Changed to jacobian coordinates everywhere
This commit is contained in:
Manuel Pégourié-Gonnard
Paul Bakker
parent
773ed546a2
commit
1c2782cc7c
3 changed files with 68 additions and 135 deletions
|
|
@ -37,15 +37,19 @@
|
|||
#define POLARSSL_ERR_ECP_GENERIC -0x007E /**< Generic ECP error */
|
||||
|
||||
/**
|
||||
* \brief ECP point structure (affine coordinates)
|
||||
* \brief ECP point structure (jacobian coordinates)
|
||||
*
|
||||
* Note: if the point is zero, X and Y are irrelevant and should be freed.
|
||||
* \note All functions expect and return points satisfying
|
||||
* the following condition: Z == 0 or Z == 1. (Other
|
||||
* values of Z are used by internal functions only.)
|
||||
* The point is zero, or "at infinity", if Z == 0.
|
||||
* Otherwise, X and Y are its standard (affine) coordinates.
|
||||
*/
|
||||
typedef struct
|
||||
{
|
||||
char is_zero; /*!< true if point at infinity */
|
||||
mpi X; /*!< the point's X coordinate */
|
||||
mpi Y; /*!< the point's Y coordinate */
|
||||
mpi Z; /*!< the point's Z coordinate */
|
||||
}
|
||||
ecp_point;
|
||||
|
||||
|
|
@ -119,8 +123,11 @@ void ecp_group_free( ecp_group *grp );
|
|||
|
||||
/**
|
||||
* \brief Set a point to zero
|
||||
*
|
||||
* \return 0 if successful,
|
||||
* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
|
||||
*/
|
||||
void ecp_set_zero( ecp_point *pt );
|
||||
int ecp_set_zero( ecp_point *pt );
|
||||
|
||||
/**
|
||||
* \brief Copy the contents of point Q into P
|
||||
|
|
|
|||
182
library/ecp.c
182
library/ecp.c
|
|
@ -46,9 +46,9 @@ void ecp_point_init( ecp_point *pt )
|
|||
if( pt == NULL )
|
||||
return;
|
||||
|
||||
pt->is_zero = 1;
|
||||
mpi_init( &pt->X );
|
||||
mpi_init( &pt->Y );
|
||||
mpi_init( &pt->Z );
|
||||
}
|
||||
|
||||
/*
|
||||
|
|
@ -78,9 +78,9 @@ void ecp_point_free( ecp_point *pt )
|
|||
if( pt == NULL )
|
||||
return;
|
||||
|
||||
pt->is_zero = 1;
|
||||
mpi_free( &( pt->X ) );
|
||||
mpi_free( &( pt->Y ) );
|
||||
mpi_free( &( pt->Z ) );
|
||||
}
|
||||
|
||||
/*
|
||||
|
|
@ -100,11 +100,16 @@ void ecp_group_free( ecp_group *grp )
|
|||
/*
|
||||
* Set point to zero
|
||||
*/
|
||||
void ecp_set_zero( ecp_point *pt )
|
||||
int ecp_set_zero( ecp_point *pt )
|
||||
{
|
||||
pt->is_zero = 1;
|
||||
mpi_free( &pt->X );
|
||||
mpi_free( &pt->Y );
|
||||
int ret;
|
||||
|
||||
MPI_CHK( mpi_lset( &pt->X , 1 ) );
|
||||
MPI_CHK( mpi_lset( &pt->Y , 1 ) );
|
||||
MPI_CHK( mpi_lset( &pt->Z , 0 ) );
|
||||
|
||||
cleanup:
|
||||
return( ret );
|
||||
}
|
||||
|
||||
/*
|
||||
|
|
