x26, 0x13, 0xaa, 0xc6, 0x6e, 0x5f,
+                 0x53, 0x52, 0x99, 0x5a, 0xaa, 0x59, 0x66, 0xd7, 0x31, 0x09,
+                 0x82, 0xf9, 0x6f, 0x6a, 0x00, 0xab, 0x23, 0x47, 0xfc, 0x09,
+                 0x4e, 0x10, 0x3a, 0x12, 0xd4, 0xf5, 0x58, 0x7e, 0xbb, 0x16,
+                 0x12, 0x92, 0xa0, 0xa7, 0x17, 0x24, 0x3e, 0x78, 0x79, 0x75,
+                 0x97, 0xd7, 0x1f, 0xc8, 0xa3, 0x4b, 0x6a, 0xcb, 0x88, 0xd1,
+                 0xc1, 0x5b, 0x53, 0xee, 0x63, 0x4c, 0xcc, 0x74, 0x17, 0x81,
+                 0x1a, 0x3a, 0x57, 0x29, 0xc4, 0xd3, 0x34, 0x1f, 0x37, 0xc7,
+                 0xad, 0xcc, 0xc3, 0xae, 0x2f, 0x76, 0x2a, 0x22, 0xdf, 0xbe,
+                 0x74, 0x21, 0xc8, 0x0d, 0x42, 0x18, 0x7c, 0xd3, 0x47, 0xfa,
+                 0x2f, 0x31, 0xab, 0xe1, 0xee, 0x6d, 0xe6, 0x0f, 0x5e, 0xb5,
+                 0x8f, 0x94, 0xdb, 0xae, 0xbc, 0xb3, 0x65, 0xff, 0x70, 0x1b,
+                 0xd7, 0x8e, 0xac, 0x9e, 0x70, 0x41, 0xb4, 0xbf, 0x11, 0x6d,
+                 0x69, 0xc4, 0x24, 0xae, 0xff, 0x37, 0xb7, 0xd8, 0xb8, 0x5a,
+                 0xca, 0x32, 0x23, 0x2e, 0x1d, 0x7a, 0x83, 0xc0, 0xec, 0xf6,
+                 0x10, 0x74, 0x0b, 0x4c, 0x9a, 0xd2, 0xb7, 0xee, 0x11, 0x2f,
+                 0xc7, 0x3c, 0x21, 0xd5, 0x20, 0xcd, 0x17, 0x84, 0x36, 0x72,
+                 0xe1, 0xa4, 0x76, 0x91, 0xfe, 0xcb, 0x8d, 0x2c, 0xc4, 0x36,
+                 0xb0, 0xc9, 0x5c, 0x8f, 0x24, 0x88, 0x93, 0xf5, 0xc1, 0x49,
+                 0xe0, 0x0d, 0x0a, 0x8c, 0xa2, 0x39, 0x84, 0xe5, 0xc0, 0x38,
+                 0x4b, 0xbe, 0x53, 0x87, 0x90, 0x38, 0xd8, 0xbe, 0x1a, 0xc3,
+                 0x6d, 0xc6, 0x0c, 0xdc, 0x53, 0x2a, 0xe3, 0xbd, 0xa9, 0x3d,
+                 0x92, 0x3d, 0x03, 0x19, 0xf1, 0xb7, 0xd7, 0xdc, 0xc2, 0xca,
+                 0x4b, 0x6b, 0x5a, 0x60, 0xdf, 0x42, 0x31, 0x12, 0xcf, 0x5b,
+                 0xad, 0xcc, 0xea, 0xa5, 0x2d, 0x11, 0xde, 0x04, 0xd2, 0xcc,
+                 0xdd, 0x22, 0x0c, 0x6e ),
+       SHARED ( 0x91, 0xc9, 0x53, 0x77, 0xf4, 0x76, 0x43, 0xdc, 0x15, 0x7e,
+                0x96, 0x68, 0x4a, 0x82, 0x58, 0xfb, 0x01, 0x01, 0x20, 0x0c,
+                0x8c, 0x89, 0x2c, 0x46, 0x1a, 0x0b, 0xcd, 0x51, 0xcc, 0x4b,
+                0x87, 0x3b, 0x0b, 0xba, 0x9d, 0xfc, 0x11, 0x2d, 0x18, 0xae,
