Added ecp_sub() as a variant of ecp_add()

include/polarssl/ecp.h

@@ -200,6 +200,20 @@ int ecp_use_known_dp( ecp_group *grp, size_t index );
 int ecp_add( const ecp_group *grp, ecp_point *R,
              const ecp_point *P, const ecp_point *Q );
 
+/**
+ * \brief           Subtraction: R = P - Q
+ *
+ * \param grp       ECP group
+ * \param R         Destination point
+ * \param P         Left-hand point
+ * \param Q         Right-hand point
+ *
+ * \return          0 if successful,
+ *                  POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
+ */
+int ecp_sub( const ecp_group *grp, ecp_point *R,
+             const ecp_point *P, const ecp_point *Q );
+
 /**
  * \brief           Multiplication by an integer: R = m * P
  *

library/ecp.c

@@ -550,24 +550,44 @@ cleanup:
 }
 
 /*
- * Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
+ * Addition or subtraction: R = P + Q or R = P + Q,
- * The coordinates of Q must be normalized (= affine).
+ * mixed affine-Jacobian coordinates (GECC 3.22)
+ *
+ * The coordinates of Q must be normalized (= affine),
+ * but those of P don't need to. R is not normalized.
+ *
+ * If sign >= 0, perform addition, otherwise perform subtraction,
+ * taking advantage of the fact that, for Q != 0, we have
+ * -Q = (Q.X, -Q.Y, Q.Z)
  */
 static int ecp_add_mixed( const ecp_group *grp, ecp_point *R,
-                          const ecp_point *P, const ecp_point *Q )
+                          const ecp_point *P, const ecp_point *Q,
+                          signed char sign )
 {
     int ret;
     mpi T1, T2, T3, T4, X, Y, Z;
 
     /*
      * Trivial cases: P == 0 or Q == 0
+     * (Check Q first, so that we know Q != 0 when we compute -Q.)
      */
-    if( mpi_cmp_int( &P->Z, 0 ) == 0 )
-        return( ecp_copy( R, Q ) );
-
     if( mpi_cmp_int( &Q->Z, 0 ) == 0 )
         return( ecp_copy( R, P ) );
 
+    if( mpi_cmp_int( &P->Z, 0 ) == 0 )
+    {
+        ret = ecp_copy( R, Q );
+
+        /*
+         * -R.Y mod P = P - R.Y unless R.Y == 0
+         */
+        if( ret == 0 && sign < 0)
+            if( mpi_cmp_int( &R->Y, 0 ) != 0 )
+                ret = mpi_sub_mpi( &R->Y, &grp->P, &R->Y );
+
+        return( ret );
+    }
+
     /*
      * Make sure Q coordinates are normalized
      */
@@ -581,6 +601,17 @@ static int ecp_add_mixed( const ecp_group *grp, ecp_point *R,
     MPI_CHK( mpi_mul_mpi( &T2,  &T1,    &P->Z ) );  MOD_MUL( T2 );
     MPI_CHK( mpi_mul_mpi( &T1,  &T1,    &Q->X ) );  MOD_MUL( T1 );
     MPI_CHK( mpi_mul_mpi( &T2,  &T2,    &Q->Y ) );  MOD_MUL( T2 );
+
+    /*
+     * For subtraction, -Q.Y should have been used instead of Q.Y,
+     * so we replace T2 by -T2, which is P - T2 mod P
+     */
+    if( sign < 0 )
+    {
+        MPI_CHK( mpi_sub_mpi( &T2, &grp->P, &T2 ) );
+        MOD_SUB( T2 );
+    }
+
     MPI_CHK( mpi_sub_mpi( &T1,  &T1,    &P->X ) );  MOD_SUB( T1 );
     MPI_CHK( mpi_sub_mpi( &T2,  &T2,    &P->Y ) );  MOD_SUB( T2 );
 
@@ -631,7 +662,22 @@ int ecp_add( const ecp_group *grp, ecp_point *R,
 {
     int ret;
 