@ -114,14 +119,9 @@ int ecp_copy( ecp_point *P, const ecp_point *Q )
|
|||
{
|
||||
int ret;
|
||||
|
||||
if( Q->is_zero ) {
|
||||
ecp_set_zero( P );
|
||||
return( 0 );
|
||||
}
|
||||
|
||||
P->is_zero = Q->is_zero;
|
||||
MPI_CHK( mpi_copy( &P->X, &Q->X ) );
|
||||
MPI_CHK( mpi_copy( &P->Y, &Q->Y ) );
|
||||
MPI_CHK( mpi_copy( &P->Z, &Q->Z ) );
|
||||
|
||||
cleanup:
|
||||
return( ret );
|
||||
|
|
@ -135,9 +135,9 @@ int ecp_point_read_string( ecp_point *P, int radix,
|
|||
{
|
||||
int ret;
|
||||
|
||||
P->is_zero = 0;
|
||||
MPI_CHK( mpi_read_string( &P->X, radix, x ) );
|
||||
MPI_CHK( mpi_read_string( &P->Y, radix, y ) );
|
||||
MPI_CHK( mpi_lset( &P->Z, 1 ) );
|
||||
|
||||
cleanup:
|
||||
return( ret );
|
||||
|
|
@ -459,109 +459,35 @@ int ecp_use_known_dp( ecp_group *grp, size_t index )
|
|||
MPI_CHK( mpi_sub_mpi( &N, &N, &grp->P ) )
|
||||
|
||||
/*
|
||||
* Internal point format used for fast (that is, without mpi_inv_mod)
|
||||
* addition/doubling/multiplication: Jacobian coordinates (GECC ex 3.20)
|
||||
* Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1)
|
||||
*/
|
||||
typedef struct
|
||||
{
|
||||
mpi X, Y, Z;
|
||||
}
|
||||
ecp_ptjac;
|
||||
|
||||
/*
|
||||
* Initialize a point in Jacobian coordinates
|
||||
*/
|
||||
static void ecp_ptjac_init( ecp_ptjac *P )
|
||||
{
|
||||
mpi_init( &P->X ); mpi_init( &P->Y ); mpi_init( &P->Z );
|
||||
}
|
||||
|
||||
/*
|
||||
* Free a point in Jacobian coordinates
|
||||
*/
|
||||
static void ecp_ptjac_free( ecp_ptjac *P )
|
||||
{
|
||||
mpi_free( &P->X ); mpi_free( &P->Y ); mpi_free( &P->Z );
|
||||
}
|
||||
|
||||
/*
|
||||
* Copy P to R in Jacobian coordinates
|
||||
*/
|
||||
static int ecp_ptjac_copy( ecp_ptjac *R, const ecp_ptjac *P )
|
||||
{
|
||||
int ret;
|
||||
|
||||
MPI_CHK( mpi_copy( &R->X, &P->X ) );
|
||||
MPI_CHK( mpi_copy( &R->Y, &P->Y ) );
|
||||
MPI_CHK( mpi_copy( &R->Z, &P->Z ) );
|
||||
|
||||
cleanup:
|
||||
return( ret );
|
||||
}
|
||||
|
||||
/*
|
||||
* Set P to zero in Jacobian coordinates
|
||||
*/
|
||||
static int ecp_ptjac_set_zero( ecp_ptjac *P )
|
||||
{
|
||||
int ret;
|
||||
|
||||
MPI_CHK( mpi_lset( &P->X, 1 ) );
|
||||
MPI_CHK( mpi_lset( &P->Y, 1 ) );
|
||||
MPI_CHK( mpi_lset( &P->Z, 0 ) );
|
||||
|
||||
cleanup:
|
||||
return( ret );
|
||||
}
|
||||
|
||||
/*
|
||||
* Convert from affine to Jacobian coordinates
|
||||
*/
|
||||
static int ecp_aff_to_jac( ecp_ptjac *jac, const ecp_point *aff )
|
||||
{
|
||||
int ret;
|
||||
|
||||
if( aff->is_zero )
|
||||
return( ecp_ptjac_set_zero( jac ) );
|
||||
|
||||
