mphell_tuto_conversion_weierstrass_to_jacobi_quartic.c

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/* 
  MPHELL-5.0 
  Author(s): The MPHELL team
 
 (C) Copyright 2015-2021 - 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/>.
*/
 
#include <stdio.h>
#include "mphell/mphell.h"
 
int main()
{
    /* Initialise MPHELL with 256 bits of security strength for the entropy, RANDOM_AES256 as DRBG and DEVURANDOM as entropy source */
    
    init_mphell(256, RANDOM_AES256, DEVURANDOM);
    
    /* Allocate a field of size 6*block_SIZE = 6*64 = 384 on 64 bits architecture */
    
    field k;
    field_alloc(k, FP, bits_to_nblock(384), NULL);
       
    /* Allocate temporary memory */
    
    number p;
    field_elt a, b;
    ec_point G, res, res_jq;
    number n, h;
    field_elt teta;
 
    number_init(&p, bits_to_nblock(384));
 
    /* Set the number p from a string in base 16 */
    
    number_set_str(p, "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff", 16);
#if MPHELL_USE_AMNS == 1
    amns AMNS;
#if MPHELL_USE_AMNS_32 == 0
    amns_alloc_init_str(&AMNS, "[0, 7, [-2, 0, 0, 0, 0, 0, 0, 1], 59, 8010427042960414838884725536003025378504357914088932113335334539926383793809451548018236227209625700052722361381087, [-8576931003528147, 12963241998501462, -11685779024318585, 12198217901242760, 5469056521909520, -16952339206744690, -7801587214757611], [936600828956320511, 17864700281010200544, 7457034104920941375, 4906978974859566336, 1521310033682434027, 11977106235113612084, 6613199331606154624], [-48661600919137196, -16406260014740521, -9043881017757559, -15840327204754192, -4503903233538141, -10931797952018020, 3933578076642458], [-10700965224081570, -31747207631521220, -21134995866173053, -3985617456248275, -932744058138743, -25427794319760237, -2489368063126092]]", p);
#else
    amns_alloc_init_str(&AMNS, "[0, 18, [-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 26, 28816340648335589686749390875939188706868735452517709312097740458242732054770156839198296353641579295263032233716200, [-51353, 1463368, 1158979, 544183, -726450, 976213, 144497, -886193, -264198, 688818, 1070182, -170086, 864472, -144241, -360825, -510521, 1017098, -59072], [3993315613, 3730700630, 867896355, 1312786307, 471958917, 4205419201, 2925107995, 1257333470, 1009072108, 3882493844, 334530385, 923966745, 2062755457, 1054721524, 1062123069, 2491481070, 813468425, 1351925765], [1499105, 1805368, 3513276, 2380622, 4551927, 3187369, 3810913, 2129326, 3493684, 1909307, 1981401, 2013148, 1633911, 2996996, 2975679, 3661385, 2455278, 1909836], [5854047, 6627253, 2246346, 3861327, 2251173, 2334257, 1163302, 3551220, 4498564, 4312125, 4221299, 3184071, 2952719, 307544, 1633107, 2468475, 2132615, 2940733]]", p);
#endif
    field_set_amns(k, AMNS);
#endif
    
    /* Create the field of characteristic p */
    
    field_create(k, "", STACK_1, 1, p);
    
    ec_point_alloc(res, k);
    ec_point_init(res, k);
    ec_point_alloc(res_jq, k);
    ec_point_init(res_jq, k);
 
    field_elt_alloc(&a, k);
    field_elt_init(a, k);
    field_elt_alloc(&b, k);
    field_elt_init(b, k);
    ec_point_alloc(G, k);
    ec_point_init(G, k);
    number_init(&n, bits_to_nblock(384));
    number_init(&h, bits_to_nblock(384));
    field_elt_alloc(&teta, k); 
    field_elt_init(teta, k); 
    
    field_elt_set_str(a, "e6d121fc8cfc85448e51524d40b0a3f6146006a7e2001270385be91a918ba0c2066c8ae2615a9bf927b73c9756bce6b2", 16, false, k, STACK_1);
    field_elt_set_str(b, "a36e0555338282573d94a77351044dfad63d30aac6505bcd470ad021e3a4b057d81fc21d6c92ef0190798b386c38f9ba", 16, false, k, STACK_1);
    ec_point_set_aff_str(G, "a3f0d2b9cbda17b9201391877f744cbc69f7efe29f56e2552439582e70238edbdb70193133bae1d9a8b659d2d7692931", "c467049b488e283fdf78669237ca9387b347f63d17ce4fac5e6bbe737b4d8e306dfcb80eee28477ab6a0e06f262e47d2", false, 16, WEIERSTRASS, k, STACK_1);
    number_set_str(h, "15ad3c423d6df1572016199efaeee94ca5242a87a4", 16);
    number_set_str(n, "bcf569c46c00fa8b5f4c7d41b55e14295468dac4097918b25e24499", 16);
    
    /* Allocate curves */
    
    ec_curve E, E_jq;
    ec_alloc (E, k);
    ec_init(E, k);
    ec_alloc (E_jq, k);
    ec_init(E_jq, k);
    
    /* Create curve */
    
    ec_create(E, "RandP384", k, a, b, G, h, n, WEIERSTRASS, PROJECTIVE, STACK_1);
    
    printf("The weierstrass departing curve \nE: \n"); ec_curve_print(E, 16, STACK_1); printf("\n");
 
    /* Creation of a random point on the weierstras elliptic curve */
    
    weierstrass_point_random(res, E, STACK_1);
    printf("random point, res = "); ec_point_print(res, 16, true, k, STACK_1); printf("\n");
    printf("res belongs to E : %d\n\n", weierstrass_belongs(res, E, STACK_1));
 
    /* Conversion to one (specific) of the possible Jacobi_Quartic curve */
    
    weierstrass_to_jacobi_quartic(E_jq, E, false, teta, STACK_1);
                                           /* Here false signifies that teta is not specified and that the function have to find the isomorphism for which b_j=1 */
 
    printf("The Jacobi Quartic curve isomorphic to E calculated with teta not specified \n"); 
    printf("E_jq: \n"); ec_curve_print(E_jq, 16, STACK_1); printf("\n");
 
    weierstrass_to_jacobi_quartic(E_jq, E, true, teta, STACK_1);
                                           /* Here true signifies that teta is specified  */
    
    printf("The Jacobi Quartic curve calculated with teta specified \n"); 
    printf("E_jq: \n"); ec_curve_print(E_jq, 16, STACK_1); printf("\n");
 
    /* Conversion of a point on an Jacobi Quartic Elliptic curve*/
    
    weierstrass_point_to_jacobi_quartic_point(res_jq, res, E_jq, STACK_1);
    printf("Jacobi Quartic random point, res_jq = "); ec_point_print(res_jq, 16, true, k, STACK_1); printf("\n");
    printf("res_jq belongs to E_jq : %d\n\n", jacobi_quartic_belongs(res_jq, E_jq, STACK_1));
 
    ec_free(E_jq); 
 
    /* Free allocated memory */
    
    field_elt_free(&teta, k);  
    field_elt_free(&a, k);
    field_elt_free(&b, k);
    ec_point_free(G, k);
    number_free(&n);
    number_free(&h);
    ec_point_free(res, k);
    ec_point_free(res_jq, k);
    number_free(&p);
    field_free(k);
#if MPHELL_USE_AMNS == 1
    amns_free(&AMNS);
#endif
    ec_free(E);
    
    free_mphell();
 
    return 0;
}