mphell-jacobi.h

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/* 
  MPHELL-4.0 
  Author(s): The MPHELL team

 (C) Copyright 2015-2018 - Institut Fourier / Univ. Grenoble Alpes (France) 

 This file is part of the MPHELL Library.
 MPHELL is free software: you can redistribute it and/or modify
 it under the terms of the GNU Lesser General Public License as published by
 the Free Software Foundation, version 3 of the License.
 
 MPHELL is distributed in the hope that it will be useful,
 but WITHOUT ANY WARRANTY; without even the implied warranty of
 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 GNU Lesser General Public License for more details.

 You should have received a copy of the GNU Lesser General Public License
 along with MPHELL.  If not, see <http://www.gnu.org/licenses/>.
*/

#ifndef MPHELL_JACOBI_H
#define MPHELL_JACOBI_H
/* E: y^2 = x^4 + 2ax^2 + 1 */
/* extended Jacobi Quartic with d=1 in affine coordinates */
/* which can be extented to the extended Jacobi Quartic (with Projective equation) E_ext: y^2 = bx^4 + 2ax^2z^2 + z^4 */
/* Homogeneous projective coordinates represent an affine point (x,y) on an extended Jacobi Quartic  E: y^2 = x^4 + 2ax^2 + 1  as (X:Y:T:Z) satisfying Y^2 = Z^2 + 2aX^2 + T^2; X^2 = ZT; a != 1 Here (X:Y:T:Z) = (sX:sY:T:sZ) for all nonzero s. */
/* The Quadruplet (X, Y, T, Z) with X^2=ZT represents the affine point (X / Z, Y / Z) */
/* We work here only with homogeneous projective coordinates. */


/************************************SETTERS**********************************/

void
jacobi_quartic_compute_disc(ec_curve E, uint8_t stack);

bool 
jacobi_quartic_verify_random_generation(ec_curve E, const char * seed, uint8_t stack);

void 
jacobi_quartic_curve_random_generation(fe_ptr a, char * seed_res, field_srcptr k, uint8_t stack);

void 
jacobi_quartic_point_set_neutral (ec_point_ptr dst, ec_curve_srcptr E, uint8_t stack);

void 
jacobi_quartic_point_set_aff (ec_point_ptr P, fe_srcptr x, fe_srcptr y, field_srcptr k, uint8_t stack);

void 
jacobi_quartic_point_set_aff_str (ec_point_ptr P, const char *str_x, 
        const char *str_y, const bool is_reduced, const uint8_t base, 
        field_srcptr k, uint8_t stack);

bool
jacobi_quartic_belongs (ec_point_srcptr P, ec_curve_srcptr E, uint8_t stack);

void 
jacobi_quartic_point_random (ec_point_ptr P, ec_curve_srcptr E, uint8_t stack);

void
jacobi_quartic_point_norm (ec_point_ptr P, ec_curve_srcptr E, uint8_t stack);

void
jacobi_quartic_point_get_x_affine (field_elt x, ec_point_ptr P, ec_curve_srcptr E, uint8_t stack);

void
jacobi_quartic_point_get_y_affine (field_elt y, ec_point_ptr P, ec_curve_srcptr E, uint8_t stack);



/*******************************COMPARISON************************************/

bool 
jacobi_quartic_point_is_neutral (ec_point_srcptr P, ec_curve_srcptr E);

bool
jacobi_quartic_point_are_equal (ec_point_srcptr P1, ec_point_srcptr P2, 
        ec_curve_srcptr E, uint8_t stack);


/*******************************OPERATIONS************************************/

void 
jacobi_quartic_point_neg (ec_point_ptr P3, ec_point_srcptr P1, ec_curve_srcptr E);

/* UNIFIED => Resistant to SPA */

void 
jacobi_quartic_point_add_unified (ec_point_ptr P3, ec_point_srcptr P1, ec_point_srcptr P2,
        ec_curve_srcptr E, uint8_t stack);

/* DEDICATED => Not resistant to SPA, but faster 
 * Only the doubling is implemented as dedicated because the dedicated addition is not faster than the unified addition 
 */

void 
jacobi_quartic_point_dbl_dedicated (ec_point_ptr P3, ec_point_srcptr P1, ec_curve_srcptr E, uint8_t stack);


#endif