MPI_CHK( mpi_copy( &jac->X, &aff->X ) );
|
||||
MPI_CHK( mpi_copy( &jac->Y, &aff->Y ) );
|
||||
MPI_CHK( mpi_lset( &jac->Z, 1 ) );
|
||||
|
||||
cleanup:
|
||||
return( ret );
|
||||
}
|
||||
|
||||
/*
|
||||
* Convert from Jacobian to affine coordinates
|
||||
*/
|
||||
static int ecp_jac_to_aff( const ecp_group *grp,
|
||||
ecp_point *aff, const ecp_ptjac *jac )
|
||||
static int ecp_normalize( const ecp_group *grp, ecp_point *pt )
|
||||
{
|
||||
int ret;
|
||||
mpi Zi, ZZi, T;
|
||||
|
||||
if( mpi_cmp_int( &jac->Z, 0 ) == 0 ) {
|
||||
ecp_set_zero( aff );
|
||||
if( mpi_cmp_int( &pt->Z, 0 ) == 0 )
|
||||
return( 0 );
|
||||
}
|
||||
|
||||
mpi_init( &Zi ); mpi_init( &ZZi ); mpi_init( &T );
|
||||
|
||||
aff->is_zero = 0;
|
||||
/*
|
||||
* X = X / Z^2 mod p
|
||||
*/
|
||||
MPI_CHK( mpi_inv_mod( &Zi, &pt->Z, &grp->P ) );
|
||||
MPI_CHK( mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
|
||||
MPI_CHK( mpi_mul_mpi( &pt->X, &pt->X, &ZZi ) ); MOD_MUL( pt->X );
|
||||
|
||||
/*
|
||||
* aff.X = jac.X / (jac.Z)^2 mod p
|
||||
* Y = Y / Z^3 mod p
|
||||
*/
|
||||
MPI_CHK( mpi_inv_mod( &Zi, &jac->Z, &grp->P ) );
|
||||
MPI_CHK( mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
|
||||
MPI_CHK( mpi_mul_mpi( &aff->X, &jac->X, &ZZi ) ); MOD_MUL( aff->X );
|
||||
MPI_CHK( mpi_mul_mpi( &pt->Y, &pt->Y, &ZZi ) ); MOD_MUL( pt->Y );
|
||||
MPI_CHK( mpi_mul_mpi( &pt->Y, &pt->Y, &Zi ) ); MOD_MUL( pt->Y );
|
||||
|
||||
/*
|
||||
* aff.Y = jac.Y / (jac.Z)^3 mod p
|
||||
* Z = 1
|
||||
*/
|
||||
MPI_CHK( mpi_mul_mpi( &aff->Y, &jac->Y, &ZZi ) ); MOD_MUL( aff->Y );
|
||||
MPI_CHK( mpi_mul_mpi( &aff->Y, &aff->Y, &Zi ) ); MOD_MUL( aff->Y );
|
||||
MPI_CHK( mpi_lset( &pt->Z, 1 ) );
|
||||
|
||||
cleanup:
|
||||
|
||||
|
|
@ -573,14 +499,14 @@ cleanup:
|
|||
/*
|
||||
* Point doubling R = 2 P, Jacobian coordinates (GECC 3.21)
|
||||
*/
|
||||
static int ecp_double_jac( const ecp_group *grp, ecp_ptjac *R,
|
||||
const ecp_ptjac *P )
|
||||
static int ecp_double_jac( const ecp_group *grp, ecp_point *R,
|
||||
const ecp_point *P )
|
||||
{
|
||||
int ret;
|
||||
mpi T1, T2, T3, X, Y, Z;
|
||||
|
||||
if( mpi_cmp_int( &P->Z, 0 ) == 0 )
|
||||
return( ecp_ptjac_set_zero( R ) );
|
||||
return( ecp_set_zero( R ) );
|
||||
|
||||
mpi_init( &T1 ); mpi_init( &T2 ); mpi_init( &T3 );
|
||||
mpi_init( &X ); mpi_init( &Y ); mpi_init( &Z );
|
||||
|
|
@ -625,9 +551,10 @@ cleanup:
|
|||
|
||||
/*
|
||||
* Addition: R = P + Q, mixed affine-Jacobian coordinates (GECC 3.22)
|
||||
* The coordinates of Q must be normalized (= affine).
