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Don't special-case a = -3, not worth it

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Manuel Pégourié-Gonnard 2013-10-10 15:55:39 +02:00
parent b8012fca5f
commit 0cd6f98c0f
2 changed files with 17 additions and 88 deletions
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5
include/polarssl/ecp.h
View File

@ -105,9 +105,6 @@ ecp_point;
* The curves we consider are defined by y^2 = x^3 + A x + B mod P,
* and a generator for a large subgroup of order N is fixed.
*
* If A is not set (ie A.p == NULL) then the value A = -3 is assumed,
* which allows the used of slightly faster point doubling formulas.
*
* pbits and nbits must be the size of P and N in bits.
*
* If modp is NULL, reduction modulo P is done using a generic algorithm.
@ -121,7 +118,7 @@ typedef struct
{
ecp_group_id id; /*!< internal group identifier */
mpi P; /*!< prime modulus of the base field */
mpi A; /*!< linear term in the equation (default: -3) */
mpi A; /*!< linear term in the equation */
mpi B; /*!< constant term in the equation */
ecp_point G; /*!< generator of the subgroup used */
mpi N; /*!< the order of G */

100
library/ecp.c
View File

@ -288,15 +288,20 @@ cleanup:
}
/*
* Import an ECP group from ASCII strings, case A == -3 (A cleared)
* Import an ECP group from ASCII strings, case A == -3
*/
int ecp_group_read_string( ecp_group *grp, int radix,
const char *p, const char *b,
const char *gx, const char *gy, const char *n)
{
int ret = ecp_group_read_string_gen( grp, radix, p, "00", b, gx, gy, n );
int ret;
mpi_free( &grp->A );
MPI_CHK( ecp_group_read_string_gen( grp, radix, p, "00", b, gx, gy, n ) );
MPI_CHK( mpi_add_int( &grp->A, &grp->P, -3 ) );
cleanup:
if( ret != 0 )
ecp_group_free( grp );
return( ret );
}
@ -1055,72 +1060,23 @@ cleanup:
}
/*
* Point doubling R = 2 P, Jacobian coordinates with a == -3 (GECC 3.21)
*/
static int ecp_double_jac_am3( 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_set_zero( R ) );
mpi_init( &T1 ); mpi_init( &T2 ); mpi_init( &T3 );
mpi_init( &X ); mpi_init( &Y ); mpi_init( &Z );
MPI_CHK( mpi_mul_mpi( &T1, &P->Z, &P->Z ) ); MOD_MUL( T1 );
MPI_CHK( mpi_sub_mpi( &T2, &P->X, &T1 ) ); MOD_SUB( T2 );
MPI_CHK( mpi_add_mpi( &T1, &P->X, &T1 ) ); MOD_ADD( T1 );
MPI_CHK( mpi_mul_mpi( &T2, &T2, &T1 ) ); MOD_MUL( T2 );
MPI_CHK( mpi_mul_int( &T2, &T2, 3 ) ); MOD_ADD( T2 );
MPI_CHK( mpi_mul_int( &Y, &P->Y, 2 ) ); MOD_ADD( Y );
MPI_CHK( mpi_mul_mpi( &Z, &Y, &P->Z ) ); MOD_MUL( Z );
MPI_CHK( mpi_mul_mpi( &Y, &Y, &Y ) ); MOD_MUL( Y );
MPI_CHK( mpi_mul_mpi( &T3, &Y, &P->X ) ); MOD_MUL( T3 );
MPI_CHK( mpi_mul_mpi( &Y, &Y, &Y ) ); MOD_MUL( Y );
/*
