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implementing GLV for G2

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MITSUNARI Shigeo 8 years ago
parent 744feda4e5
commit 84d7bb67dc
1 changed files with 152 additions and 62 deletions
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  1. 214
      test/glv_test.cpp

214
test/glv_test.cpp
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@ -110,11 +110,8 @@ void compareLength(const GLV1& rhs, const GLV2& lhs)
printf("eq=%d small is better rhs=%d, lhs=%d\n", eq, Rc, Lc);
}
void testGLV(const mcl::bn::CurveParam& cp)
void testGLV1()
{
bn384init(cp);
G1::setCompressedExpression(false);
G1 P0, P1, P2;
BN::mapToG1(P0, 1);
cybozu::XorShift rg;
@ -164,99 +161,192 @@ struct GLV2 {
{
this->r = r;
m = mcl::gmp::getBitSize(r);
// m = (m + mcl::fp::UnitBitSize - 1) & ~(mcl::fp::UnitBitSize - 1);// a little better size
#if 1
v[0] = (1 + z * (3 + z * 2));
v[1] = (z * (1 + z * (8 + z * 12)));
v[2] = (z * (1 + z * (4 + z * 6)));
v[3] = -(z * (1 + z * 2));
#else
m = (m + mcl::fp::UnitBitSize - 1) & ~(mcl::fp::UnitBitSize - 1);// a little better size
/*
v[] = [1, 0, 0, 0] * B^(-1) = [2z^2+3z+1, 12z^3+8z^2+z, 6z^3+4z^2+z, -(2z+1)]
*/
v[0] = ((1 + z * (3 + z * 2)) << m) / r;
v[1] = ((z * (1 + z * (8 + z * 12))) << m) / r;
v[2] = ((z * (1 + z * (4 + z * 6))) << m) / r;
v[3] = -((z * (1 + z * 2)) << m) / r;
#endif
PUT(v[0]);
PUT(v[1]);
PUT(v[2]);
PUT(v[3]);
{
const mpz_class z2p1 = z * 2 + 1;
B[0][0] = z + 1;
B[0][1] = z;
B[0][2] = z;
B[0][3] = -2 * z;
B[1][0] = z2p1;
B[1][1] = -z;
B[1][2] = -(z + 1);
B[1][3] = -z;
B[2][0] = 2 * z;
B[2][1] = z2p1;
B[2][2] = z2p1;
B[2][3] = z2p1;
B[3][0] = z - 1;
B[3][1] = 2 * z2p1;
B[3][2] = -2 * z + 1;
B[3][3] = z - 1;
}
const mpz_class z2p1 = z * 2 + 1;
B[0][0] = z + 1;
B[0][1] = z;
B[0][2] = z;
B[0][3] = -2 * z;
B[1][0] = z2p1;
B[1][1] = -z;
B[1][2] = -(z + 1);
B[1][3] = -z;
B[2][0] = 2 * z;
B[2][1] = z2p1;
B[2][2] = z2p1;
B[2][3] = z2p1;
B[3][0] = z - 1;
B[3][1] = 2 * z2p1;
B[3][2] = -2 * z + 1;
B[3][3] = z - 1;
}
void split(mpz_class u[4], const mpz_class& n) const
/*
u[] = [x, 0, 0, 0] - v[] * x * B
*/
void split(mpz_class u[4], const mpz_class& x) const
{
mpz_class t[4];
for (int i = 0; i < 4; i++) {
// t[i] = (n * v[i]) >> m;
t[i] = (n * v[i]) / r;
PUT(n * v[i]);
PUT(t[i]);
t[i] = (x * v[i]) >> m;
}
for (int i = 0; i < 4; i++) {
u[i] = (i == 0) ? n : 0;
u[i] = (i == 0) ? x : 0;
for (int j = 0; j < 4; j++) {
u[i] -= t[j] * B[j][i];
}
}
}
void mulOrg(G2& Q, const G2& P, mpz_class x) const
{
x %= r;
if (x == 0) {
Q.clear();
return;
}
if (x < 0) {
x += r;
}
mpz_class u[4];
split(u, x);
G2 in[4];
in[0] = P;
BN::FrobeniusOnTwist(in[1], in[0]);
BN::FrobeniusOnTwist(in[2], in[1]);
BN::FrobeniusOnTwist(in[3], in[2]);
for (int i = 0; i < 4; i++) {
G2::mul(in[i], in[i], u[i]);
}
G2::add(Q, in[0], in[1]);
Q += in[2];
Q += in[3];
}
