Now reducing mod p after every single operation
This commit is contained in:
Manuel Pégourié-Gonnard
Paul Bakker
parent
e0c16922f9
commit
84d1aea1ac
125
library/ecp.c
125
library/ecp.c
@ -206,6 +206,25 @@ int ecp_use_known_dp( ecp_group *grp, size_t index )
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return( POLARSSL_ERR_ECP_GENERIC );
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}
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/*
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* Reduce a mpi mod p in-place, general case, to use after mpi_mul_mpi
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*/
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#define MOD_MUL( N ) MPI_CHK( mpi_mod_mpi( &N, &N, &grp->P ) )
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/*
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* Reduce a mpi mod p in-place, to use after mpi_sub_mpi
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*/
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#define MOD_SUB( N ) \
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while( mpi_cmp_int( &N, 0 ) < 0 ) \
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MPI_CHK( mpi_add_mpi( &N, &N, &grp->P ) )
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/*
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* Reduce a mpi mod p in-place, to use after mpi_add_mpi and mpi_mul_int
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*/
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#define MOD_ADD( N ) \
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while( mpi_cmp_mpi( &N, &grp->P ) >= 0 ) \
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MPI_CHK( mpi_sub_mpi( &N, &N, &grp->P ) )
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/*
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* Internal point format used for fast addition/doubling/multiplication:
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* Jacobian coordinates (GECC example 3.20)
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@ -274,7 +293,7 @@ static int ecp_aff_to_jac( ecp_ptjac *jac, const ecp_point *aff )
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MPI_CHK( mpi_copy( &jac->X, &aff->X ) );
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MPI_CHK( mpi_copy( &jac->Y, &aff->Y ) );
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MPI_CHK( mpi_lset( &jac->Z, 1 ) );
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MPI_CHK( mpi_lset( &jac->Z, 1 ) );
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cleanup:
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return( ret );
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@ -301,17 +320,15 @@ static int ecp_jac_to_aff( const ecp_group *grp,
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/*
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* aff.X = jac.X / (jac.Z)^2 mod p
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*/
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MPI_CHK( mpi_inv_mod( &Zi, &jac->Z, &grp->P ) );
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MPI_CHK( mpi_mul_mpi( &ZZi, &Zi, &Zi ) );
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MPI_CHK( mpi_mul_mpi( &T, &jac->X, &ZZi ) );
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MPI_CHK( mpi_mod_mpi( &aff->X, &T, &grp->P ) );
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MPI_CHK( mpi_inv_mod( &Zi, &jac->Z, &grp->P ) );
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MPI_CHK( mpi_mul_mpi( &ZZi, &Zi, &Zi ) ); MOD_MUL( ZZi );
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MPI_CHK( mpi_mul_mpi( &aff->X, &jac->X, &ZZi ) ); MOD_MUL( aff->X );
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/*
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* aff.Y = jac.Y / (jac.Z)^3 mod p
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*/
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MPI_CHK( mpi_mul_mpi( &T, &jac->Y, &ZZi ) );
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MPI_CHK( mpi_mul_mpi( &T, &T, &Zi ) );
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MPI_CHK( mpi_mod_mpi( &aff->Y, &T, &grp->P ) );
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MPI_CHK( mpi_mul_mpi( &aff->Y, &jac->Y, &ZZi ) ); MOD_MUL( aff->Y );
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MPI_CHK( mpi_mul_mpi( &aff->Y, &aff->Y, &Zi ) ); MOD_MUL( aff->Y );
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cleanup:
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@ -335,29 +352,37 @@ static int ecp_double_jac( const ecp_group *grp, ecp_ptjac *R,
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mpi_init( &T1 ); mpi_init( &T2 ); mpi_init( &T3 );
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mpi_init( &X ); mpi_init( &Y ); mpi_init( &Z );
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MPI_CHK( mpi_mul_mpi( &T1, &P->Z, &P->Z ) );
