mphell_tuto_fp.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 128 bits of security strength for the entropy, RANDOM_AES128 as DRBG and DEVURANDOM as entropy source */
    
    init_mphell(128, RANDOM_AES128, DEVURANDOM);
    
    /* Allocate a field of size 3*block_SIZE = 3*64 = 192 on 64 bits architecture */
    
    field k;
    field_alloc(k, FP, bits_to_nblock(192), NULL);
    
    /* Allocate a number of size 3*block_SIZE = 3*64 = 192 on 64 bits architecture */
    
    number p;
    number_init(&p, bits_to_nblock(192));
    
    /* Set the number p from a string in base 16 */
    
    number_set_str(p, "fffffffffffffffffffffffffffffffeffffffffffffffff", 16);
#if MPHELL_USE_AMNS == 1
    amns AMNS;
#if MPHELL_USE_AMNS_32 == 0
    amns_alloc_init_str(&AMNS, "[16, 4, [-2, 0, 0, 0, 1], 52, 6172336866035235830030737468594796900503843124202341567269, [276558595304361, 45414025950417, -34859774231597, -43697934106541], [15163021665183677629, 10328824020132901291, 3520630562803742874, 2017188797426544734], [175018852767439, 167878561785955, 39999505818260, -16528460836324], [197873551048475, 174802838528544, 29957080636796, 208984152402038]]", p);
#else
    amns_alloc_init_str(&AMNS, "[1, 9, [-2, 0, 0, 0, 0, 0, 0, 0, 0, 1], 25, 778621639070749301272595529543640079614006395911121441202, [701093, -169839, 992868, -808873, -49859, -1298542, 346565, 1453220, 10927], [3371333987, 1139504849, 3063325107, 1068215102, 2225669310, 3489025068, 823765184, 3434826107, 24083075], [2398376, 1499579, -352758, -1034120, -179340, 1441412, 1982754, 1026111, 990222], [1506274, 1189710, -669416, 2638499, 1835063, 598693, 1905562, -10756, 308592]]", p);
#endif
    field_set_amns(k, AMNS);
#endif
    
    /* Create the field of characteristic p */
 
    field_create(k, "", STACK_1, 1, p);
    
    /* Allocate element of the field k */
    
    field_elt x;
    field_elt y;
    field_elt res;
    field_elt_alloc(&x, k);
    field_elt_init(x, k);
    field_elt_alloc(&y, k);
    field_elt_init(y, k);
    field_elt_alloc(&res, k);
    field_elt_init(res, k);
    
    /* Set field element from string in base 16, which are not under Montgomery form */
    
    field_elt_set_str(x, "f14b8dbafa22b6ba35626d40d2d00001381bef07d2c3017", 16, false, k, STACK_1);
    field_elt_set_str(y, "85ca4bcae9e156f1eab07c7b6cc500004ebbc0e5e3b237ce", 16, false, k, STACK_1);
    
    printf("x = "); field_elt_print(x, 16, true, k, STACK_1); printf("\n");
    printf("y = "); field_elt_print(y, 16, true, k, STACK_1); printf("\n");
    
    /* Addition */
    
    field_elt_inc(res, x, k);
    printf("x+1 = "); field_elt_print(res, 16, true, k, STACK_1); printf("\n");
    
    field_elt_add(res, x, y, k);
    printf("x+y = "); field_elt_print(res, 16, true, k, STACK_1); printf("\n");
    
    /* Substraction */
    
    field_elt_dec(res, x, k);
    printf("x-1 = "); field_elt_print(res, 16, true, k, STACK_1); printf("\n");
    
    field_elt_sub(res, x, y, k);
    printf("x-y = "); field_elt_print(res, 16, true, k, STACK_1); printf("\n");
    
    /* Multiplication */
    
    field_elt_mul(res, x, y, k, STACK_1);
    printf("x*y = "); field_elt_print(res, 16, true, k, STACK_1); printf("\n");
    
    field_elt_sqr(res, x, k, STACK_1);
    printf("x^2 = "); field_elt_print(res, 16, true, k, STACK_1); printf("\n");
    
    /* Division */
    
    field_elt_div(res, x, y, k, STACK_1);
    printf("x/y = "); field_elt_print(res, 16, true, k, STACK_1); printf("\n");
    
    /* Power */
    
    field_elt_pow_ui(res, x, 3, k, STACK_1);
    printf("x^3 = "); field_elt_print(res, 16, true, k, STACK_1); printf("\n");
    printf("Res is a power of 3 : %d\n", field_elt_ispower_ui(res, 3, k, STACK_1)>0);
    
    number n; number_init(&n, bits_to_nblock(192)); number_set_str(n, "f14b8dbafa22b6ba35626d40d2d00001381bef07d2c3015", 16);
    field_elt_pow_number(res, x, n, k, STACK_1);
    printf("x^n = "); field_elt_print(res, 16, true, k, STACK_1); printf("\n");
    printf("Res is a power of n : %d\n", field_elt_ispower_number(res, n, k, STACK_1)>0);
    number_free(&n);
    
    /* Inverse */
    
    field_elt_inv(res, x, k, STACK_1);
    printf("x^(-1) = "); field_elt_print(res, 16, true, k, STACK_1); printf("\n");
    
    /* Roots */
    
    field_elt_sqrt(res, x, k, STACK_1);
    printf("x is square : %d\n", field_elt_issquare(x, k, STACK_1)>0);
    printf("x^(1/2) = "); field_elt_print(res, 16, true, k, STACK_1); printf("\n");
    
    field_elt_cube_root(res, x, k, STACK_1);
    printf("x is a power of 3 : %d\n", field_elt_ispower_ui(x, 3, k, STACK_1)>0);
    printf("x^(1/3) = "); field_elt_print(res, 16, true, k, STACK_1); printf("\n");
    
    /* Free allocated memory */
    
    field_elt_free(&x, k);
    field_elt_free(&y, k);
    field_elt_free(&res, k);
    number_free(&p);
    field_free(k);
#if MPHELL_USE_AMNS == 1
    amns_free(&AMNS);
#endif
    
    free_mphell();
 
    return 0;
}