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Added ecp_sub() as a variant of ecp_add()

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Manuel Pégourié-Gonnard 2012-11-19 21:23:27 +01:00 committed by Paul Bakker
parent 1c2782cc7c
commit 9674fd0d5e
4 changed files with 132 additions and 8 deletions
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14
include/polarssl/ecp.h
View file

@ -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
*

62
library/ecp.c
View file

@ -550,24 +550,44 @@ cleanup:
}
/*
* Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
* The coordinates of Q must be normalized (= affine).
* Addition or subtraction: R = P + Q or R = P + Q,
* 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 )

27
tests/suites/test_suite_ecp.data
View file

@ -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

37
tests/suites/test_suite_ecp.function
View file

@ -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
{