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Add basic arithmetic for Curve25519

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Manuel Pégourié-Gonnard 2013-12-03 12:02:28 +01:00
parent 3c0b4ea97e
commit d9ea82e7d9
1 changed files with 110 additions and 0 deletions
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110
library/ecp.c
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@ -1347,6 +1347,116 @@ cleanup:
return( ret );
}
/*
* Normalize Montgomery x/z coordinates: X = X/Z, Z = 1
* Cost: 1M + 1I
*/
static int ecp_normalize_mxz( const ecp_group *grp, ecp_point *P )
{
int ret;
MPI_CHK( mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
MPI_CHK( mpi_mul_mpi( &P->X, &P->X, &P->Z ) ); MOD_MUL( P->X );
MPI_CHK( mpi_lset( &P->Z, 1 ) );
cleanup:
return( ret );
}
/*
* Double-and-add: R = 2P, S = P + Q, with d = X(P - Q),
* for Montgomery curves in x/z coordinates.
*
* http://www.hyperelliptic.org/EFD/g1p/auto-code/montgom/xz/ladder/mladd-1987-m.op3
* with
* d = X1
* P = (X2, Z2)
* Q = (X3, Z3)
* R = (X4, Z4)
* S = (X5, Z5)
* and eliminating temporary variables tO, ..., t4.
*
* Cost: 5M + 4S
*/
static int ecp_double_add_mxz( const ecp_group *grp,
ecp_point *R, ecp_point *S,
const ecp_point *P, const ecp_point *Q,
const mpi *d )
{
int ret;
mpi A, AA, B, BB, E, C, D, DA, CB;
mpi_init( &A ); mpi_init( &AA ); mpi_init( &B );
mpi_init( &BB ); mpi_init( &E ); mpi_init( &C );
mpi_init( &D ); mpi_init( &DA ); mpi_init( &CB );
MPI_CHK( mpi_add_mpi( &A, &P->X, &P->Z ) ); MOD_ADD( A );
MPI_CHK( mpi_mul_mpi( &AA, &A, &A ) ); MOD_MUL( AA );
MPI_CHK( mpi_sub_mpi( &B, &P->X, &P->Z ) ); MOD_SUB( B );
MPI_CHK( mpi_mul_mpi( &BB, &B, &B ) ); MOD_MUL( BB );
MPI_CHK( mpi_sub_mpi( &E, &AA, &BB ) ); MOD_SUB( E );
MPI_CHK( mpi_add_mpi( &C, &Q->X, &Q->Z ) ); MOD_ADD( C );
MPI_CHK( mpi_sub_mpi( &D, &Q->X, &Q->Z ) ); MOD_SUB( D );
MPI_CHK( mpi_mul_mpi( &DA, &D, &A ) ); MOD_MUL( DA );
MPI_CHK( mpi_mul_mpi( &CB, &C, &B ) ); MOD_MUL( CB );
MPI_CHK( mpi_add_mpi( &S->X, &DA, &CB ) ); MOD_MUL( S->X );
MPI_CHK( mpi_mul_mpi( &S->X, &S->X, &S->X ) ); MOD_MUL( S->X );
MPI_CHK( mpi_sub_mpi( &S->Z, &DA, &CB ) ); MOD_SUB( S->Z );
MPI_CHK( mpi_mul_mpi( &S->Z, &S->Z, &S->Z ) ); MOD_MUL( S->Z );
MPI_CHK( mpi_mul_mpi( &S->Z, d, &S->Z ) ); MOD_MUL( S->Z );
MPI_CHK( mpi_mul_mpi( &R->X, &AA, &BB ) ); MOD_MUL( R->X );
MPI_CHK( mpi_mul_mpi( &R->Z, &grp->A, &E ) ); MOD_MUL( R->Z );
MPI_CHK( mpi_add_mpi( &R->Z, &BB, &R->Z ) ); MOD_ADD( R->Z );
MPI_CHK( mpi_mul_mpi( &R->Z, &E, &R->Z ) ); MOD_MUL( R->Z );
cleanup:
mpi_free( &A ); mpi_free( &AA ); mpi_free( &B );
mpi_free( &BB ); mpi_free( &E ); mpi_free( &C );
mpi_free( &D ); mpi_free( &DA ); mpi_free( &CB );
return( ret );
}
/*
* Multiplication with Montgomery ladder in x/z coordinates
*/
int ecp_mul_mxz( ecp_group *grp, ecp_point *R,
const mpi *m, const ecp_point *P,
int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
{
int ret;
size_t i;
ecp_point RP;
mpi PX;
ecp_point_init( &RP ); mpi_init( &PX );
/* Save PX and read P before writing to R, in case P == R */
mpi_copy( &PX, &P->X );
MPI_CHK( ecp_copy( &RP, P ) );
MPI_CHK( ecp_set_zero( R ) );
// TODO: randomize RP coordinates
(void) f_rng; (void) p_rng;
i = mpi_msb( m ) + 1;
while( i-- > 0 )
{
// TODO: no branch, and constant memory-access pattern
if( mpi_get_bit( m, i ) )
MPI_CHK( ecp_double_add_mxz( grp, &RP, R, &RP, R, &PX ) );
else
MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
}
MPI_CHK( ecp_normalize_mxz( grp, R ) );
cleanup:
ecp_point_free( &RP ); mpi_free( &PX );
return( ret );
}
/*
* Check that a point is valid as a public key (SEC1 3.2.3.1)
*/