+                0xe8, 0x06, 0xdd, 0xc4, 0x62, 0x2a, 0x6e, 0xe5, 0x5b, 0x63,
+                0x9d, 0xa1, 0xa2, 0x90, 0xec, 0xb4, 0xa2, 0x14, 0x87, 0x03,
+                0x3e, 0xf7, 0x5c, 0x32, 0x07, 0x18, 0xec, 0x7f, 0xef, 0xee,
+                0xac, 0x98, 0x2c, 0x56, 0xae, 0xdc, 0x05, 0x26, 0x43, 0x62,
+                0xd2, 0x4d, 0x10, 0xc9, 0xc6, 0x77, 0xc7, 0x26, 0x8e, 0xb2,
+                0x9d, 0x58, 0xda, 0xaf, 0x39, 0x03, 0xf1, 0xb6, 0xec, 0x37,
+                0x5b, 0xf6, 0x2b, 0x6f, 0xe8, 0x4a, 0x11, 0xa0, 0xbb, 0x37,
+                0x2e, 0xff, 0x02, 0xed, 0xa1, 0x45, 0x80, 0xf3, 0xbc, 0x50,
+                0x38, 0x17, 0x27, 0x9e, 0x12, 0xe7, 0xdb, 0x41, 0x7e, 0xe6,
+                0x42, 0x73, 0xa6, 0x84, 0x36, 0x97, 0xbf, 0x60, 0xf1, 0x99,
+                0x6d, 0xd7, 0xd5, 0xe9, 0xd7, 0x6e, 0x67, 0x89, 0x8a, 0x19,
+                0xf8, 0x90, 0x08, 0x68, 0x84, 0x1e, 0x15, 0xfa, 0xbb, 0x27,
+                0xa5, 0xd9, 0x73, 0x5b, 0x79, 0x9f, 0x5b, 0xf2, 0xbf, 0x2a,
+                0x7a, 0x5c, 0x67, 0x84, 0xd9, 0xae, 0x85, 0xad, 0x29, 0x06,
+                0x6e, 0x70, 0x53, 0x25, 0xc6, 0xf5, 0xc5, 0x5e, 0x66, 0xc1,
+                0x3b, 0xf1, 0xd0, 0xaf, 0x5a, 0x83, 0xb0, 0x37, 0x36, 0xbc,
+                0xd5, 0x87, 0x2e, 0xfb, 0xc0, 0xf7, 0xaa, 0x77, 0x6c, 0x98,
+                0x38, 0x91, 0xf7, 0x8b, 0xd5, 0xb7, 0x5a, 0x20, 0x2c, 0xf6,
+                0x69, 0xf9, 0x28, 0x32, 0x64, 0x81, 0x97, 0x67, 0x84, 0xee,
+                0x4d, 0x5b, 0x1e, 0xa8, 0x55, 0xf3, 0x34, 0xc8, 0xda, 0x90,
+                0x1f, 0xf7, 0xcb, 0x34, 0x69, 0xc5, 0x20, 0xf0, 0x3a, 0xbc,
+                0x05, 0x22, 0x95, 0xd3, 0x74, 0x00, 0x1d, 0x82, 0x93, 0x6f,
+                0x1d, 0xb5, 0x0c, 0xaa, 0x74, 0xc5, 0x0a, 0xce, 0x42, 0x0d,
+                0x78, 0xe6, 0x5d, 0x75, 0x7e, 0x91, 0x36, 0x5e, 0xd7, 0x1a,
+                0x2a, 0x1c, 0x2d, 0xe2, 0x8a, 0x86, 0x95, 0x4b, 0x34, 0x92,
+                0x39, 0x6a, 0xed, 0x87, 0x19, 0xa7, 0xe1, 0xed, 0xb9, 0x1a,
+                0x89, 0x06, 0x11, 0x7d, 0x64, 0x07, 0xff, 0x9d, 0xb7, 0x86,
+                0x5f, 0x3f, 0xd6, 0x1b, 0xba, 0x17, 0xda, 0x76, 0x34, 0x84,
+                0x6a, 0xc6, 0x95, 0x72, 0xbc, 0xb4, 0xa9, 0xe1, 0x00, 0xe1,
