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ton/crypto/ellcurve/TwEdwards.cpp
2019-09-07 14:33:36 +04:00

256 lines
6.8 KiB
C++

/*
This file is part of TON Blockchain Library.
TON Blockchain Library 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, either version 2 of the License, or
(at your option) any later version.
TON Blockchain Library 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 TON Blockchain Library. If not, see <http://www.gnu.org/licenses/>.
Copyright 2017-2019 Telegram Systems LLP
*/
#include "ellcurve/TwEdwards.h"
#include <assert.h>
#include <cstring>
namespace ellcurve {
using namespace arith;
class TwEdwardsCurve;
TwEdwardsCurve::TwEdwardsCurve(const Residue& _D, const Residue& _Gy, td::Ref<ResidueRing> _R)
: ring(_R)
, D(_D)
, D2(_D + _D)
, Gy(_Gy)
, P_(_R->get_modulus())
, cofactor_short(0)
, G(_R)
, O(_R)
, table_lines(0)
, table() {
init();
}
TwEdwardsCurve::~TwEdwardsCurve() {
}
void TwEdwardsCurve::init() {
assert(D != ring->zero() && D != ring->convert(-1));
O.X = O.Z = ring->one();
G = SegrePoint(*this, Gy, 0);
assert(!G.XY.is_zero());
}
void TwEdwardsCurve::set_order_cofactor(const Bignum& order, int cof) {
assert(order > 0);
assert(cof >= 0);
assert(cof == 0 || (order % cof) == 0);
Order = order;
cofactor = cofactor_short = cof;
if (cof > 0) {
L = order / cof;
assert(is_prime(L));
assert(!power_gen(1).is_zero());
assert(power_gen(L).is_zero());
}
}
TwEdwardsCurve::SegrePoint::SegrePoint(const TwEdwardsCurve& E, const Residue& y, bool x_sign)
: XY(y), X(E.get_base_ring()), Y(y), Z(E.get_base_ring()->one()) {
Residue x(y.ring_ref());
if (E.recover_x(x, y, x_sign)) {
XY *= x;
X = x;
} else {
XY = Y = Z = E.get_base_ring()->zero();
}
}
bool TwEdwardsCurve::recover_x(Residue& x, const Residue& y, bool x_sign) const {
// recovers x from equation -x^2+y^2 = 1+d*x^2*y^2
Residue z = inverse(ring->one() + D * sqr(y));
if (z.is_zero()) {
return false;
}
z *= sqr(y) - ring->one();
Residue t = sqrt(z);
if (sqr(t) == z) {
x = (t.extract().odd() == x_sign) ? t : -t;
//std::cout << "x=" << x << ", y=" << y << std::endl;
return true;
} else {
return false;
}
}
void TwEdwardsCurve::add_points(SegrePoint& Res, const SegrePoint& P, const SegrePoint& Q) const {
Residue a((P.X + P.Y) * (Q.X + Q.Y));
Residue b((P.X - P.Y) * (Q.X - Q.Y));
Residue c(P.Z * Q.Z * ring->convert(2));
Residue d(P.XY * Q.XY * D2);
Residue x_num(a - b); // 2(x1y2+x2y1)
Residue y_num(a + b); // 2(x1x2+y1y2)
Residue x_den(c + d); // 2(1+dx1x2y1y2)
Residue y_den(c - d); // 2(1-dx1x2y1y2)
Res.X = x_num * y_den; // x = x_num/x_den, y = y_num/y_den
Res.Y = y_num * x_den;
Res.XY = x_num * y_num;
Res.Z = x_den * y_den;
}
TwEdwardsCurve::SegrePoint TwEdwardsCurve::add_points(const SegrePoint& P, const SegrePoint& Q) const {
SegrePoint Res(ring);
add_points(Res, P, Q);
return Res;
}
void TwEdwardsCurve::double_point(SegrePoint& Res, const SegrePoint& P) const {
add_points(Res, P, P);
}
TwEdwardsCurve::SegrePoint TwEdwardsCurve::double_point(const SegrePoint& P) const {
SegrePoint Res(ring);