void mul(G2& Q, const G2& P, mpz_class x) const
{
x %= r;
if (x == 0) {
Q.clear();
return;
}
if (x < 0) {
x += r;
}
mpz_class u[4];
split(u, x);
G2 in[4];
in[0] = P;
BN::FrobeniusOnTwist(in[1], in[0]);
BN::FrobeniusOnTwist(in[2], in[1]);
BN::FrobeniusOnTwist(in[3], in[2]);
for (int i = 0; i < 4; i++) {
if (u[i] < 0) {
u[i] = -u[i];
G2::neg(in[i], in[i]);
}
in[i].normalize();
}
#if 0
for (int i = 0; i < 4; i++) {
G2::mul(in[i], in[i], u[i]);
}
G2::add(Q, in[0], in[1]);
Q += in[2];
Q += in[3];
#else
G2 tbl[16];
for (size_t i = 0; i < 16; i++) {
tbl[i].clear();
}
for (size_t i = 0; i < 16; i++) {
if (i & 1) {
tbl[i] += in[0];
}
if (i & 2) {
tbl[i] += in[1];
}
if (i & 4) {
tbl[i] += in[2];
}
if (i & 8) {
tbl[i] += in[3];
}
}
for (size_t i = 0; i < 16; i++) {
tbl[i].normalize();
}
typedef mcl::fp::Unit Unit;
const size_t maxUnit = 4;
int bitTbl[4]; // bit size of u[i]
Unit w[4][maxUnit]; // unit array of u[i]
for (int i = 0; i < 4; i++) {
mcl::gmp::getArray(w[i], maxUnit, u[i]);
bitTbl[i] = (int)mcl::gmp::getBitSize(u[i]);
}
int maxBit = bitTbl[0]; // max bit of u[i]
for (int i = 1; i < 4; i++) {
maxBit = std::max(maxBit, bitTbl[i]);
}
assert(maxBit > 0);
int maxN = maxBit / mcl::fp::UnitBitSize;
int m = maxBit % mcl::fp::UnitBitSize;
Q.clear();
for (int i = maxN - 1; i >= 0; i--) {
for (int j = m; j >= 0; j--) {
G2::dbl(Q, Q);
Unit b0 = (w[0][i] >> j) & 1;
Unit b1 = (w[1][i] >> j) & 1;
Unit b2 = (w[2][i] >> j) & 1;
Unit b3 = (w[3][i] >> j) & 1;
Unit c = b3 * 8 + b2 * 4 + b1 * 2 + b0;
Q += tbl[c];
}
m = (int)mcl::fp::UnitBitSize - 1;
}
#endif
}
};
/*
lambda = 6 * z * z
mul (lambda * 2) = FrobeniusOnTwist * 2
*/
void testGLV2(const mcl::bn::CurveParam& cp)
void testGLV2()
{
bn384init(cp);
G2::setCompressedExpression(false);
G2 Q0, Q1, Q2;
mpz_class z = BN::param.z;
mpz_class r = BN::param.r;
//z = 10267;
r = 36*z*z*z*z+36*z*z*z+18*z*z+6*z+1;
mpz_class lambda = 6 * z * z;
GLV2<Fp2> glv2;
glv2.init(r, z);
mpz_class u[4];
mpz_class n;
cybozu::XorShift rg;
// std::cout << std::hex;
for (int i = 0; i < 3; i++) {
for (int i = 1; i < 5; i++) {
mcl::gmp::getRand(n, glv2.m, rg);
n %= r;
//n.set_str("123456789123456789", 10);
glv2.split(u, n);
PUT(n);
PUT(u[0]); PUT(mcl::gmp::getBitSize(u[0]));
PUT(u[1]);
PUT(u[2]);
PUT(u[3]);
mpz_class v = u[0] + lambda * (u[1] + lambda * (u[2] + lambda * u[3]));
PUT((n - v) % r);
BN::mapToG2(Q0, i);
G2::mul(Q1, Q0, n);
glv2.mul(Q2, Q0, n);
CYBOZU_TEST_EQUAL(Q1, Q2);
}
}
CYBOZU_TEST_AUTO(glv)
{
// testGLV2(mcl::bn::CurveFp254BNb);
//return;
testGLV(mcl::bn::CurveFp254BNb);
testGLV(mcl::bn::CurveFp382_1);
testGLV(mcl::bn::CurveFp382_2);
const mcl::bn::CurveParam tbl[] = {
mcl::bn::CurveFp254BNb,
mcl::bn::CurveFp382_1,
mcl::bn::CurveFp382_2,
};
for (size_t i = 0; i < CYBOZU_NUM_OF_ARRAY(tbl); i++) {
const mcl::bn::CurveParam& cp = tbl[i];
bn384init(cp);
testGLV1();
// testGLV2();
}
}

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