-    MPI_CHK( ecp_add_mixed( grp, R, P, Q ) );
+    MPI_CHK( ecp_add_mixed( grp, R, P, Q , 1 ) );
+    MPI_CHK( ecp_normalize( grp, R ) );
+
+cleanup:
+    return( ret );
+}
+
+/*
+ * Subtraction: R = P - Q, result's coordinates normalized
+ */
+int ecp_sub( const ecp_group *grp, ecp_point *R,
+             const ecp_point *P, const ecp_point *Q )
+{
+    int ret;
+
+    MPI_CHK( ecp_add_mixed( grp, R, P, Q, -1 ) );
     MPI_CHK( ecp_normalize( grp, R ) );
 
 cleanup:
@@ -667,7 +713,7 @@ int ecp_mul( const ecp_group *grp, ecp_point *R,
     for( pos = mpi_msb( m ) - 1 ; ; pos-- )
     {
         MPI_CHK( ecp_double_jac( grp, &Q[0], &Q[0] ) );
-        MPI_CHK( ecp_add_mixed( grp, &Q[1], &Q[0], P ) );
+        MPI_CHK( ecp_add_mixed( grp, &Q[1], &Q[0], P, 1 ) );
         MPI_CHK( ecp_copy( &Q[0], &Q[ mpi_get_bit( m, pos ) ] ) );
 
         if( pos == 0 )

tests/suites/test_suite_ecp.data

@@ -22,6 +22,33 @@ ecp_small_add:0:"37":"31":0:"37":"31":0:21:32
 ECP small addition #8
 ecp_small_add:0:"14":"11":0:"14":"11":0:27:30
 
+ECP small subtraction #1
+ecp_small_sub:1:"":"":1:"":"":1:0:0
+
+ECP small subtraction #2
+ecp_small_sub:1:"":"":0:"14":"11":0:14:36
+
+ECP small subtraction #3
+ecp_small_sub:1:"":"":0:"13":"00":0:13:00
+
+ECP small subtraction #4
+ecp_small_sub:0:"13":"00":0:"13":"00":1:0:0
+
+ECP small subtraction #5
+ecp_small_sub:0:"14":"11":0:"14":"11":1:0:0
+
+ECP small subtraction #6
+ecp_small_sub:0:"13":"00":0:"37":"16":0:34:14
+
+ECP small subtraction #7
+ecp_small_sub:0:"14":"11":0:"37":"16":0:45:07
+
+ECP small subtraction #8
+ecp_small_sub:0:"37":"31":0:"37":"16":0:21:32
+
+ECP small subtraction #9
+ecp_small_sub:0:"14":"11":0:"14":"36":0:27:30
+
 ECP small multiplication negative
 ecp_small_mul:-1:0:0:0:POLARSSL_ERR_ECP_GENERIC
 

tests/suites/test_suite_ecp.function

@@ -53,6 +53,43 @@ ecp_small_add:a_zero:x_a:y_a:b_zero:x_b:y_b:c_zero:x_c:y_c
 }
 END_CASE
 
+BEGIN_CASE
+ecp_small_sub:a_zero:x_a:y_a:b_zero:x_b:y_b:c_zero:x_c:y_c
+{
+    ecp_group grp;
+    ecp_point A, B, C;
+
+    ecp_group_init( &grp );
+    ecp_point_init( &A ); ecp_point_init( &B ); ecp_point_init( &C );
+
+    TEST_ASSERT( ecp_group_read_string( &grp, 10,
+                "47", "4", "17", "42", "13" ) == 0 );
+
+    if( {a_zero} )
+        ecp_set_zero( &A );
+    else
+        TEST_ASSERT( ecp_point_read_string( &A, 10, {x_a}, {y_a} ) == 0 );
+
+    if( {b_zero} )
+        ecp_set_zero( &B );
+    else
+        TEST_ASSERT( ecp_point_read_string( &B, 10, {x_b}, {y_b} ) == 0 );
+
+    TEST_ASSERT( ecp_sub( &grp, &C, &A, &B ) == 0 );
+
+    if( {c_zero} )
+        TEST_ASSERT( mpi_cmp_int( &C.Z, 0 ) == 0 );
+    else
+    {
+        TEST_ASSERT( mpi_cmp_int( &C.X, {x_c} ) == 0 );
+        TEST_ASSERT( mpi_cmp_int( &C.Y, {y_c} ) == 0 );
+    }
+
+    ecp_group_free( &grp );
+    ecp_point_free( &A ); ecp_point_free( &B ); ecp_point_free( &C );
+}
+END_CASE
+
 BEGIN_CASE
 ecp_small_mul:m:r_zero:x_r:y_r:ret
 {