+                0x2b, 0x35, 0x76, 0xea, 0xfb, 0x0f, 0x6d, 0x0f, 0xd7, 0x00,
+                0xe2, 0x60, 0x22, 0x1f, 0xcc, 0xea, 0x08, 0x45, 0xdf, 0x65,
+                0x25, 0x50, 0x48, 0x32, 0x83, 0x8e, 0x43, 0x00, 0x7e, 0xc2,
+                0xa9, 0x6e, 0xaa, 0xf3, 0xae, 0x37, 0x29, 0x7d, 0x8a, 0xb9,
+                0x77, 0xa4, 0xae, 0x16, 0x52, 0x1c, 0x1b, 0x42, 0xf3, 0x7a,
+                0x68, 0xeb, 0xe9, 0x8e ) );
+
+/* MODP4096, randomly generated keys */
+EXCHANGE_TEST ( modp4096_random, &modp4096_algorithm,
+       PRIVATE ( 0x1a, 0xab, 0xaa, 0xb7, 0x88, 0xe8, 0x67, 0x12, 0x06, 0x09,
+                 0xfa, 0x76, 0xa8, 0x92, 0x22, 0x4c, 0xd6, 0x50, 0x1f, 0x8b,
+                 0xf1, 0xe1, 0xd3, 0xfc, 0xdf, 0x4e, 0x0e, 0x95, 0xab, 0xbb,
+                 0x8a, 0x7d, 0x24, 0xe9, 0x7e, 0x0d, 0x80, 0xe4, 0xa4, 0xa0,
+                 0x6c ),
+       PARTNER ( 0x91, 0x64, 0x1b, 0x78, 0x09, 0x7b, 0xd4, 0x7a, 0x21, 0xb0,
+                 0xda, 0xc9, 0x8e, 0x15, 0xf1, 0xf8, 0x36, 0xed, 0x87, 0xa4,
+                 0xa0, 0xf2, 0x34, 0xcb, 0xdc, 0xba, 0x67, 0xae, 0x1d, 0xb2,
+                 0xf8, 0x9c, 0x1c, 0x14, 0x81, 0x38, 0xee, 0xf7, 0xb3, 0x10,
+                 0xc3, 0xea, 0xb6, 0xe3, 0x0c, 0x32, 0x39, 0xb3, 0xac, 0xd5,
+                 0xe9, 0x77, 0xa9, 0x6c, 0x75, 0x88, 0x2c, 0x60, 0x47, 0x7f,
+                 0x6f, 0x64, 0x7b, 0x32, 0x20, 0xe1, 0x1e, 0x2c, 0x03, 0x1d,
+                 0x0a, 0x4e, 0x87, 0x9c, 0x8c, 0x3e, 0x4d, 0x5d, 0x33, 0x0d,
+                 0xe2, 0x53, 0x5a, 0xe8, 0xc7, 0x01, 0xdb, 0xde, 0xdb, 0x55,
+                 0x47, 0x48, 0x86, 0x3b, 0x74, 0xb4, 0x69, 0x3d, 0x0a, 0x17,
+                 0xeb, 0x31, 0x8b, 0x0c, 0xe8, 0x35, 0xca, 0x94, 0x7e, 0xd1,
+                 0xe8, 0x08, 0xf0, 0x37, 0xba, 0x4b, 0xd9, 0x43, 0xad, 0xfd,
+                 0x27, 0x08, 0xc6, 0x45, 0x49, 0x39, 0xba, 0x8a, 0x16, 0xe1,
+                 0x10, 0x98, 0xcc, 0x4a, 0xf0, 0x82, 0xba, 0x09, 0xc5, 0x98,
+                 0x66, 0x0a, 0xe2, 0x88, 0x48, 0xbd, 0x1b, 0xa9, 0x93, 0xc9,
+                 0x64, 0xe8, 0xe4, 0x5a, 0x41, 0x2c, 0xbd, 0x7e, 0x7e, 0x20,
+                 0xec, 0x6e, 0x3f, 0xf1, 0x8e, 0xd1, 0xee, 0x60, 0xa1, 0x69,
