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Changed to jacobian coordinates everywhere

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Manuel Pégourié-Gonnard 2012-11-19 20:16:28 +01:00 committed by Paul Bakker
parent 773ed546a2
commit 1c2782cc7c
3 changed files with 68 additions and 135 deletions
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15
include/polarssl/ecp.h
View File

@ -37,15 +37,19 @@
#define POLARSSL_ERR_ECP_GENERIC -0x007E /**< Generic ECP error */ #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 typedef struct
{ {
char is_zero; /*!< true if point at infinity */
mpi X; /*!< the point's X coordinate */ mpi X; /*!< the point's X coordinate */
mpi Y; /*!< the point's Y coordinate */ mpi Y; /*!< the point's Y coordinate */
mpi Z; /*!< the point's Z coordinate */
} }
ecp_point; ecp_point;
@ -119,8 +123,11 @@ void ecp_group_free( ecp_group *grp );
/** /**
* \brief Set a point to zero * \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 * \brief Copy the contents of point Q into P

182
library/ecp.c
View File

@ -46,9 +46,9 @@ void ecp_point_init( ecp_point *pt )
if( pt == NULL ) if( pt == NULL )
return; return;
pt->is_zero = 1;
mpi_init( &pt->X ); mpi_init( &pt->X );
mpi_init( &pt->Y ); mpi_init( &pt->Y );
mpi_init( &pt->Z );
} }
/* /*
@ -78,9 +78,9 @@ void ecp_point_free( ecp_point *pt )
if( pt == NULL ) if( pt == NULL )
return; return;
pt->is_zero = 1;
mpi_free( &( pt->X ) ); mpi_free( &( pt->X ) );
mpi_free( &( pt->Y ) ); mpi_free( &( pt->Y ) );
mpi_free( &( pt->Z ) );
} }
/* /*
@ -100,11 +100,16 @@ void ecp_group_free( ecp_group *grp )
/* /*
* Set point to zero * Set point to zero
*/ */
void ecp_set_zero( ecp_point *pt ) int ecp_set_zero( ecp_point *pt )
{ {
pt->is_zero = 1; int ret;
mpi_free( &pt->X );
mpi_free( &pt->Y ); 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; 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->X, &Q->X ) );
MPI_CHK( mpi_copy( &P->Y, &Q->Y ) ); MPI_CHK( mpi_copy( &P->Y, &Q->Y ) );
MPI_CHK( mpi_copy( &P->Z, &Q->Z ) );
cleanup: cleanup:
return( ret ); return( ret );
@ -135,9 +135,9 @@ int ecp_point_read_string( ecp_point *P, int radix,
{ {
int ret; int ret;
P->is_zero = 0;
MPI_CHK( mpi_read_string( &P->X, radix, x ) ); MPI_CHK( mpi_read_string( &P->X, radix, x ) );
MPI_CHK( mpi_read_string( &P->Y, radix, y ) ); MPI_CHK( mpi_read_string( &P->Y, radix, y ) );
MPI_CHK( mpi_lset( &P->Z, 1 ) );
cleanup: cleanup:
return( ret ); 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 ) ) MPI_CHK( mpi_sub_mpi( &N, &N, &grp->P ) )
/* /*
* Internal point format used for fast (that is, without mpi_inv_mod) * Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1)
* addition/doubling/multiplication: Jacobian coordinates (GECC ex 3.20)
*/ */
typedef struct static int ecp_normalize( const ecp_group *grp, ecp_point *pt )
{
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 )
{ {
int ret; int ret;
mpi Zi, ZZi, T; mpi Zi, ZZi, T;
if( mpi_cmp_int( &jac->Z, 0 ) == 0 ) { if( mpi_cmp_int( &pt->Z, 0 ) == 0 )
ecp_set_zero( aff );
return( 0 ); return( 0 );
}
mpi_init( &Zi ); mpi_init( &ZZi ); mpi_init( &T ); mpi_init( &Zi ); mpi_init( &ZZi ); mpi_init( &T );
aff->is_zero = 0;
/* /*
* aff.X = jac.X / (jac.Z)^2 mod p * X = X / Z^2 mod p
*/ */
MPI_CHK( mpi_inv_mod( &Zi, &jac->Z, &grp->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( &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->X, &pt->X, &ZZi ) ); MOD_MUL( pt->X );
/* /*
* aff.Y = jac.Y / (jac.Z)^3 mod p * Y = Y / Z^3 mod p
*/ */
MPI_CHK( mpi_mul_mpi( &aff->Y, &jac->Y, &ZZi ) ); MOD_MUL( aff->Y ); MPI_CHK( mpi_mul_mpi( &pt->Y, &pt->Y, &ZZi ) ); MOD_MUL( pt->Y );
MPI_CHK( mpi_mul_mpi( &aff->Y, &aff->Y, &Zi ) ); MOD_MUL( aff->Y ); MPI_CHK( mpi_mul_mpi( &pt->Y, &pt->Y, &Zi ) ); MOD_MUL( pt->Y );
/*
* Z = 1
*/
MPI_CHK( mpi_lset( &pt->Z, 1 ) );
cleanup: cleanup:
@ -573,14 +499,14 @@ cleanup:
/* /*
* Point doubling R = 2 P, Jacobian coordinates (GECC 3.21) * Point doubling R = 2 P, Jacobian coordinates (GECC 3.21)
*/ */
static int ecp_double_jac( const ecp_group *grp, ecp_ptjac *R, static int ecp_double_jac( const ecp_group *grp, ecp_point *R,
const ecp_ptjac *P ) const ecp_point *P )
{ {
int ret; int ret;
mpi T1, T2, T3, X, Y, Z; mpi T1, T2, T3, X, Y, Z;
if( mpi_cmp_int( &P->Z, 0 ) == 0 ) 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( &T1 ); mpi_init( &T2 ); mpi_init( &T3 );
mpi_init( &X ); mpi_init( &Y ); mpi_init( &Z ); 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) * 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, static int ecp_add_mixed( const ecp_group *grp, ecp_point *R,
const ecp_ptjac *P, const ecp_point *Q ) const ecp_point *P, const ecp_point *Q )
{ {
int ret; int ret;
mpi T1, T2, T3, T4, X, Y, Z; 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 * Trivial cases: P == 0 or Q == 0
*/ */
if( mpi_cmp_int( &P->Z, 0 ) == 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 ) if( mpi_cmp_int( &Q->Z, 0 ) == 0 )
return( ecp_ptjac_copy( R, P ) ); 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( &T1 ); mpi_init( &T2 ); mpi_init( &T3 ); mpi_init( &T4 );
mpi_init( &X ); mpi_init( &Y ); mpi_init( &Z ); 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 else
{ {
ret = ecp_ptjac_set_zero( R ); ret = ecp_set_zero( R );
goto cleanup; 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, int ecp_add( const ecp_group *grp, ecp_point *R,
const ecp_point *P, const ecp_point *Q ) const ecp_point *P, const ecp_point *Q )
{ {
int ret; int ret;
ecp_ptjac J;
ecp_ptjac_init( &J ); MPI_CHK( ecp_add_mixed( grp, R, P, Q ) );
MPI_CHK( ecp_normalize( grp, R ) );
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 ) );
cleanup: cleanup:
ecp_ptjac_free( &J );
return( ret ); return( ret );
} }
@ -720,7 +646,7 @@ int ecp_mul( const ecp_group *grp, ecp_point *R,
{ {
int ret, cmp; int ret, cmp;
size_t pos; size_t pos;
ecp_ptjac Q[2]; ecp_point Q[2];
cmp = mpi_cmp_int( m, 0 ); 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 * The general method works only for m != 0
*/ */
if( cmp == 0 ) { if( cmp == 0 ) {
ecp_set_zero( R ); return( ecp_set_zero( R ) );
return( 0 );
} }
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-- ) for( pos = mpi_msb( m ) - 1 ; ; pos-- )
{ {
MPI_CHK( ecp_double_jac( grp, &Q[0], &Q[0] ) ); 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 ) );
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 ) if( pos == 0 )
break; 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: cleanup:
ecp_ptjac_free( &Q[0] ); ecp_ptjac_free( &Q[1] ); ecp_point_free( &Q[0] ); ecp_point_free( &Q[1] );
return( ret ); return( ret );
} }