double_point(Res, P);
return Res;
}
// computes u([n]P) in form (xy,x,y,1)*Z
TwEdwardsCurve::SegrePoint TwEdwardsCurve::power_point(const SegrePoint& A, const Bignum& n, bool uniform) const {
assert(n >= 0);
if (n == 0) {
return O;
}
int k = n.num_bits();
SegrePoint P(A);
if (uniform) {
SegrePoint Q(double_point(A));
for (int i = k - 2; i >= 0; --i) {
if (n[i]) {
add_points(P, P, Q);
double_point(Q, Q);
} else {
// we do more operations than necessary for uniformicity
add_points(Q, P, Q);
double_point(P, P);
}
}
} else {
for (int i = k - 2; i >= 0; --i) {
double_point(P, P);
if (n[i]) {
add_points(P, P, A); // may optimize further if A.z = 1
}
}
}
return P;
}
int TwEdwardsCurve::build_table() {
if (table.size()) {
return -1;
}
table_lines = (P_.num_bits() >> 2) + 2;
table.reserve(table_lines * 15 + 1);
table.emplace_back(get_base_point());
for (int i = 0; i < table_lines; i++) {
for (int j = 0; j < 15; j++) {
table.emplace_back(add_points(table[15 * i + j], table[15 * i]));
}
}
return 1;
}
int get_nibble(const Bignum& n, int idx) {
return n[idx * 4 + 3] * 8 + n[idx * 4 + 2] * 4 + n[idx * 4 + 1] * 2 + n[idx * 4];
}
TwEdwardsCurve::SegrePoint TwEdwardsCurve::power_gen(const Bignum& n, bool uniform) const {
if (uniform || n.num_bits() > table_lines * 4) {
return power_point(G, n, uniform);
} else if (n.is_zero()) {
return O;
} else {
int k = (n.num_bits() + 3) >> 2;
assert(k > 0 && k <= table_lines);
int x = get_nibble(n, k - 1);
assert(x > 0 && x < 16);
SegrePoint P(table[15 * (k - 1) + x - 1]);
for (int i = k - 2; i >= 0; i--) {
x = get_nibble(n, i);
assert(x >= 0 && x < 16);
if (x > 0) {
add_points(P, P, table[15 * i + x - 1]);
}
}
return P;
}
}
bool TwEdwardsCurve::SegrePoint::export_point(unsigned char buffer[32], bool need_x) const {
if (!is_normalized()) {
if (Z.is_zero()) {
std::memset(buffer, 0xff, 32);
return false;
}
Residue f(inverse(Z));
Bignum y((Y * f).extract());
assert(!y[255]);
if (need_x) {
y[255] = (X * f).extract().odd();
}
y.export_lsb(buffer, 32);
} else {
Bignum y(Y.extract());
assert(!y[255]);
if (need_x) {
y[255] = X.extract().odd();
}
y.export_lsb(buffer, 32);
}
return true;
}
bool TwEdwardsCurve::SegrePoint::export_point_u(unsigned char buffer[32]) const {
if (Z == Y) {
std::memset(buffer, 0xff, 32);
return false;
}
Residue f(inverse(Z - Y));
((Z + Y) * f).extract().export_lsb(buffer, 32);
assert(!(buffer[31] & 0x80));
return true;
}
TwEdwardsCurve::SegrePoint TwEdwardsCurve::import_point(const unsigned char point[32], bool& ok) const {
Bignum y;
y.import_lsb(point, 32);
bool x_sign = y[255];
y[255] = 0;
Residue yr(y, ring);
Residue xr(ring);
ok = recover_x(xr, yr, x_sign);
return ok ? SegrePoint(xr, yr) : SegrePoint(ring);
}
const TwEdwardsCurve& Ed25519() {
static const TwEdwardsCurve Ed25519 = [] {
TwEdwardsCurve res(Fp25519()->frac(-121665, 121666), Fp25519()->frac(4, 5), Fp25519());
res.set_order_cofactor(hex_string{"80000000000000000000000000000000a6f7cef517bce6b2c09318d2e7ae9f68"}, 8);
res.build_table();
return res;
}();
return Ed25519;
}
} // namespace ellcurve