From de532ee73fb78a2b84067793ed031ab4f09e5997 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Manuel=20P=C3=A9gouri=C3=A9-Gonnard?= <mpg@elzevir.fr>
Date: Tue, 6 Nov 2012 16:10:47 +0100
Subject: [PATCH] Implemented generic doubling

---
 library/ecp.c | 67 ++++++++++++++++++++++++++++++++++++++++++---------
 1 file changed, 56 insertions(+), 11 deletions(-)

diff --git a/library/ecp.c b/library/ecp.c
index 99d57cd4c..857839afc 100644
--- a/library/ecp.c
+++ b/library/ecp.c
@@ -180,7 +180,6 @@ static int ecp_add_generic( const ecp_group *grp, ecp_point *R,
 
     /*
      * LL = L^2  mod p
-     * X  = L^2 - P.X - Q.X
      */
     MPI_CHK( mpi_mul_mpi( &LL, &L, &L ) );
     MPI_CHK( mpi_mod_mpi( &LL, &LL, &grp->P ) );
@@ -215,15 +214,60 @@ cleanup:
 
 /*
  * Doubling: R = 2 * P, generic case (P != 0, R != 0)
+ * Cf SEC1 v2 p. 7, item 5
  */
 static int ecp_double_generic( const ecp_group *grp, ecp_point *R,
                                const ecp_point *P )
 {
     int ret = 0;
+    mpi LN, LD, K, L, LL, X, Y;
 
-    (void) grp;
-    (void) R;
-    (void) P;
+    mpi_init( &LN ); mpi_init( &LD ); mpi_init( &K ); mpi_init( &L );
+    mpi_init( &LL ); mpi_init( &X ); mpi_init( &Y );
+
+    /*
+     * L = 3 (P.X - 1) (P.X + 1) / (2 P.Y) mod p
+     */
+    MPI_CHK( mpi_copy( &LD, &P->Y ) );
+    MPI_CHK( mpi_shift_l( &LD, 1 ) );
+    MPI_CHK( mpi_inv_mod( &K, &LD, &grp->P ) );
+    MPI_CHK( mpi_mul_int( &K, &K, 3 ) );
+    MPI_CHK( mpi_sub_int( &LN, &P->X, 1 ) );
+    MPI_CHK( mpi_mul_mpi( &K, &K, &LN ) );
+    MPI_CHK( mpi_add_int( &LN, &P->X, 1 ) );
+    MPI_CHK( mpi_mul_mpi( &K, &K, &LN ) );
+    MPI_CHK( mpi_mod_mpi( &L, &K, &grp->P ) );
+
+    /*
+     * LL = L^2  mod p
+     */
+    MPI_CHK( mpi_mul_mpi( &LL, &L, &L ) );
+    MPI_CHK( mpi_mod_mpi( &LL, &LL, &grp->P ) );
+
+    /*
+     * X  = L^2 - 2 * P.X
+     */
+    MPI_CHK( mpi_sub_mpi( &X, &LL, &P->X ) );
+    MPI_CHK( mpi_sub_mpi( &X, &X,  &P->X ) );
+
+    /*
+     * Y = L * (P.X - X) - P.Y
+     */
+    MPI_CHK( mpi_sub_mpi( &Y, &P->X, &X) );
+    MPI_CHK( mpi_mul_mpi( &Y, &Y, &L ) );
+    MPI_CHK( mpi_sub_mpi( &Y, &Y, &P->Y ) );
+
+    /*
+     * R = (X mod p, Y mod p)
+     */
+    R->is_zero = 0;
+    MPI_CHK( mpi_mod_mpi( &R->X, &X, &grp->P ) );
+    MPI_CHK( mpi_mod_mpi( &R->Y, &Y, &grp->P ) );
+
+cleanup:
+
+    mpi_free( &LN ); mpi_init( &LD ); mpi_init( &K ); mpi_init( &L );
+    mpi_free( &LL ); mpi_init( &X ); mpi_init( &Y );
 
     return( ret );
 }
@@ -264,7 +308,6 @@ int ecp_add( const ecp_group *grp, ecp_point *R,
     return ret;
 }
 
-
 #if defined(POLARSSL_SELF_TEST)
 
 /*
@@ -290,7 +333,6 @@ static void ecp_point_print( const ecp_point *P )
         printf( "(%lu, %lu)\n", P->X.p[0], P->Y.p[0] );
 }
 
-
 /*
  * Checkup routine
  *
@@ -303,20 +345,21 @@ int ecp_self_test( int verbose )
     int ret = 0;
     unsigned i;
     ecp_group grp;
-    ecp_point O, A, B, C, D, E, F, G, TMP;
+    ecp_point O, A, B, C, D, E, F, G, H, TMP;
     ecp_point *add_tbl[][3] =
     {
         {&O, &O, &O}, {&O, &A, &A}, {&A, &O, &A},
         {&A, &A, &O}, {&B, &C, &O}, {&C, &B, &O},
         {&A, &D, &E}, {&D, &A, &E},
         {&B, &D, &F}, {&D, &B, &F},
-        // {&D, &D, &G},
+        {&D, &D, &G}, {&B, &B, &H},
     };
 
     ecp_group_init( &grp );
     ecp_point_init( &O ); ecp_point_init( &A ); ecp_point_init( &B );
     ecp_point_init( &C ); ecp_point_init( &D ); ecp_point_init( &E );
-    ecp_point_init( &F ); ecp_point_init( &G ); ecp_point_init( &TMP );
+    ecp_point_init( &F ); ecp_point_init( &G ); ecp_point_init( &H );
+    ecp_point_init( &TMP );
 
     ecp_set_zero( &O );
     MPI_CHK( ecp_group_read_string( &grp, 10, "47", "4", "17", "42", "13" ) );
@@ -327,6 +370,7 @@ int ecp_self_test( int verbose )
     MPI_CHK( ecp_point_read_string( &E, 10, "34", "14" ) );
     MPI_CHK( ecp_point_read_string( &F, 10, "45",  "7" ) );
     MPI_CHK( ecp_point_read_string( &G, 10, "21", "32" ) );
+    MPI_CHK( ecp_point_read_string( &H, 10, "27", "30" ) );
 
     if( verbose != 0 )
         printf( "  ECP test #1 (ecp_add): " );
@@ -350,7 +394,7 @@ int ecp_self_test( int verbose )
     }
 
     if (verbose != 0 )
-        printf( " passed\n" );
+        printf( "passed\n" );
 
 cleanup:
 
@@ -360,7 +404,8 @@ cleanup:
     ecp_group_free( &grp );
     ecp_point_free( &O ); ecp_point_free( &A ); ecp_point_free( &B );
     ecp_point_free( &C ); ecp_point_free( &D ); ecp_point_free( &E );
-    ecp_point_free( &F ); ecp_point_free( &G );
+    ecp_point_free( &F ); ecp_point_free( &G ); ecp_point_free( &H );
+    ecp_point_free( &TMP );
 
     if( verbose != 0 )
         printf( "\n" );