Basic support for Curve448, similar to the current level of support for Curve25519
diff --git a/library/ecp_curves.c b/library/ecp_curves.c
index df5ac3e..58630e3 100644
--- a/library/ecp_curves.c
+++ b/library/ecp_curves.c
@@ -627,6 +627,9 @@
#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 @@
}
#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 @@
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 @@
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 @@
}
#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)