From 08f3ef1861478587211971494541a6b0e97cfdc7 Mon Sep 17 00:00:00 2001 From: Nicholas Wilson Date: Tue, 10 Nov 2015 13:10:01 +0000 Subject: [PATCH] Basic support for Curve448, similar to the current level of support for Curve25519 --- include/mbedtls/config.h | 1 + include/mbedtls/ecp.h | 3 +- library/ecp.c | 24 ++++-- library/ecp_curves.c | 128 ++++++++++++++++++++++++++++++- library/version_features.c | 3 + programs/test/benchmark.c | 91 +++++++++++++--------- tests/suites/test_suite_ecp.data | 4 + 7 files changed, 209 insertions(+), 45 deletions(-) diff --git a/include/mbedtls/config.h b/include/mbedtls/config.h index 48c32d4aa..9585e6922 100644 --- a/include/mbedtls/config.h +++ b/include/mbedtls/config.h @@ -609,6 +609,7 @@ #define MBEDTLS_ECP_DP_BP384R1_ENABLED #define MBEDTLS_ECP_DP_BP512R1_ENABLED #define MBEDTLS_ECP_DP_CURVE25519_ENABLED +#define MBEDTLS_ECP_DP_CURVE448_ENABLED /** * \def MBEDTLS_ECP_NIST_OPTIM diff --git a/include/mbedtls/ecp.h b/include/mbedtls/ecp.h index b00ba4da8..710fc3a6b 100644 --- a/include/mbedtls/ecp.h +++ b/include/mbedtls/ecp.h @@ -72,7 +72,8 @@ typedef enum MBEDTLS_ECP_DP_BP256R1, /*!< 256-bits Brainpool curve */ MBEDTLS_ECP_DP_BP384R1, /*!< 384-bits Brainpool curve */ MBEDTLS_ECP_DP_BP512R1, /*!< 512-bits Brainpool curve */ - MBEDTLS_ECP_DP_CURVE25519, /*!< Curve25519 */ + MBEDTLS_ECP_DP_CURVE25519, /*!< Curve25519 */ + MBEDTLS_ECP_DP_CURVE448, /*!< Curve448 */ MBEDTLS_ECP_DP_SECP192K1, /*!< 192-bits "Koblitz" curve */ MBEDTLS_ECP_DP_SECP224K1, /*!< 224-bits "Koblitz" curve */ MBEDTLS_ECP_DP_SECP256K1, /*!< 256-bits "Koblitz" curve */ diff --git a/library/ecp.c b/library/ecp.c index b41baef27..92a188b66 100644 --- a/library/ecp.c +++ b/library/ecp.c @@ -26,6 +26,7 @@ * GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone * FIPS 186-3 http://csrc.nist.gov/publications/fips/fips186-3/fips_186-3.pdf * RFC 4492 for the related TLS structures and constants + * RFC 7748 for the Curve448 and Curve25519 curve definitions * * [Curve25519] http://cr.yp.to/ecdh/curve25519-20060209.pdf * @@ -99,7 +100,8 @@ static unsigned long add_count, dbl_count, mul_count; #define ECP_SHORTWEIERSTRASS #endif -#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) +#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) || \ + defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) #define ECP_MONTGOMERY #endif @@ -1852,6 +1854,8 @@ cleanup: static int ecp_check_pubkey_mx( const mbedtls_ecp_group *grp, const mbedtls_ecp_point *pt ) { /* [Curve25519 p. 5] Just check X is the correct number of bytes */ + /* Allow any public value, if it's too big then we'll just reduce it mod p + * (RFC 7748 sec. 5 para. 3). */ if( mbedtls_mpi_size( &pt->X ) > ( grp->nbits + 7 ) / 8 ) return( MBEDTLS_ERR_ECP_INVALID_KEY ); @@ -1887,14 +1891,18 @@ int mbedtls_ecp_check_privkey( const mbedtls_ecp_group *grp, const mbedtls_mpi * #if defined(ECP_MONTGOMERY) if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY ) { - /* see [Curve25519] page 5 */ + /* see RFC 7748 sec. 5 para. 5 */ if( mbedtls_mpi_get_bit( d, 0 ) != 0 || mbedtls_mpi_get_bit( d, 1 ) != 0 || - mbedtls_mpi_get_bit( d, 2 ) != 0 || mbedtls_mpi_bitlen( d ) - 1 != grp->nbits ) /* mbedtls_mpi_bitlen is one-based! */ return( MBEDTLS_ERR_ECP_INVALID_KEY ); else - return( 0 ); + + /* see [Curve25519] page 5 */ + if( grp->nbits == 254 && mbedtls_mpi_get_bit( d, 2 ) != 0 ) + return( MBEDTLS_ERR_ECP_INVALID_KEY ); + + return( 0 ); } #endif /* ECP_MONTGOMERY */ #if defined(ECP_SHORTWEIERSTRASS) @@ -1941,10 +1949,14 @@ int mbedtls_ecp_gen_keypair_base( mbedtls_ecp_group *grp, else MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, grp->nbits, 1 ) ); - /* Make sure the last three bits are unset */ + /* Make sure the last two bits are unset for Curve448, three bits for + Curve25519 */ MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 0, 0 ) ); MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 1, 0 ) ); - MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) ); + if( grp->nbits == 254 ) + { + MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( d, 2, 0 ) ); + } } else #endif /* ECP_MONTGOMERY */ diff --git a/library/ecp_curves.c b/library/ecp_curves.c index df5ac3eea..58630e3d0 100644 --- a/library/ecp_curves.c +++ b/library/ecp_curves.c @@ -627,6 +627,9 @@ static int ecp_mod_p521( mbedtls_mpi * ); #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) static int ecp_mod_p255( mbedtls_mpi * ); #endif +#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) +static int ecp_mod_p448( mbedtls_mpi * ); +#endif #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) static int ecp_mod_p192k1( mbedtls_mpi * ); #endif @@ -687,6 +690,52 @@ cleanup: } #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ +#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) +/* + * Specialized function for creating the Curve448 group + */ +static int ecp_use_curve448( mbedtls_ecp_group *grp ) +{ + mbedtls_mpi Ns; + int ret; + + mbedtls_mpi_init( &Ns ); + + /* Actually ( A + 2 ) / 4 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &grp->A, 16, "98AA" ) ); + + /* P = 2^448 - 2^224 - 1 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->P, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &grp->P, 224 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &grp->P, &grp->P, 1 ) ); + grp->pbits = mbedtls_mpi_bitlen( &grp->P ); + + /* Y intentionally not set, since we use x/z coordinates. + * This is used as a marker to identify Montgomery curves! */ + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.X, 5 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &grp->G.Z, 1 ) ); + mbedtls_mpi_free( &grp->G.Y ); + + /* N = 2^446 - 13818066809895115352007386748515426880336692474882178609894547503885 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &grp->N, 446, 1 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &Ns, 16, + "8335DC163BB124B65129C96FDE933D8D723A70AADC873D6D54A7BB0D" ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &grp->N, &grp->N, &Ns ) ); + + /* Actually, the required msb for private keys */ + grp->nbits = 447; + +cleanup: + mbedtls_mpi_free( &Ns ); + if( ret != 0 ) + mbedtls_ecp_group_free( grp ); + + return( ret ); +} +#endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ + /* * Set a group using well-known domain parameters */ @@ -767,6 +816,12 @@ int mbedtls_ecp_group_load( mbedtls_ecp_group *grp, mbedtls_ecp_group_id id ) return( ecp_use_curve25519( grp ) ); #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ +#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) + case MBEDTLS_ECP_DP_CURVE448: + grp->modp = ecp_mod_p448; + return( ecp_use_curve448( grp ) ); +#endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ + default: mbedtls_ecp_group_free( grp ); return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE ); @@ -1176,7 +1231,7 @@ static int ecp_mod_p255( mbedtls_mpi *N ) M.s = 1; M.n = N->n - ( P255_WIDTH - 1 ); if( M.n > P255_WIDTH + 1 ) - M.n = P255_WIDTH + 1; + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); M.p = Mp; memset( Mp, 0, sizeof Mp ); memcpy( Mp, N->p + P255_WIDTH - 1, M.n * sizeof( mbedtls_mpi_uint ) ); @@ -1197,6 +1252,77 @@ cleanup: } #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ +#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) + +/* Size of p448 in terms of mbedtls_mpi_uint */ +#define P448_WIDTH ( 448 / 8 / sizeof( mbedtls_mpi_uint ) ) + +/* Number of limbs fully occupied by 2^224 (max), and limbs used by it (min) */ +#define DIV_ROUND_UP( X, Y ) ( ( ( X ) + ( Y ) - 1 ) / ( Y ) ) +#define P224_WIDTH_MIN ( 28 / sizeof( mbedtls_mpi_uint ) ) +#define P224_WIDTH_MAX DIV_ROUND_UP( 28, sizeof( mbedtls_mpi_uint ) ) +#define P224_UNUSED_BITS ( ( P224_WIDTH_MAX * sizeof( mbedtls_mpi_uint ) * 8 ) - 224 ) + +/* + * Fast quasi-reduction modulo p448 = 2^448 - 2^224 - 1 + * Write N as A0 + 2^448 A1 and A1 as B0 + 2^224 B1, and return + * A0 + A1 + B1 + (B0 + B1) * 2^224. This is different to the reference + * implementation of Curve448, which uses its own special 56-bit limbs rather + * than a generic bignum library. We could squeeze some extra speed out on + * 32-bit machines by splitting N up into 32-bit limbs and doing the + * arithmetic using the limbs directly as we do for the NIST primes above, + * but for 64-bit targets it should use half the number of operations if we do + * the reduction with 224-bit limbs, since mpi_add_mpi will then use 64-bit adds. + */ +static int ecp_mod_p448( mbedtls_mpi *N ) +{ + int ret; + size_t i; + mbedtls_mpi M, Q; + mbedtls_mpi_uint Mp[P448_WIDTH + 1], Qp[P448_WIDTH]; + + if( N->n <= P448_WIDTH ) + return( 0 ); + + /* M = A1 */ + M.s = 1; + M.n = N->n - ( P448_WIDTH ); + if( M.n > P448_WIDTH ) + /* Shouldn't be called with N larger than 2^896! */ + return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA ); + M.p = Mp; + memset( Mp, 0, sizeof( Mp ) ); + memcpy( Mp, N->p + P448_WIDTH, M.n * sizeof( mbedtls_mpi_uint ) ); + + /* N = A0 */ + for( i = P448_WIDTH; i < N->n; i++ ) + N->p[i] = 0; + + /* N += A1 */ + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) ); + + /* Q = B1, N += B1 */ + Q = M; + Q.p = Qp; + memcpy( Qp, Mp, sizeof( Qp ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Q, 224 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &Q ) ); + + /* M = (B0 + B1) * 2^224, N += M */ + if( sizeof( mbedtls_mpi_uint ) > 4 ) + Mp[P224_WIDTH_MIN] &= ( (mbedtls_mpi_uint)-1 ) >> ( P224_UNUSED_BITS ); + for( i = P224_WIDTH_MAX; i < M.n; ++i ) + Mp[i] = 0; + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &M, &M, &Q ) ); + M.n = P448_WIDTH + 1; /* Make room for shifted carry bit from the addition */ + MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &M, 224 ) ); + MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( N, N, &M ) ); + +cleanup: + return( ret ); +} +#endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ + #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED) || \ defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED) || \ defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED) diff --git a/library/version_features.c b/library/version_features.c index 1b06ff322..a452caf5e 100644 --- a/library/version_features.c +++ b/library/version_features.c @@ -309,6 +309,9 @@ static const char *features[] = { #if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) "MBEDTLS_ECP_DP_CURVE25519_ENABLED", #endif /* MBEDTLS_ECP_DP_CURVE25519_ENABLED */ +#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) + "MBEDTLS_ECP_DP_CURVE448_ENABLED", +#endif /* MBEDTLS_ECP_DP_CURVE448_ENABLED */ #if defined(MBEDTLS_ECP_NIST_OPTIM) "MBEDTLS_ECP_NIST_OPTIM", #endif /* MBEDTLS_ECP_NIST_OPTIM */ diff --git a/programs/test/benchmark.c b/programs/test/benchmark.c index 1945b30d9..cecf3e363 100644 --- a/programs/test/benchmark.c +++ b/programs/test/benchmark.c @@ -766,9 +766,16 @@ int main( int argc, char *argv[] ) if( todo.ecdh ) { mbedtls_ecdh_context ecdh; -#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) mbedtls_mpi z; + const mbedtls_ecp_curve_info montgomery_curve_list[] = { +#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) + { MBEDTLS_ECP_DP_CURVE25519, 0, 0, "Curve25519" }, #endif +#if defined(MBEDTLS_ECP_DP_CURVE448_ENABLED) + { MBEDTLS_ECP_DP_CURVE448, 0, 0, "Curve448" }, +#endif + { MBEDTLS_ECP_DP_NONE, 0, 0, 0 } + }; const mbedtls_ecp_curve_info *curve_info; size_t olen; @@ -797,27 +804,32 @@ int main( int argc, char *argv[] ) mbedtls_ecdh_free( &ecdh ); } - /* Curve25519 needs to be handled separately */ -#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) - mbedtls_ecdh_init( &ecdh ); - mbedtls_mpi_init( &z ); - - if( mbedtls_ecp_group_load( &ecdh.grp, MBEDTLS_ECP_DP_CURVE25519 ) != 0 || - mbedtls_ecdh_gen_public( &ecdh.grp, &ecdh.d, &ecdh.Qp, myrand, NULL ) != 0 ) + /* Montgomery curves need to be handled separately */ + for ( curve_info = montgomery_curve_list; + curve_info->grp_id != MBEDTLS_ECP_DP_NONE; + curve_info++ ) { - mbedtls_exit( 1 ); + mbedtls_ecdh_init( &ecdh ); + mbedtls_mpi_init( &z ); + + if( mbedtls_ecp_group_load( &ecdh.grp, curve_info->grp_id ) != 0 || + mbedtls_ecdh_gen_public( &ecdh.grp, &ecdh.d, &ecdh.Qp, myrand, NULL ) != 0 ) + { + mbedtls_exit( 1 ); + } + + mbedtls_snprintf( title, sizeof(title), "ECDHE-%s", + curve_info->name ); + TIME_PUBLIC( title, "handshake", + ret |= mbedtls_ecdh_gen_public( &ecdh.grp, &ecdh.d, &ecdh.Q, + myrand, NULL ); + ret |= mbedtls_ecdh_compute_shared( &ecdh.grp, &z, &ecdh.Qp, &ecdh.d, + myrand, NULL ) ); + + mbedtls_ecdh_free( &ecdh ); + mbedtls_mpi_free( &z ); } - TIME_PUBLIC( "ECDHE-Curve25519", "handshake", - ret |= mbedtls_ecdh_gen_public( &ecdh.grp, &ecdh.d, &ecdh.Q, - myrand, NULL ); - ret |= mbedtls_ecdh_compute_shared( &ecdh.grp, &z, &ecdh.Qp, &ecdh.d, - myrand, NULL ) ); - - mbedtls_ecdh_free( &ecdh ); - mbedtls_mpi_free( &z ); -#endif - for( curve_info = mbedtls_ecp_curve_list(); curve_info->grp_id != MBEDTLS_ECP_DP_NONE; curve_info++ ) @@ -843,26 +855,31 @@ int main( int argc, char *argv[] ) mbedtls_ecdh_free( &ecdh ); } - /* Curve25519 