#define PUT(x) std::cout << #x "=" << (x) << std::endl; #include #include #include #if 1 #include using namespace mcl::bn384; #else #include 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 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 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(); } }