+                 0x8b, 0xb7, 0xb1, 0xc9, 0x83, 0xcc, 0x14, 0x30, 0x52, 0xdc,
+                 0x1d, 0xf7, 0xc0, 0xd1, 0x7b, 0xb5, 0x35, 0x83, 0x6a, 0xf4,
+                 0x26, 0xb3, 0x13, 0x67, 0x10, 0x38, 0x9c, 0xf5, 0x87, 0x67,
+                 0x86, 0xb7, 0x5d, 0xb6, 0x02, 0x21, 0xcd, 0x80, 0x6b, 0x3d,
+                 0x40, 0xec, 0xd2, 0xbd, 0x3c, 0x38, 0xe8, 0xa5, 0xe7, 0xb8,
+                 0x73, 0x72, 0xdf, 0x9b, 0x2c, 0xc6, 0xc9, 0xe6, 0xfd, 0xf2,
+                 0x6d, 0xc3, 0x62, 0xdf, 0xe9, 0x1c, 0x2c, 0x33, 0xe0, 0xc8,
+                 0xb8, 0x36, 0x46, 0x4e, 0xce, 0xc2, 0x16, 0x6a, 0x79, 0x2d,
+                 0xb8, 0x87, 0x97, 0x40, 0x3e, 0x7e, 0xa9, 0x1d, 0x00, 0xe0,
+                 0xd0, 0x15, 0xb1, 0x8d, 0xe3, 0x4b, 0x0c, 0x0c, 0x98, 0x99,
+                 0x89, 0x8e, 0x2a, 0x49, 0x11, 0x55, 0x7e, 0xd2, 0x09, 0xe6,
+                 0xec, 0xbf, 0x89, 0x99, 0x3d, 0x06, 0xc5, 0x3b, 0x0a, 0xb9,
+                 0x92, 0x41, 0x38, 0x7c, 0x24, 0x93, 0xa2, 0xae, 0x8d, 0x9b,
+                 0x59, 0x11, 0xd8, 0x2d, 0x3a, 0x01, 0x59, 0xd4, 0xcb, 0x9e,
+                 0x9a, 0xab, 0x82, 0x96, 0xe0, 0xd2, 0x41, 0x5a, 0x7b, 0x4c,
+                 0xbe, 0xae, 0x8c, 0xcc, 0xe6, 0x80, 0xc7, 0x43, 0x38, 0x74,
+                 0x33, 0x1a, 0x92, 0x53, 0xaf, 0x11, 0xbc, 0x18, 0x67, 0x54,
+                 0x76, 0x68, 0xd0, 0xe8, 0x0e, 0xdc, 0xb1, 0x4e, 0x54, 0x72,
+                 0xd9, 0x20, 0x82, 0xa3, 0x45, 0x5c, 0x6a, 0x9d, 0xd7, 0xa2,
+                 0xf9, 0x32, 0x18, 0x59, 0xc5, 0x10, 0xa6, 0xda, 0xd3, 0xb8,
+                 0x9c, 0xc0, 0xb6, 0xb6, 0xbc, 0xa0, 0x4d, 0x7e, 0x73, 0x2f,
+                 0xc8, 0x81, 0xde, 0xfb, 0xc4, 0xb6, 0xad, 0xae, 0x12, 0x28,
+                 0xa4, 0x59, 0xe5, 0x0c, 0x7c, 0x37, 0x75, 0x37, 0x40, 0x06,
+                 0x2c, 0xf6, 0x79, 0xde, 0xba, 0x31, 0x41, 0x9a, 0xf2, 0x75,
+                 0xae, 0xec, 0x0d, 0xe6, 0xf6, 0x0f, 0x57, 0x77, 0xfc, 0x2d,
+                 0x5d, 0x6d, 0xab, 0xf4, 0xb5, 0x61, 0x04, 0xc9, 0xed, 0xe3,
+                 0xd9, 0x66, 0xd9, 0x7d, 0xab, 0x0b, 0x28, 0xc7, 0x35, 0xa0,
+                 0x35, 0xf5, 0xce, 0xcc, 0x99, 0xd6, 0x98, 0x41, 0x8c, 0x31,
+                 0x20, 0xe5, 0x06, 0xfe, 0xa3, 0x29, 0xf7, 0x12, 0x52, 0x6f,