needs to be handled separately */ -#if defined(MBEDTLS_ECP_DP_CURVE25519_ENABLED) - mbedtls_ecdh_init( &ecdh ); - mbedtls_mpi_init( &z ); - - if( mbedtls_ecp_group_load( &ecdh.grp, MBEDTLS_ECP_DP_CURVE25519 ) != 0 || - mbedtls_ecdh_gen_public( &ecdh.grp, &ecdh.d, &ecdh.Qp, - myrand, NULL ) != 0 || - mbedtls_ecdh_gen_public( &ecdh.grp, &ecdh.d, &ecdh.Q, myrand, NULL ) != 0 ) + /* Montgomery curves need to be handled separately */ + for ( curve_info = montgomery_curve_list; + curve_info->grp_id != MBEDTLS_ECP_DP_NONE; + curve_info++) { - mbedtls_exit( 1 ); + mbedtls_ecdh_init( &ecdh ); + mbedtls_mpi_init( &z ); + + if( mbedtls_ecp_group_load( &ecdh.grp, curve_info->grp_id ) != 0 || + mbedtls_ecdh_gen_public( &ecdh.grp, &ecdh.d, &ecdh.Qp, + myrand, NULL ) != 0 || + mbedtls_ecdh_gen_public( &ecdh.grp, &ecdh.d, &ecdh.Q, myrand, NULL ) != 0 ) + { + mbedtls_exit( 1 ); + } + + mbedtls_snprintf( title, sizeof(title), "ECDH-%s", + curve_info->name ); + TIME_PUBLIC( title, "handshake", + ret |= mbedtls_ecdh_compute_shared( &ecdh.grp, &z, &ecdh.Qp, &ecdh.d, + myrand, NULL ) ); + + mbedtls_ecdh_free( &ecdh ); + mbedtls_mpi_free( &z ); } - - TIME_PUBLIC( "ECDH-Curve25519", "handshake", - ret |= mbedtls_ecdh_compute_shared( &ecdh.grp, &z, &ecdh.Qp, &ecdh.d, - myrand, NULL ) ); - - mbedtls_ecdh_free( &ecdh ); - mbedtls_mpi_free( &z ); -#endif } #endif diff --git a/tests/suites/test_suite_ecp.data b/tests/suites/test_suite_ecp.data index a43e7d75d..8e9d9fa49 100644 --- a/tests/suites/test_suite_ecp.data +++ b/tests/suites/test_suite_ecp.data @@ -330,6 +330,10 @@ ECP test vectors Curve25519 depends_on:MBEDTLS_ECP_DP_CURVE25519_ENABLED ecp_test_vec_x:MBEDTLS_ECP_DP_CURVE25519:"5AC99F33632E5A768DE7E81BF854C27C46E3FBF2ABBACD29EC4AFF517369C660":"057E23EA9F1CBE8A27168F6E696A791DE61DD3AF7ACD4EEACC6E7BA514FDA863":"47DC3D214174820E1154B49BC6CDB2ABD45EE95817055D255AA35831B70D3260":"6EB89DA91989AE37C7EAC7618D9E5C4951DBA1D73C285AE1CD26A855020EEF04":"61450CD98E36016B58776A897A9F0AEF738B99F09468B8D6B8511184D53494AB" +ECP test vectors Curve448 (RFC 7748 6.2, after decodeUCoordinate) +depends_on:MBEDTLS_ECP_DP_CURVE448_ENABLED +ecp_test_vec_x:MBEDTLS_ECP_DP_CURVE448:"eb7298a5c0d8c29a1dab27f1a6826300917389449741a974f5bac9d98dc298d46555bce8bae89eeed400584bb046cf75579f51d125498f98":"a01fc432e5807f17530d1288da125b0cd453d941726436c8bbd9c5222c3da7fa639ce03db8d23b274a0721a1aed5227de6e3b731ccf7089b":"ad997351b6106f36b0d1091b929c4c37213e0d2b97e85ebb20c127691d0dad8f1d8175b0723745e639a3cb7044290b99e0e2a0c27a6a301c":"0936f37bc6c1bd07ae3dec7ab5dc06a73ca13242fb343efc72b9d82730b445f3d4b0bd077162a46dcfec6f9b590bfcbcf520cdb029a8b73e":"9d874a5137509a449ad5853040241c5236395435c36424fd560b0cb62b281d285275a740ce32a22dd1740f4aa9161cec95ccc61a18f4ff07" + ECP test vectors secp192k1 depends_on:MBEDTLS_ECP_DP_SECP192K1_ENABLED ecp_test_vect:MBEDTLS_ECP_DP_SECP192K1:"D1E13A359F6E0F0698791938E6D60246030AE4B0D8D4E9DE":"281BCA982F187ED30AD5E088461EBE0A5FADBB682546DF79":"3F68A8E9441FB93A4DD48CB70B504FCC9AA01902EF5BE0F3":"BE97C5D2A1A94D081E3FACE53E65A27108B7467BDF58DE43":"5EB35E922CD693F7947124F5920022C4891C04F6A8B8DCB2":"60ECF73D0FC43E0C42E8E155FFE39F9F0B531F87B34B6C3C":"372F5C5D0E18313C82AEF940EC3AFEE26087A46F1EBAE923":"D5A9F9182EC09CEAEA5F57EA10225EC77FA44174511985FD"