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MPI_CHK( mpi_sub_mpi( &T2, &P->X, &T1 ) );
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MPI_CHK( mpi_add_mpi( &T1, &P->X, &T1 ) );
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MPI_CHK( mpi_mul_mpi( &T2, &T2, &T1 ) );
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MPI_CHK( mpi_mul_int( &T2, &T2, 3 ) );
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MPI_CHK( mpi_mul_mpi( &T1, &P->Z, &P->Z ) ); MOD_MUL( T1 );
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MPI_CHK( mpi_sub_mpi( &T2, &P->X, &T1 ) ); MOD_SUB( T2 );
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MPI_CHK( mpi_add_mpi( &T1, &P->X, &T1 ) ); MOD_ADD( T1 );
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MPI_CHK( mpi_mul_mpi( &T2, &T2, &T1 ) ); MOD_MUL( T2 );
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MPI_CHK( mpi_mul_int( &T2, &T2, 3 ) ); MOD_ADD( T2 );
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MPI_CHK( mpi_copy ( &Y, &P->Y ) );
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MPI_CHK( mpi_shift_l( &Y, 1 ) );
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MPI_CHK( mpi_mul_mpi( &Z, &Y, &P->Z ) );
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MPI_CHK( mpi_mul_mpi( &Y, &Y, &Y ) );
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MPI_CHK( mpi_mul_mpi( &T3, &Y, &P->X ) );
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MPI_CHK( mpi_mul_mpi( &Y, &Y, &Y ) );
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MPI_CHK( mpi_shift_r( &Y, 1 ) );
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MPI_CHK( mpi_mul_mpi( &X, &T2, &T2 ) );
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MPI_CHK( mpi_copy ( &T1, &T3 ) );
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MPI_CHK( mpi_shift_l( &T1, 1 ) );
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MPI_CHK( mpi_sub_mpi( &X, &X, &T1 ) );
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MPI_CHK( mpi_sub_mpi( &T1, &T3, &X ) );
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MPI_CHK( mpi_mul_mpi( &T1, &T1, &T2 ) );
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MPI_CHK( mpi_sub_mpi( &Y, &T1, &Y ) );
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MPI_CHK( mpi_shift_l( &Y, 1 ) ); MOD_ADD( Y );
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MPI_CHK( mpi_mul_mpi( &Z, &Y, &P->Z ) ); MOD_MUL( Z );
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MPI_CHK( mpi_mul_mpi( &Y, &Y, &Y ) ); MOD_MUL( Y );
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MPI_CHK( mpi_mul_mpi( &T3, &Y, &P->X ) ); MOD_MUL( T3 );
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MPI_CHK( mpi_mul_mpi( &Y, &Y, &Y ) ); MOD_MUL( Y );
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MPI_CHK( mpi_mod_mpi( &R->X, &X, &grp->P ) );
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MPI_CHK( mpi_mod_mpi( &R->Y, &Y, &grp->P ) );
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MPI_CHK( mpi_mod_mpi( &R->Z, &Z, &grp->P ) );
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/*
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* For Y = Y / 2 mod p, we must make sure that Y is even before
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* using right-shift. No need to reduce mod p afterwards.
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*/
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if( mpi_get_bit( &Y, 0 ) == 1 )
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MPI_CHK( mpi_add_mpi( &Y, &Y, &grp->P ) );
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MPI_CHK( mpi_shift_r( &Y, 1 ) );
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MPI_CHK( mpi_mul_mpi( &X, &T2, &T2 ) ); MOD_MUL( X );
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MPI_CHK( mpi_copy ( &T1, &T3 ) );
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MPI_CHK( mpi_shift_l( &T1, 1 ) ); MOD_ADD( T1 );
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MPI_CHK( mpi_sub_mpi( &X, &X, &T1 ) ); MOD_SUB( X );
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MPI_CHK( mpi_sub_mpi( &T1, &T3, &X ) ); MOD_SUB( T1 );
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MPI_CHK( mpi_mul_mpi( &T1, &T1, &T2 ) ); MOD_MUL( T1 );
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MPI_CHK( mpi_sub_mpi( &Y, &T1, &Y ) ); MOD_SUB( Y );
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MPI_CHK( mpi_copy( &R->X, &X ) );
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MPI_CHK( mpi_copy( &R->Y, &Y ) );
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MPI_CHK( mpi_copy( &R->Z, &Z ) );
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cleanup:
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@ -388,12 +413,12 @@ static int ecp_add_mixed( const ecp_group *grp, ecp_ptjac *R,