+                 0xc7, 0x41, 0xcf, 0x95, 0x75, 0x00, 0x9a, 0xe0, 0x23, 0x64,
+                 0xf3, 0x46, 0xce, 0xcf, 0x3f, 0x1c, 0x59, 0x2d, 0x3c, 0x03,
+                 0xc6, 0x19, 0x9f, 0x32, 0x4b, 0x65, 0x00, 0x26, 0x42, 0x9e,
+                 0x77, 0xb6, 0x66, 0x1a, 0x7f, 0x3c, 0x0d, 0x86, 0x0a, 0x8b,
+                 0x1a, 0xd8, 0x33, 0x61, 0xef, 0xcb, 0xdd, 0x43, 0xf9, 0x8a,
+                 0x07, 0x58 ),
+       PUBLIC ( 0xaf, 0x50, 0x5d, 0x22, 0x1b, 0x67, 0x26, 0x75, 0xa6, 0x74,
+                0x3e, 0x0d, 0xbe, 0x02, 0x22, 0xb6, 0x8a, 0x0e, 0x52, 0xc9,
+                0x32, 0x48, 0x65, 0x5a, 0x36, 0x55, 0x20, 0x98, 0x72, 0x46,
+                0xc0, 0x83, 0x3e, 0xb4, 0x73, 0xd9, 0x64, 0x2d, 0x10, 0xc7,
+                0x58, 0x6c, 0xae, 0x4e, 0x81, 0x3e, 0xfa, 0x03, 0x1d, 0x31,
+                0x8e, 0x4d, 0x61, 0x55, 0x6f, 0x67, 0x8b, 0xe7, 0x39, 0x64,
+                0x83, 0xfa, 0xa0, 0x56, 0x3f, 0x25, 0xf5, 0xcd, 0x74, 0x41,
+                0xbb, 0xe5, 0xf3, 0xef, 0xb8, 0xa7, 0x13, 0xf7, 0xd6, 0x78,
+                0x0f, 0x0f, 0xc1, 0xa3, 0xcb, 0xec, 0x51, 0x3d, 0xc2, 0x91,
+                0xd3, 0x88, 0xb5, 0x2a, 0x46, 0x5a, 0xa9, 0x14, 0x03, 0x34,
+                0x4e, 0x4a, 0xc0, 0x09, 0xd5, 0x22, 0x81, 0x4b, 0xc9, 0x3b,
+                0x62, 0xd1, 0xad, 0x88, 0xd3, 0x59, 0x14, 0x18, 0x2b, 0xa4,
+                0x2a, 0x5e, 0xbb, 0x71, 0x61, 0x18, 0x33, 0x8b, 0xc1, 0x83,
+                0x36, 0xb8, 0x32, 0xa5, 0x0e, 0x63, 0xb9, 0xf2, 0x5a, 0x0b,
+                0xcc, 0xa1, 0x37, 0x44, 0x33, 0x74, 0x21, 0xba, 0x6d, 0xf8,
+                0x3d, 0xdc, 0xc4, 0xf9, 0xc0, 0xcc, 0xd6, 0xdd, 0x8c, 0x7c,
+                0x70, 0xf3, 0x43, 0x11, 0x58, 0xcd, 0x5f, 0x59, 0x41, 0x03,
+                0x61, 0x5d, 0xf9, 0x9d, 0x65, 0xb1, 0x35, 0xac, 0xf6, 0x3d,
+                0x59, 0x2d, 0xe5, 0xfd, 0xa8, 0x88, 0x30, 0x11, 0x94, 0xd7,
+                0x8c, 0x84, 0x14, 0xf0, 0x53, 0xcc, 0x5f, 0x94, 0xca, 0x6a,
+                0x98, 0x7c, 0xaf, 0x30, 0x48, 0xae, 0x04, 0x90, 0x9e, 0xe1,
+                0xd5, 0xb7, 0x7d, 0xd0, 0xb2, 0x09, 0x8c, 0x88, 0xf8, 0x1c,
+                0x9f, 0xee, 0xf2, 0x7d, 0xa5, 0xa2, 0xa5, 0x54, 0xed, 0xa7,
