field_impl.h

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/***********************************************************************
 * Copyright (c) 2013, 2014 Pieter Wuille                              *
 * Distributed under the MIT software license, see the accompanying    *
 * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
 ***********************************************************************/
 
#ifndef SECP256K1_FIELD_IMPL_H
#define SECP256K1_FIELD_IMPL_H
 
#if defined HAVE_CONFIG_H
#include "libsecp256k1-config.h"
#endif
 
#include "util.h"
 
#if defined(SECP256K1_WIDEMUL_INT128)
#include "field_5x52_impl.h"
#elif defined(SECP256K1_WIDEMUL_INT64)
#include "field_10x26_impl.h"
#else
#error "Please select wide multiplication implementation"
#endif
 
SECP256K1_INLINE static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) {
    secp256k1_fe na;
    secp256k1_fe_negate(&na, a, 1);
    secp256k1_fe_add(&na, b);
    return secp256k1_fe_normalizes_to_zero(&na);
}
 
SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b) {
    secp256k1_fe na;
    secp256k1_fe_negate(&na, a, 1);
    secp256k1_fe_add(&na, b);
    return secp256k1_fe_normalizes_to_zero_var(&na);
}
 
static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a) {
    secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
    int j;
 
    VERIFY_CHECK(r != a);
 
    secp256k1_fe_sqr(&x2, a);
    secp256k1_fe_mul(&x2, &x2, a);
 
    secp256k1_fe_sqr(&x3, &x2);
    secp256k1_fe_mul(&x3, &x3, a);
 
    x6 = x3;
    for (j=0; j<3; j++) {
        secp256k1_fe_sqr(&x6, &x6);
    }
    secp256k1_fe_mul(&x6, &x6, &x3);
 
    x9 = x6;
    for (j=0; j<3; j++) {
        secp256k1_fe_sqr(&x9, &x9);
    }
    secp256k1_fe_mul(&x9, &x9, &x3);
 
    x11 = x9;
    for (j=0; j<2; j++) {
        secp256k1_fe_sqr(&x11, &x11);
    }
    secp256k1_fe_mul(&x11, &x11, &x2);
 
    x22 = x11;
    for (j=0; j<11; j++) {
        secp256k1_fe_sqr(&x22, &x22);
    }
    secp256k1_fe_mul(&x22, &x22, &x11);
 
    x44 = x22;
    for (j=0; j<22; j++) {
        secp256k1_fe_sqr(&x44, &x44);
    }
    secp256k1_fe_mul(&x44, &x44, &x22);
 
    x88 = x44;
    for (j=0; j<44; j++) {
        secp256k1_fe_sqr(&x88, &x88);
    }
    secp256k1_fe_mul(&x88, &x88, &x44);
 
    x176 = x88;
    for (j=0; j<88; j++) {
        secp256k1_fe_sqr(&x176, &x176);
    }
    secp256k1_fe_mul(&x176, &x176, &x88);
 
    x220 = x176;
    for (j=0; j<44; j++) {
        secp256k1_fe_sqr(&x220, &x220);
    }
    secp256k1_fe_mul(&x220, &x220, &x44);
 
    x223 = x220;
    for (j=0; j<3; j++) {
        secp256k1_fe_sqr(&x223, &x223);
    }
    secp256k1_fe_mul(&x223, &x223, &x3);
 
    /* The final result is then assembled using a sliding window over the blocks. */
 
    t1 = x223;
    for (j=0; j<23; j++) {
        secp256k1_fe_sqr(&t1, &t1);
    }
    secp256k1_fe_mul(&t1, &t1, &x22);
    for (j=0; j<6; j++) {
        secp256k1_fe_sqr(&t1, &t1);
    }
    secp256k1_fe_mul(&t1, &t1, &x2);
    secp256k1_fe_sqr(&t1, &t1);
    secp256k1_fe_sqr(r, &t1);
 
    /* Check that a square root was actually calculated */
 
    secp256k1_fe_sqr(&t1, r);
    return secp256k1_fe_equal(&t1, a);
}
 
#endif /* SECP256K1_FIELD_IMPL_H */