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mpi_init( &T1 ); mpi_init( &T2 ); mpi_init( &T3 ); mpi_init( &T4 );
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mpi_init( &X ); mpi_init( &Y ); mpi_init( &Z );
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MPI_CHK( mpi_mul_mpi( &T1, &P->Z, &P->Z ) );
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MPI_CHK( mpi_mul_mpi( &T2, &T1, &P->Z ) );
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MPI_CHK( mpi_mul_mpi( &T1, &T1, &Q->X ) );
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MPI_CHK( mpi_mul_mpi( &T2, &T2, &Q->Y ) );
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MPI_CHK( mpi_sub_mpi( &T1, &T1, &P->X ) );
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MPI_CHK( mpi_sub_mpi( &T2, &T2, &P->Y ) );
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MPI_CHK( mpi_mul_mpi( &T1, &P->Z, &P->Z ) ); MOD_MUL( T1 );
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MPI_CHK( mpi_mul_mpi( &T2, &T1, &P->Z ) ); MOD_MUL( T2 );
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MPI_CHK( mpi_mul_mpi( &T1, &T1, &Q->X ) ); MOD_MUL( T1 );
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MPI_CHK( mpi_mul_mpi( &T2, &T2, &Q->Y ) ); MOD_MUL( T2 );
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MPI_CHK( mpi_sub_mpi( &T1, &T1, &P->X ) ); MOD_SUB( T1 );
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MPI_CHK( mpi_sub_mpi( &T2, &T2, &P->Y ) ); MOD_SUB( T2 );
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if( mpi_cmp_int( &T1, 0 ) == 0 )
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{
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@ -409,22 +434,22 @@ static int ecp_add_mixed( const ecp_group *grp, ecp_ptjac *R,
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}
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}
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MPI_CHK( mpi_mul_mpi( &Z, &P->Z, &T1 ) );
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MPI_CHK( mpi_mul_mpi( &T3, &T1, &T1 ) );
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MPI_CHK( mpi_mul_mpi( &T4, &T3, &T1 ) );
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MPI_CHK( mpi_mul_mpi( &T3, &T3, &P->X ) );
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MPI_CHK( mpi_mul_int( &T1, &T3, 2 ) );
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MPI_CHK( mpi_mul_mpi( &X, &T2, &T2 ) );
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MPI_CHK( mpi_sub_mpi( &X, &X, &T1 ) );
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MPI_CHK( mpi_sub_mpi( &X, &X, &T4 ) );
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MPI_CHK( mpi_sub_mpi( &T3, &T3, &X ) );
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MPI_CHK( mpi_mul_mpi( &T3, &T3, &T2 ) );
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MPI_CHK( mpi_mul_mpi( &T4, &T4, &P->Y ) );
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MPI_CHK( mpi_sub_mpi( &Y, &T3, &T4 ) );
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MPI_CHK( mpi_mul_mpi( &Z, &P->Z, &T1 ) ); MOD_MUL( Z );
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MPI_CHK( mpi_mul_mpi( &T3, &T1, &T1 ) ); MOD_MUL( T3 );
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MPI_CHK( mpi_mul_mpi( &T4, &T3, &T1 ) ); MOD_MUL( T4 );
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MPI_CHK( mpi_mul_mpi( &T3, &T3, &P->X ) ); MOD_MUL( T3 );
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MPI_CHK( mpi_mul_int( &T1, &T3, 2 ) ); MOD_ADD( T1 );
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MPI_CHK( mpi_mul_mpi( &X, &T2, &T2 ) ); MOD_MUL( X );
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MPI_CHK( mpi_sub_mpi( &X, &X, &T1 ) ); MOD_SUB( X );
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MPI_CHK( mpi_sub_mpi( &X, &X, &T4 ) ); MOD_SUB( X );
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MPI_CHK( mpi_sub_mpi( &T3, &T3, &X ) ); MOD_SUB( T3 );
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MPI_CHK( mpi_mul_mpi( &T3, &T3, &T2 ) ); MOD_MUL( T3 );
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MPI_CHK( mpi_mul_mpi( &T4, &T4, &P->Y ) ); MOD_MUL( T4 );
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MPI_CHK( mpi_sub_mpi( &Y, &T3, &T4 ) ); MOD_SUB( Y );
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MPI_CHK( mpi_mod_mpi( &R->X, &X, &grp->P ) );
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MPI_CHK( mpi_mod_mpi( &R->Y, &Y, &grp->P ) );
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MPI_CHK( mpi_mod_mpi( &R->Z, &Z, &grp->P ) );
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MPI_CHK( mpi_copy( &R->X, &X ) );
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MPI_CHK( mpi_copy( &R->Y, &Y ) );
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MPI_CHK( mpi_copy( &R->Z, &Z ) );
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cleanup:
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