+                0x49, 0x92, 0x43, 0xc2, 0x5d, 0xb0, 0xe4, 0x87, 0xd0, 0xb6,
+                0xa8, 0x56, 0xf8, 0xb9, 0x80, 0xaa, 0x04, 0x28, 0x8c, 0xc3,
+                0xa9, 0x15, 0x76, 0xe1, 0xf6, 0x7a, 0x7e, 0x93, 0xee, 0x33,
+                0xae, 0xc4, 0xfe, 0xa3, 0x2d, 0x24, 0x88, 0x5d, 0x21, 0xf5,
+                0xc7, 0x7c, 0x6c, 0x3a, 0xe0, 0xa7, 0x8e, 0xef, 0xb4, 0x3c,
+                0xdf, 0x24, 0xab, 0x4f, 0xd0, 0x58, 0x0a, 0x9d, 0x29, 0xe0,
+                0x08, 0x4a, 0xa7, 0x60, 0x79, 0x1e, 0xca, 0xcc, 0x8f, 0x44,
+                0xf7, 0xb4, 0xc9, 0x9e, 0x4b, 0x38, 0xa3, 0x35, 0x48, 0x5d,
+                0x7c, 0xdd, 0xb4, 0x21, 0x98, 0xa4, 0xa5, 0x89, 0x07, 0xb0,
+                0x95, 0x61, 0x90, 0x32, 0x90, 0x5f, 0x36, 0xff, 0xa5, 0xc9,
+                0xc2, 0xf5, 0x46, 0xbf, 0x0a, 0xca, 0x54, 0x66, 0x20, 0xcb,
+                0x2c, 0x65, 0x46, 0xda, 0x56, 0x47, 0x9a, 0x37, 0xd6, 0xa2,
+                0x29, 0x6e, 0x9c, 0x58, 0xeb, 0x70, 0xa5, 0xc0, 0xb2, 0x1f,
+                0xf0, 0xf4, 0x7f, 0xaa, 0x38, 0x0c, 0x40, 0x33, 0x03, 0x04,
+                0x8e, 0x9e, 0x96, 0x63, 0xb1, 0x34, 0x20, 0x64, 0xe3, 0xc2,
+                0xa7, 0xf7, 0x2f, 0x3a, 0x7e, 0x10, 0x72, 0x75, 0xc7, 0xb2,
+                0x72, 0xd3, 0xce, 0xf6, 0xa0, 0x83, 0x5a, 0x65, 0x66, 0x8a,
+                0xc8, 0x38, 0x85, 0x5c, 0xd8, 0xfc, 0xf7, 0xbc, 0xdf, 0x53,
+                0xa5, 0xe0, 0x31, 0x0d, 0x14, 0xa5, 0xf7, 0x17, 0x16, 0xd9,
+                0x3d, 0xab, 0x36, 0x3c, 0x4e, 0x36, 0x3f, 0xf0, 0xf1, 0x4b,
+                0x1b, 0xc9, 0xdb, 0x8a, 0x91, 0x27, 0x2d, 0xd6, 0xd5, 0x8f,
+                0x26, 0x75, 0xd2, 0x9a, 0x45, 0x2d, 0x14, 0x56, 0xdf, 0xf4,
+                0x76, 0xd2, 0x99, 0xc6, 0x59, 0x97, 0x9b, 0x0b, 0x2f, 0x98,
+                0x6c, 0xba, 0x9c, 0xfb, 0xb5, 0x6f, 0x15, 0x75, 0xd7, 0x75,
+                0x4a, 0x54, 0xf8, 0xea, 0xdf, 0x63, 0xbe, 0xf9, 0x9f, 0x7f,
+                0x50, 0xdf, 0x22, 0x23, 0xbf, 0xb9, 0x3e, 0xa2, 0x85, 0x6c,
+                0x49, 0x3f, 0xd1, 0xec, 0x39, 0xde, 0xd4, 0x31, 0xfc, 0x68,
+                0xa0, 0xee, 0x98, 0x60, 0x77, 0xb4, 0xfd, 0xf9, 0xbb, 0xaf,
+                0x2e, 0x53 ),
+       SHARED ( 0x5b, 0x71, 0x82, 0x2f, 0x19, 0xc0, 0xc0, 0xe6, 0x32, 0xc7,
