139 lines
4.4 KiB
C
139 lines
4.4 KiB
C
/***********************************************************************
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* Copyright (c) 2013, 2014 Pieter Wuille *
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* Distributed under the MIT software license, see the accompanying *
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* file COPYING or https://www.opensource.org/licenses/mit-license.php.*
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***********************************************************************/
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#ifndef SECP256K1_FIELD_IMPL_H
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#define SECP256K1_FIELD_IMPL_H
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#if defined HAVE_CONFIG_H
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#include "libsecp256k1-config.h"
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#endif
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#include "util.h"
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#if defined(SECP256K1_WIDEMUL_INT128)
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#include "field_5x52_impl.h"
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#elif defined(SECP256K1_WIDEMUL_INT64)
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#include "field_10x26_impl.h"
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#else
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#error "Please select wide multiplication implementation"
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#endif
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SECP256K1_INLINE static int rustsecp256k1_v0_8_1_fe_equal(const rustsecp256k1_v0_8_1_fe *a, const rustsecp256k1_v0_8_1_fe *b) {
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rustsecp256k1_v0_8_1_fe na;
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rustsecp256k1_v0_8_1_fe_negate(&na, a, 1);
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rustsecp256k1_v0_8_1_fe_add(&na, b);
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return rustsecp256k1_v0_8_1_fe_normalizes_to_zero(&na);
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}
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SECP256K1_INLINE static int rustsecp256k1_v0_8_1_fe_equal_var(const rustsecp256k1_v0_8_1_fe *a, const rustsecp256k1_v0_8_1_fe *b) {
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rustsecp256k1_v0_8_1_fe na;
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rustsecp256k1_v0_8_1_fe_negate(&na, a, 1);
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rustsecp256k1_v0_8_1_fe_add(&na, b);
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return rustsecp256k1_v0_8_1_fe_normalizes_to_zero_var(&na);
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}
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static int rustsecp256k1_v0_8_1_fe_sqrt(rustsecp256k1_v0_8_1_fe *r, const rustsecp256k1_v0_8_1_fe *a) {
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/** Given that p is congruent to 3 mod 4, we can compute the square root of
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* a mod p as the (p+1)/4'th power of a.
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*
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* As (p+1)/4 is an even number, it will have the same result for a and for
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* (-a). Only one of these two numbers actually has a square root however,
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* so we test at the end by squaring and comparing to the input.
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* Also because (p+1)/4 is an even number, the computed square root is
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* itself always a square (a ** ((p+1)/4) is the square of a ** ((p+1)/8)).
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*/
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rustsecp256k1_v0_8_1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
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int j;
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VERIFY_CHECK(r != a);
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/** The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in
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* { 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block:
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* 1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
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*/
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rustsecp256k1_v0_8_1_fe_sqr(&x2, a);
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rustsecp256k1_v0_8_1_fe_mul(&x2, &x2, a);
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rustsecp256k1_v0_8_1_fe_sqr(&x3, &x2);
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rustsecp256k1_v0_8_1_fe_mul(&x3, &x3, a);
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x6 = x3;
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for (j=0; j<3; j++) {
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rustsecp256k1_v0_8_1_fe_sqr(&x6, &x6);
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}
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rustsecp256k1_v0_8_1_fe_mul(&x6, &x6, &x3);
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x9 = x6;
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for (j=0; j<3; j++) {
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rustsecp256k1_v0_8_1_fe_sqr(&x9, &x9);
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}
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rustsecp256k1_v0_8_1_fe_mul(&x9, &x9, &x3);
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x11 = x9;
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for (j=0; j<2; j++) {
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rustsecp256k1_v0_8_1_fe_sqr(&x11, &x11);
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}
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rustsecp256k1_v0_8_1_fe_mul(&x11, &x11, &x2);
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x22 = x11;
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for (j=0; j<11; j++) {
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rustsecp256k1_v0_8_1_fe_sqr(&x22, &x22);
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}
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rustsecp256k1_v0_8_1_fe_mul(&x22, &x22, &x11);
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x44 = x22;
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for (j=0; j<22; j++) {
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rustsecp256k1_v0_8_1_fe_sqr(&x44, &x44);
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}
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rustsecp256k1_v0_8_1_fe_mul(&x44, &x44, &x22);
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x88 = x44;
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for (j=0; j<44; j++) {
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rustsecp256k1_v0_8_1_fe_sqr(&x88, &x88);
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}
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rustsecp256k1_v0_8_1_fe_mul(&x88, &x88, &x44);
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x176 = x88;
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for (j=0; j<88; j++) {
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rustsecp256k1_v0_8_1_fe_sqr(&x176, &x176);
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}
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rustsecp256k1_v0_8_1_fe_mul(&x176, &x176, &x88);
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x220 = x176;
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for (j=0; j<44; j++) {
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rustsecp256k1_v0_8_1_fe_sqr(&x220, &x220);
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}
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rustsecp256k1_v0_8_1_fe_mul(&x220, &x220, &x44);
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x223 = x220;
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for (j=0; j<3; j++) {
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rustsecp256k1_v0_8_1_fe_sqr(&x223, &x223);
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}
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rustsecp256k1_v0_8_1_fe_mul(&x223, &x223, &x3);
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/* The final result is then assembled using a sliding window over the blocks. */
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t1 = x223;
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for (j=0; j<23; j++) {
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rustsecp256k1_v0_8_1_fe_sqr(&t1, &t1);
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}
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rustsecp256k1_v0_8_1_fe_mul(&t1, &t1, &x22);
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for (j=0; j<6; j++) {
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rustsecp256k1_v0_8_1_fe_sqr(&t1, &t1);
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}
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rustsecp256k1_v0_8_1_fe_mul(&t1, &t1, &x2);
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rustsecp256k1_v0_8_1_fe_sqr(&t1, &t1);
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rustsecp256k1_v0_8_1_fe_sqr(r, &t1);
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/* Check that a square root was actually calculated */
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rustsecp256k1_v0_8_1_fe_sqr(&t1, r);
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return rustsecp256k1_v0_8_1_fe_equal(&t1, a);
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}
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#endif /* SECP256K1_FIELD_IMPL_H */
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