|
||||
*/
|
||||
static int ecp_add_mixed( const ecp_group *grp, ecp_ptjac *R,
|
||||
const ecp_ptjac *P, const ecp_point *Q )
|
||||
static int ecp_add_mixed( const ecp_group *grp, ecp_point *R,
|
||||
const ecp_point *P, const ecp_point *Q )
|
||||
{
|
||||
int ret;
|
||||
mpi T1, T2, T3, T4, X, Y, Z;
|
||||
|
|
@ -636,10 +563,16 @@ static int ecp_add_mixed( const ecp_group *grp, ecp_ptjac *R,
|
|||
* Trivial cases: P == 0 or Q == 0
|
||||
*/
|
||||
if( mpi_cmp_int( &P->Z, 0 ) == 0 )
|
||||
return( ecp_aff_to_jac( R, Q ) );
|
||||
return( ecp_copy( R, Q ) );
|
||||
|
||||
if( Q->is_zero )
|
||||
return( ecp_ptjac_copy( R, P ) );
|
||||
if( mpi_cmp_int( &Q->Z, 0 ) == 0 )
|
||||
return( ecp_copy( R, P ) );
|
||||
|
||||
/*
|
||||
* Make sure Q coordinates are normalized
|
||||
*/
|
||||
if( mpi_cmp_int( &Q->Z, 1 ) != 0 )
|
||||
return( POLARSSL_ERR_ECP_GENERIC );
|
||||
|
||||
mpi_init( &T1 ); mpi_init( &T2 ); mpi_init( &T3 ); mpi_init( &T4 );
|
||||
mpi_init( &X ); mpi_init( &Y ); mpi_init( &Z );
|
||||
|
|
@ -660,7 +593,7 @@ static int ecp_add_mixed( const ecp_group *grp, ecp_ptjac *R,
|
|||
}
|
||||
else
|
||||
{
|
||||
ret = ecp_ptjac_set_zero( R );
|
||||
ret = ecp_set_zero( R );
|
||||
goto cleanup;
|
||||
}
|
||||
}
|
||||
|
|
@ -691,24 +624,17 @@ cleanup:
|
|||
}
|
||||
|
||||
/*
|
||||
* Addition: R = P + Q, affine wrapper
|
||||
* Addition: R = P + Q, result's coordinates normalized
|
||||
*/
|
||||
int ecp_add( const ecp_group *grp, ecp_point *R,
|
||||
const ecp_point *P, const ecp_point *Q )
|
||||
{
|
||||
int ret;
|
||||
ecp_ptjac J;
|
||||
|
||||
ecp_ptjac_init( &J );
|
||||
|
||||
MPI_CHK( ecp_aff_to_jac( &J, P ) );
|
||||
MPI_CHK( ecp_add_mixed( grp, &J, &J, Q ) );
|
||||
MPI_CHK( ecp_jac_to_aff( grp, R, &J ) );
|
||||
MPI_CHK( ecp_add_mixed( grp, R, P, Q ) );
|
||||
MPI_CHK( ecp_normalize( grp, R ) );
|
||||
|
||||
cleanup:
|
||||
|
||||
ecp_ptjac_free( &J );
|
||||
|
||||
return( ret );
|
||||
}
|
||||
|
||||
|
|
@ -720,7 +646,7 @@ int ecp_mul( const ecp_group *grp, ecp_point *R,
|
|||
{
|
||||
int ret, cmp;
|
||||
size_t pos;
|
||||
ecp_ptjac Q[2];
|
||||