+                0x87, 0x34, 0x5e, 0xa8, 0xea, 0x76, 0x17, 0xae, 0x5c, 0x95,
+                0x9c, 0xd7, 0xd1, 0x0d, 0x60, 0x77, 0xaf, 0x93, 0x7b, 0x78,
+                0xbd, 0xf9, 0xde, 0x20, 0x37, 0x18, 0x1d, 0xfa, 0xff, 0x4b,
+                0x3c, 0x42, 0x08, 0xde, 0xf9, 0x15, 0x96, 0xa3, 0xb5, 0x58,
+                0x57, 0xa6, 0xd8, 0x2a, 0x79, 0x78, 0x54, 0xfb, 0xd5, 0x88,
+                0xf1, 0x7d, 0x9a, 0xcf, 0x19, 0x5e, 0xc1, 0x13, 0x0e, 0xfe,
+                0xb2, 0xea, 0x67, 0x82, 0x26, 0xaf, 0x8e, 0x8b, 0xfe, 0x30,
+                0x3d, 0x2f, 0xf2, 0x91, 0xf7, 0xff, 0x7d, 0x3c, 0xc7, 0xe9,
+                0xca, 0x3e, 0x87, 0x3b, 0xba, 0x77, 0xe6, 0x79, 0x29, 0x7a,
+                0xfe, 0x6c, 0x16, 0x58, 0x71, 0xb7, 0xa5, 0x50, 0x7f, 0xd0,
+                0xe6, 0x76, 0xf9, 0x65, 0x17, 0x99, 0xc6, 0x4d, 0xdd, 0x3d,
+                0x97, 0x1c, 0x11, 0x9c, 0x1e, 0x4f, 0xaa, 0xa0, 0x80, 0xf5,
+                0xf5, 0x00, 0x5e, 0x74, 0xac, 0x69, 0xe8, 0x40, 0xb8, 0x62,
+                0x52, 0xac, 0x98, 0x2f, 0xc5, 0xeb, 0x43, 0xd4, 0x34, 0x28,
+                0xfd, 0x82, 0x99, 0xb5, 0x51, 0x6e, 0x90, 0xf0, 0x41, 0x73,
+                0x4b, 0x48, 0x29, 0xe5, 0x86, 0xcd, 0xb9, 0x05, 0xb4, 0x66,
+                0x5a, 0xee, 0x6a, 0xe4, 0xab, 0x22, 0x24, 0xf1, 0xfe, 0xf9,
+                0x78, 0x80, 0x7c, 0x6a, 0x1a, 0x8f, 0xf2, 0xe3, 0x56, 0xe4,
+                0xa4, 0xea, 0x7e, 0x94, 0x53, 0xaf, 0xe8, 0x3b, 0x76, 0x25,
+                0xf2, 0xa2, 0xf2, 0xed, 0x44, 0x10, 0xcf, 0xe0, 0xf1, 0x90,
+                0x91, 0x3f, 0x4d, 0x3a, 0x3e, 0x65, 0x4c, 0x3c, 0xa4, 0x78,
+                0x30, 0x7f, 0x6a, 0x24, 0xc3, 0xe0, 0x36, 0xbe, 0x15, 0xf4,
+                0x4a, 0x15, 0xd2, 0x64, 0xe6, 0xa7, 0x9c, 0x4c, 0xea, 0xe9,
+                0x4e, 0x2f, 0xe2, 0x16, 0x9a, 0xc2, 0x95, 0x23, 0x15, 0x6a,
+                0xa6, 0x19, 0x5d, 0xcd, 0xe7, 0x19, 0xd0, 0x79, 0x79, 0x5d,
+                0x12, 0xe3, 0x52, 0x16, 0xd3, 0xde, 0x14, 0x62, 0x7e, 0xd7,
+                0xb4, 0x19, 0xe4, 0x63, 0x4f, 0xcb, 0x9b, 0x0a, 0x0b, 0xe9,
+                0x39, 0xcf, 0xe7, 0x44, 0xda, 0x7a, 0x6d, 0x60, 0xba, 0x33,
+                0x16, 0x8c, 0xeb, 0x6e, 0xa5, 0xa1, 0xca, 0xa8, 0x27, 0x0b,