* For Y = Y / 2 mod p, we must make sure that Y is even before
* using right-shift. No need to reduce mod p afterwards.
*/
if( mpi_get_bit( &Y, 0 ) == 1 )
MPI_CHK( mpi_add_mpi( &Y, &Y, &grp->P ) );
MPI_CHK( mpi_shift_r( &Y, 1 ) );
MPI_CHK( mpi_mul_mpi( &X, &T2, &T2 ) ); MOD_MUL( X );
MPI_CHK( mpi_mul_int( &T1, &T3, 2 ) ); MOD_ADD( T1 );
MPI_CHK( mpi_sub_mpi( &X, &X, &T1 ) ); MOD_SUB( X );
MPI_CHK( mpi_sub_mpi( &T1, &T3, &X ) ); MOD_SUB( T1 );
MPI_CHK( mpi_mul_mpi( &T1, &T1, &T2 ) ); MOD_MUL( T1 );
MPI_CHK( mpi_sub_mpi( &Y, &T1, &Y ) ); MOD_SUB( Y );
MPI_CHK( mpi_copy( &R->X, &X ) );
MPI_CHK( mpi_copy( &R->Y, &Y ) );
MPI_CHK( mpi_copy( &R->Z, &Z ) );
cleanup:
mpi_free( &T1 ); mpi_free( &T2 ); mpi_free( &T3 );
mpi_free( &X ); mpi_free( &Y ); mpi_free( &Z );
return( ret );
}
/*
* Point doubling R = 2 P, Jacobian coordinates with general A
* Point doubling R = 2 P, Jacobian coordinates
*
* http://www.hyperelliptic.org/EFD/g1p/auto-code/shortw/jacobian/doubling/dbl-2007-bl.op3
* with heavy variable renaming, some reordering and one minor modification
* (a = 2 * b, c = d - 2a replaced with c = d, c = c - b, c = c - b)
* in order to use a lot less intermediate variables (6 vs 25).
*/
static int ecp_double_jac_gen( const ecp_group *grp, ecp_point *R,
const ecp_point *P )
static int ecp_double_jac( const ecp_group *grp, ecp_point *R,
const ecp_point *P )
{
int ret;
mpi T1, T2, T3, X3, Y3, Z3;
#if defined(POLARSSL_SELF_TEST)
dbl_count++;
#endif
mpi_init( &T1 ); mpi_init( &T2 ); mpi_init( &T3 );
mpi_init( &X3 ); mpi_init( &Y3 ); mpi_init( &Z3 );
@ -1160,22 +1116,6 @@ cleanup:
return( ret );
}
/*
* Point doubling R = 2 P, dispatcher function
*/
static int ecp_double_jac( const ecp_group *grp, ecp_point *R,
const ecp_point *P )
{
#if defined(POLARSSL_SELF_TEST)
dbl_count++;
#endif
if( grp->A.p != NULL )
return( ecp_double_jac_gen( grp, R, P ) );
else
return( ecp_double_jac_am3( grp, R, P ) );
}
/*
* Addition or subtraction: R = P + Q or R = P + Q,
* mixed affine-Jacobian coordinates (GECC 3.22)
@ -1669,18 +1609,10 @@ int ecp_check_pubkey( const ecp_group *grp, const ecp_point *pt )
/*
* YY = Y^2
* RHS = X (X^2 + A) + B = X^3 + A X + B
* with, as usual, A = -3 if A is ommited
*/
MPI_CHK( mpi_mul_mpi( &YY, &pt->Y, &pt->Y ) ); MOD_MUL( YY );
MPI_CHK( mpi_mul_mpi( &RHS, &pt->X, &pt->X ) ); MOD_MUL( RHS );
if( grp->A.p == NULL )
{
MPI_CHK( mpi_add_int( &RHS, &RHS, -3 ) ); MOD_SUB( RHS );
}
else
{
MPI_CHK( mpi_add_mpi( &RHS, &RHS, &grp->A ) ); MOD_ADD( RHS );
}
MPI_CHK( mpi_add_mpi( &RHS, &RHS, &grp->A ) ); MOD_ADD( RHS );
MPI_CHK( mpi_mul_mpi( &RHS, &RHS, &pt->X ) ); MOD_MUL( RHS );
MPI_CHK( mpi_add_mpi( &RHS, &RHS, &grp->B ) ); MOD_ADD( RHS );