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#define PUT(x) std::cout << #x "=" << (x) << std::endl;
#include <cybozu/test.hpp>
#include <cybozu/xorshift.hpp>
#include <cybozu/benchmark.hpp>
#if 1
#include <mcl/bn384.hpp>
using namespace mcl::bn384;
#else
#include <mcl/bn256.hpp>
using namespace mcl::bn256;
#endif
#define PUT(x) std::cout << #x "=" << (x) << std::endl;
/*
Skew Frobenius Map and Efficient Scalar Multiplication for Pairing-Based Cryptography
Y. Sakemi, Y. Nogami, K. Okeya, H. Kato, Y. Morikawa
*/
struct oldGLV {
Fp w; // (-1 + sqrt(-3)) / 2
mpz_class r;
mpz_class v; // 6z^2 + 4z + 1 > 0
mpz_class c; // 2z + 1
void init(const mpz_class& r, const mpz_class& z)
{
if (!Fp::squareRoot(w, -3)) throw cybozu::Exception("oldGLV:init");
w = (w - 1) / 2;
this->r = r;
v = 1 + z * (4 + z * 6);
c = 2 * z + 1;
}
/*
(p^2 mod r) (x, y) = (wx, -y)
*/
void mulP2(G1& Q, const G1& P) const
{
Fp::mul(Q.x, P.x, w);
Fp::neg(Q.y, P.y);
Q.z = P.z;
}
/*
x = ap^2 + b mod r
assume(x < r);
*/
void split(mpz_class& a, mpz_class& b, const mpz_class& x) const
{
assert(0 < x && x < r);
/*
x = s1 * v + s2 // s1 = x / v, s2 = x % v
= s1 * c * p^2 + s2 // vP = cp^2 P
= (s3 * v + s4) * p^2 + s2 // s3 = (s1 * c) / v, s4 = (s1 * c) % v
= (s3 * c * p^2 + s4) * p^2 + s2
= (s3 * c) * p^4 + s4 * p^2 + s2 // s5 = s3 * c, p^4 = p^2 - 1
= s5 * (p^2 - 1) + s4 * p^2 + s2
= (s4 + s5) * p^2 + (s2 - s5)
*/
mpz_class t;
mcl::gmp::divmod(a, t, x, v); // a = t / v, t = t % v
a *= c;
mcl::gmp::divmod(b, a, a, v); // b = a / v, a = a % v
b *= c;
a += b;
b = t - b;
}
template<class G1>
void mul(G1& Q, const G1& P, const mpz_class& x) const
{
G1 A, B;
mpz_class a, b;
split(a, b, x);
mulP2(A, P);
G1::mul(A, A, a);
G1::mul(B, P, b);
G1::add(Q, A, B);
}
};
template<class GLV1, class GLV2>
void compareLength(const GLV1& rhs, const GLV2& lhs)
{
cybozu::XorShift rg;
int lt = 0;
int eq = 0;
int gt = 0;
mpz_class R0, R1, L0, L1, x;
Fr r;
for (int i = 1; i < 1000; i++) {
r.setRand(rg);
x = r.getMpz();
rhs.split(R0, R1, x);
lhs.split(L0, L1, x);
size_t R0n = mcl::gmp::getBitSize(R0);
size_t R1n = mcl::gmp::getBitSize(R1);
size_t L0n = mcl::gmp::getBitSize(L0);
size_t L1n = mcl::gmp::getBitSize(L1);
size_t Rn = std::max(R0n, R1n);
size_t Ln = std::max(L0n, L1n);
if (Rn == Ln) {
eq++;
}
if (Rn > Ln) {
gt++;
}
if (Rn < Ln) {
lt++;
}
}
printf("#of{<} = %d, #of{=} = %d #of{>} = %d\n", lt, eq, gt);
}
void testGLV1()
{
G1 P0, P1, P2;
mapToG1(P0, 1);
cybozu::XorShift rg;
oldGLV oldGlv;
if (!BN::param.isBLS12) {
oldGlv.init(BN::param.r, BN::param.z);
}
mcl::bn::local::GLV1 glv;
glv.init(BN::param.r, BN::param.z, BN::param.isBLS12);
if (!BN::param.isBLS12) {
compareLength(glv, oldGlv);
}
for (int i = 1; i < 100; i++) {
mapToG1(P0, i);
Fr s;
s.setRand(rg);
mpz_class ss = s.getMpz();
G1::mulGeneric(P1, P0, ss);
glv.mul(P2, P0, ss);
CYBOZU_TEST_EQUAL(P1, P2);
glv.mul(P2, P0, ss, true);
CYBOZU_TEST_EQUAL(P1, P2);
if (!BN::param.isBLS12) {
oldGlv.mul(P2, P0, ss);
CYBOZU_TEST_EQUAL(P1, P2);
}
}
for (int i = -100; i < 100; i++) {
mpz_class ss = i;
G1::mulGeneric(P1, P0, ss);
glv.mul(P2, P0, ss);
CYBOZU_TEST_EQUAL(P1, P2);
glv.mul(P2, P0, ss, true);
CYBOZU_TEST_EQUAL(P1, P2);
}
Fr s;
mapToG1(P0, 123);
CYBOZU_BENCH_C("Ec::mul", 100, P1 = P0; s.setRand(rg); G1::mulGeneric, P2, P1, s.getMpz());
CYBOZU_BENCH_C("Ec::glv", 100, P1 = P0; s.setRand(rg); glv.mul, P2, P1, s.getMpz());
}
/*
lambda = 6 * z * z
mul (lambda * 2) = FrobeniusOnTwist * 2
*/
void testGLV2()
{
G2 Q0, Q1, Q2;
mpz_class z = BN::param.z;
mpz_class r = BN::param.r;
mpz_class lambda = 6 * z * z;
mcl::bn::local::GLV2 glv2;
glv2.init(r, z, BN::param.isBLS12);
mpz_class n;
cybozu::XorShift rg;
mapToG2(Q0, 1);
for (int i = -10; i < 10; i++) {
n = i;
G2::mulGeneric(Q1, Q0, n);
glv2.mul(Q2, Q0, n);
CYBOZU_TEST_EQUAL(Q1, Q2);
}
for (int i = 1; i < 100; i++) {
mcl::gmp::getRand(n, glv2.rBitSize, rg);
n %= r;
n -= r/2;
mapToG2(Q0, i);
G2::mulGeneric(Q1, Q0, n);
glv2.mul(Q2, Q0, n);
CYBOZU_TEST_EQUAL(Q1, Q2);
}
Fr s;
mapToG2(Q0, 123);
CYBOZU_BENCH_C("G2::mul", 1000, Q2 = Q0; s.setRand(rg); G2::mulGeneric, Q2, Q1, s.getMpz());
CYBOZU_BENCH_C("G2::glv", 1000, Q1 = Q0; s.setRand(rg); glv2.mul, Q2, Q1, s.getMpz());
}
CYBOZU_TEST_AUTO(glv)
{
const mcl::CurveParam tbl[] = {
mcl::BN254,
mcl::BN381_1,
mcl::BN381_2,
mcl::BLS12_381,
};
for (size_t i = 0; i < CYBOZU_NUM_OF_ARRAY(tbl); i++) {
const mcl::CurveParam& cp = tbl[i];
initPairing(cp);
testGLV1();
testGLV2();
}
}
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