ecp_point Q[2];
|
||||
|
||||
cmp = mpi_cmp_int( m, 0 );
|
||||
|
||||
|
|
@ -731,29 +657,29 @@ int ecp_mul( const ecp_group *grp, ecp_point *R,
|
|||
* The general method works only for m != 0
|
||||
*/
|
||||
if( cmp == 0 ) {
|
||||
ecp_set_zero( R );
|
||||
return( 0 );
|
||||
return( ecp_set_zero( R ) );
|
||||
}
|
||||
|
||||
ecp_ptjac_init( &Q[0] ); ecp_ptjac_init( &Q[1] );
|
||||
ecp_point_init( &Q[0] ); ecp_point_init( &Q[1] );
|
||||
|
||||
ecp_ptjac_set_zero( &Q[0] );
|
||||
MPI_CHK( ecp_set_zero( &Q[0] ) );
|
||||
|
||||
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_ptjac_copy( &Q[0], &Q[ mpi_get_bit( m, pos ) ] ) );
|
||||
MPI_CHK( ecp_copy( &Q[0], &Q[ mpi_get_bit( m, pos ) ] ) );
|
||||
|
||||
if( pos == 0 )
|
||||
break;
|
||||
}
|
||||
|
||||
MPI_CHK( ecp_jac_to_aff( grp, R, &Q[0] ) );
|
||||
MPI_CHK( ecp_copy( R, &Q[0] ) );
|
||||
MPI_CHK( ecp_normalize( grp, R ) );
|
||||
|
||||
cleanup:
|
||||
|
||||
ecp_ptjac_free( &Q[0] ); ecp_ptjac_free( &Q[1] );
|
||||
ecp_point_free( &Q[0] ); ecp_point_free( &Q[1] );
|
||||
|
||||
return( ret );
|
||||
}
|
||||
|
|
|
|||
|
|
@ -31,7 +31,7 @@ ecp_small_add:a_zero:x_a:y_a:b_zero:x_b:y_b:c_zero:x_c:y_c
|
|||
TEST_ASSERT( ecp_add( &grp, &C, &A, &B ) == 0 );
|
||||
|
||||
if( {c_zero} )
|
||||
TEST_ASSERT( C.is_zero );
|
||||
TEST_ASSERT( mpi_cmp_int( &C.Z, 0 ) == 0 );
|
||||
else
|
||||
{
|
||||
TEST_ASSERT( mpi_cmp_int( &C.X, {x_c} ) == 0 );
|
||||
|
|
@ -41,7 +41,7 @@ ecp_small_add:a_zero:x_a:y_a:b_zero:x_b:y_b:c_zero:x_c:y_c
|
|||
TEST_ASSERT( ecp_add( &grp, &C, &B, &A ) == 0 );
|
||||
|
||||
if( {c_zero} )
|
||||
TEST_ASSERT( C.is_zero );
|
||||
TEST_ASSERT( mpi_cmp_int( &C.Z, 0 ) == 0 );
|
||||
else
|
||||
{
|
||||
TEST_ASSERT( mpi_cmp_int( &C.X, {x_c} ) == 0 );
|
||||
|
|
@ -72,7 +72,7 @@ ecp_small_mul:m:r_zero:x_r:y_r:ret
|
|||
TEST_ASSERT( ecp_mul( &grp, &R, &m, &grp.G ) == {ret} );
|
||||
|
||||
if( {r_zero} )
|
||||
TEST_ASSERT( R.is_zero );
|
||||
TEST_ASSERT( mpi_cmp_int( &R.Z, 0 ) == 0 );
|
||||
else
|
||||
{
|
||||
TEST_ASSERT( mpi_cmp_int( &R.X, {x_r} ) == 0 );
|
||||
|
|
|
|||
Loading…
Reference in a new issue