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Started introducting Jacobian coordinates

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Manuel Pégourié-Gonnard 2012-11-08 17:40:51 +01:00 committed by Paul Bakker
parent 52a422f6a1
commit d070f51224
1 changed files with 75 additions and 1 deletions
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76
library/ecp.c
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@ -27,7 +27,7 @@
* References:
*
* SEC1 http://www.secg.org/index.php?action=secg,docs_secg
* Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
* GECC = Guide to Elliptic Curve Cryptography - Hankerson, Menezes, Vanstone
*/
#include "polarssl/config.h"
@ -206,6 +206,80 @@ int ecp_use_known_dp( ecp_group *grp, size_t index )
return( POLARSSL_ERR_ECP_GENERIC );
}
/*
* Internal point format used for fast addition/doubling/multiplication:
* Jacobian coordinates (GECC example 3.20)
*/
typedef struct
{
mpi X, Y, Z;
}
ecp_ptjac;
/*
* Convert from affine to Jacobian coordinates
*/
static int ecp_aff_to_jac( ecp_ptjac *jac, ecp_point *aff )
{
int ret = 0;
if( aff->is_zero )
{
MPI_CHK( mpi_lset( &jac->X, 1 ) );
MPI_CHK( mpi_lset( &jac->Y, 1 ) );
MPI_CHK( mpi_lset( &jac->Z, 0 ) );
}
else
{
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, ecp_ptjac *jac )
{
int ret = 0;
mpi Zi, ZZi, T;
if( mpi_cmp_int( &jac->Z, 0 ) == 0 ) {
ecp_set_zero( aff );
return( 0 );
}
mpi_init( &Zi ); mpi_init( &ZZi ); mpi_init( &T );
aff->is_zero = 0;
/*
* aff.X = jac.X / (jac.Z)^2 mod p
*/
MPI_CHK( mpi_inv_mod( &Zi, &jac->Z, &grp->P ) );
MPI_CHK( mpi_mul_mpi( &ZZi, &Zi, &Zi ) );
MPI_CHK( mpi_mul_mpi( &T, &jac->X, &ZZi ) );
MPI_CHK( mpi_mod_mpi( &aff->X, &T, &grp->P ) );
/*
* aff.Y = jac.Y / (jac.Z)^3 mod p
*/
MPI_CHK( mpi_mul_mpi( &T, &jac->Y, &ZZi ) );
MPI_CHK( mpi_mul_mpi( &T, &T, &Zi ) );
MPI_CHK( mpi_mod_mpi( &aff->Y, &T, &grp->P ) );
cleanup:
mpi_free( &Zi ); mpi_free( &ZZi ); mpi_free( &T );
return( ret );
}
/*
* Addition: R = P + Q, generic case (P != Q, P != 0, Q != 0, R != 0)
* Cf SEC1 v2 p. 7, item 4