Add basic arithmetic for Curve25519
diff --git a/library/ecp.c b/library/ecp.c
index 544b5a6..d87df02 100644
--- a/library/ecp.c
+++ b/library/ecp.c
@@ -1348,6 +1348,116 @@
}
/*
+ * Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
+ * Cost: 1M + 1I
+ */
+static int ecp_normalize_mxz( const ecp_group *grp, ecp_point *P )
+{
+ int ret;
+
+ MPI_CHK( mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
+ MPI_CHK( mpi_mul_mpi( &P->X, &P->X, &P->Z ) ); MOD_MUL( P->X );
+ MPI_CHK( mpi_lset( &P->Z, 1 ) );
+
+cleanup:
+ return( ret );
+}
+
+/*
+ * Double-and-add: R = 2P, S = P + Q, with d = X(P - Q),
+ * for Montgomery curves in x/z coordinates.
+ *
+ * http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3
+ * with
+ * d = X1
+ * P = (X2, Z2)
+ * Q = (X3, Z3)
+ * R = (X4, Z4)
+ * S = (X5, Z5)
+ * and eliminating temporary variables tO, ..., t4.
+ *
+ * Cost: 5M + 4S
+ */
+static int ecp_double_add_mxz( const ecp_group *grp,
+ ecp_point *R, ecp_point *S,
+ const ecp_point *P, const ecp_point *Q,
+ const mpi *d )
+{
+ int ret;
+ mpi A, AA, B, BB, E, C, D, DA, CB;
+
+ mpi_init( &A ); mpi_init( &AA ); mpi_init( &B );
+ mpi_init( &BB ); mpi_init( &E ); mpi_init( &C );
+ mpi_init( &D ); mpi_init( &DA ); mpi_init( &CB );
+
+ MPI_CHK( mpi_add_mpi( &A, &P->X, &P->Z ) ); MOD_ADD( A );
+ MPI_CHK( mpi_mul_mpi( &AA, &A, &A ) ); MOD_MUL( AA );
+ MPI_CHK( mpi_sub_mpi( &B, &P->X, &P->Z ) ); MOD_SUB( B );
+ MPI_CHK( mpi_mul_mpi( &BB, &B, &B ) ); MOD_MUL( BB );
+ MPI_CHK( mpi_sub_mpi( &E, &AA, &BB ) ); MOD_SUB( E );
+ MPI_CHK( mpi_add_mpi( &C, &Q->X, &Q->Z ) ); MOD_ADD( C );
+ MPI_CHK( mpi_sub_mpi( &D, &Q->X, &Q->Z ) ); MOD_SUB( D );
+ MPI_CHK( mpi_mul_mpi( &DA, &D, &A ) ); MOD_MUL( DA );
+ MPI_CHK( mpi_mul_mpi( &CB, &C, &B ) ); MOD_MUL( CB );
+ MPI_CHK( mpi_add_mpi( &S->X, &DA, &CB ) ); MOD_MUL( S->X );
+ MPI_CHK( mpi_mul_mpi( &S->X, &S->X, &S->X ) ); MOD_MUL( S->X );
+ MPI_CHK( mpi_sub_mpi( &S->Z, &DA, &CB ) ); MOD_SUB( S->Z );
+ MPI_CHK( mpi_mul_mpi( &S->Z, &S->Z, &S->Z ) ); MOD_MUL( S->Z );
+ MPI_CHK( mpi_mul_mpi( &S->Z, d, &S->Z ) ); MOD_MUL( S->Z );
+ MPI_CHK( mpi_mul_mpi( &R->X, &AA, &BB ) ); MOD_MUL( R->X );
+ MPI_CHK( mpi_mul_mpi( &R->Z, &grp->A, &E ) ); MOD_MUL( R->Z );
+ MPI_CHK( mpi_add_mpi( &R->Z, &BB, &R->Z ) ); MOD_ADD( R->Z );
+ MPI_CHK( mpi_mul_mpi( &R->Z, &E, &R->Z ) ); MOD_MUL( R->Z );
+
+cleanup:
+ mpi_free( &A ); mpi_free( &AA ); mpi_free( &B );
+ mpi_free( &BB ); mpi_free( &E ); mpi_free( &C );
+ mpi_free( &D ); mpi_free( &DA ); mpi_free( &CB );
+
+ return( ret );
+}
+
+/*
+ * Multiplication with Montgomery ladder in x/z coordinates
+ */
+int ecp_mul_mxz( ecp_group *grp, ecp_point *R,
+ const mpi *m, const ecp_point *P,
+ int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
+{
+ int ret;
+ size_t i;
+ ecp_point RP;
+ mpi PX;
+
+ ecp_point_init( &RP ); mpi_init( &PX );
+
+ /* Save PX and read P before writing to R, in case P == R */
+ mpi_copy( &PX, &P->X );
+ MPI_CHK( ecp_copy( &RP, P ) );
+ MPI_CHK( ecp_set_zero( R ) );
+
+ // TODO: randomize RP coordinates
+ (void) f_rng; (void) p_rng;
+
+ i = mpi_msb( m ) + 1;
+ while( i-- > 0 )
+ {
+ // TODO: no branch, and constant memory-access pattern
+ if( mpi_get_bit( m, i ) )
+ MPI_CHK( ecp_double_add_mxz( grp, &RP, R, &RP, R, &PX ) );
+ else
+ MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
+ }
+
+ MPI_CHK( ecp_normalize_mxz( grp, R ) );
+
+cleanup:
+ ecp_point_free( &RP ); mpi_free( &PX );
+
+ return( ret );
+}
+
+/*
* Check that a point is valid as a public key (SEC1 3.2.3.1)
*/
int ecp_check_pubkey( const ecp_group *grp, const ecp_point *pt )