6
tests/suites/test_suite_ecp.function
View File

@ -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 ); TEST_ASSERT( ecp_add( &grp, &C, &A, &B ) == 0 );
if( {c_zero} ) if( {c_zero} )
TEST_ASSERT( C.is_zero ); TEST_ASSERT( mpi_cmp_int( &C.Z, 0 ) == 0 );
else else
{ {
TEST_ASSERT( mpi_cmp_int( &C.X, {x_c} ) == 0 ); 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 ); TEST_ASSERT( ecp_add( &grp, &C, &B, &A ) == 0 );
if( {c_zero} ) if( {c_zero} )
TEST_ASSERT( C.is_zero ); TEST_ASSERT( mpi_cmp_int( &C.Z, 0 ) == 0 );
else else
{ {
TEST_ASSERT( mpi_cmp_int( &C.X, {x_c} ) == 0 ); 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} ); TEST_ASSERT( ecp_mul( &grp, &R, &m, &grp.G ) == {ret} );
if( {r_zero} ) if( {r_zero} )
TEST_ASSERT( R.is_zero ); TEST_ASSERT( mpi_cmp_int( &R.Z, 0 ) == 0 );
else else
{ {
TEST_ASSERT( mpi_cmp_int( &R.X, {x_r} ) == 0 ); TEST_ASSERT( mpi_cmp_int( &R.X, {x_r} ) == 0 );