+                0xdc, 0x83, 0x42, 0x01, 0xf7, 0xe3, 0x9c, 0x62, 0xb3, 0x24,
+                0xb1, 0xe1, 0x2e, 0x45, 0x3c, 0x43, 0x8d, 0x25, 0x71, 0x58,
+                0x10, 0x91, 0x4c, 0x3f, 0x88, 0xe4, 0x64, 0x34, 0xc6, 0xbf,
+                0x21, 0xfb, 0x92, 0xe3, 0x0b, 0xf4, 0xa3, 0xf8, 0x32, 0x6f,
+                0x2f, 0x47, 0x94, 0x39, 0xbe, 0xec, 0x7d, 0xfa, 0x73, 0x3d,
+                0xc8, 0xcd, 0x78, 0x43, 0x68, 0x28, 0x69, 0xd2, 0x5b, 0xe9,
+                0x01, 0x30, 0x12, 0xd9, 0x43, 0x0c, 0xc1, 0x9a, 0x0b, 0x6c,
+                0x94, 0x10, 0x2f, 0x4e, 0x07, 0x5f, 0xa8, 0xc7, 0xba, 0x6e,
+                0x78, 0x46, 0x53, 0x36, 0xce, 0x6b, 0xdd, 0x42, 0x4f, 0xd3,
+                0x8e, 0xe6, 0xca, 0x1c, 0x94, 0xe8, 0xa5, 0xe6, 0xc0, 0x66,
+                0x08, 0xb9, 0x06, 0x47, 0x3b, 0x93, 0xdc, 0x04, 0x58, 0xed,
+                0x0e, 0xce, 0x38, 0xec, 0x2b, 0xbe, 0x2a, 0xe1, 0x2e, 0xfb,
+                0x6d, 0xd3, 0x8a, 0x99, 0x83, 0xc2, 0x36, 0x84, 0x94, 0x0c,
+                0x75, 0x04, 0xf4, 0xa0, 0x8a, 0x0b, 0x94, 0x46, 0x40, 0x68,
+                0x8d, 0xc1, 0x49, 0x9e, 0x11, 0x60, 0xec, 0xc1, 0x51, 0x63,
+                0x52, 0xdd, 0x1e, 0x35, 0xfd, 0xce, 0x57, 0xbd, 0xcb, 0x2b,
+                0x00, 0xc7, 0x17, 0xf4, 0x4a, 0x76, 0x0a, 0x4a, 0xe5, 0x2a,
+                0x52, 0x5d, 0xf5, 0x18, 0x08, 0x86, 0x95, 0x12, 0x64, 0xbf,
+                0x0e, 0xea, 0xcd, 0xd0, 0x76, 0x0e, 0xfd, 0x22, 0x42, 0x61,
+                0x1e, 0xd9, 0xbf, 0x42, 0x1c, 0xf7, 0x16, 0x43, 0x29, 0xf9,
+                0xcd, 0xe8, 0x51, 0x6b, 0x24, 0x14, 0x1b, 0x5b, 0xe5, 0xea,
+                0x75, 0xb5 ) );
+
 /* FFDHE2048, invalid partner key (0) */
 EXCHANGE_TEST ( ffdhe2048_zero, &ffdhe2048_algorithm,
        PRIVATE ( 0x00, 0xd2, 0xf5, 0xb3, 0xfb, 0x1d, 0xbd, 0x64, 0x6e, 0xcf,
@@ -597,6 +969,9 @@ static void ffdhe_test_exec ( void ) {
        exchange_ok ( &ffdhe2048_random );
        exchange_ok ( &ffdhe3072_random );
        exchange_ok ( &ffdhe4096_random );
+       exchange_ok ( &modp2048_random );
+       exchange_ok ( &modp3072_random );
+       exchange_ok ( &modp4096_random );
 
        /* Invalid partner keys */
        exchange_ok ( &ffdhe2048_zero );