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rename FrobeniusOnTwist to G2withF::Frobenius

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MITSUNARI Shigeo 8 years ago
parent fe583d9be0
commit d64d2666a4
3 changed files with 105 additions and 145 deletions
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  1. 209
      include/mcl/bn.hpp
  2. 39
      include/mcl/fp_tower.hpp
  3. 2
      test/glv_test.cpp

209
include/mcl/bn.hpp
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@ -258,6 +258,37 @@ struct GLV1 {
}
};
/*
twisted Frobenius for G2
*/
template<class G2>
struct AddFrobenius : public G2 {
typedef typename G2::Fp Fp2;
/*
FrobeniusOnTwist
p mod 6 = 1, w^6 = xi
Frob(x', y') = phi Frob phi^-1(x', y')
= phi Frob (x' w^2, y' w^3)
= phi (x'^p w^2p, y'^p w^3p)
= (F(x') w^2(p - 1), F(y') w^3(p - 1))
= (F(x') g^2, F(y') g^3)
*/
static void Frobenius(G2& D, const G2& S)
{
Fp2::Frobenius(D.x, S.x);
Fp2::Frobenius(D.y, S.y);
Fp2::Frobenius(D.z, S.z);
D.x *= Fp2::get_gTbl()[0];
D.y *= Fp2::get_gTbl()[3];
}
static void Frobenius(AddFrobenius& y, const AddFrobenius& x)
{
Frobenius(static_cast<G2&>(y), static_cast<const G2&>(x));
}
};
/*
GLV method for G2 and GT
*/
template<class Fp2>
struct GLV2 {
typedef typename Fp2::BaseFp Fp;
@ -267,12 +298,10 @@ struct GLV2 {
mpz_class B[4][4];
mpz_class r;
mpz_class v[4];
void (*FrobeniusOnTwist)(G2&, const G2&);
GLV2() : m(0), FrobeniusOnTwist(0) {}
void init(const mpz_class& r, const mpz_class& z, void FrobeniusOnTwist(G2&, const G2&))
GLV2() : m(0) {}
void init(const mpz_class& r, const mpz_class& z)
{
this->r = r;
this->FrobeniusOnTwist = FrobeniusOnTwist;
m = mcl::gmp::getBitSize(r);
m = (m + mcl::fp::UnitBitSize - 1) & ~(mcl::fp::UnitBitSize - 1);// a little better size
/*
@ -316,12 +345,13 @@ struct GLV2 {
}
}
}
void mul(G2& Q, const G2& P, mpz_class x, bool constTime = false) const
template<class T>
void mul(T& Q, const T& P, mpz_class x, bool constTime = false) const
{
#ifndef NDEBUG
{
G2 R;
G2::mulGeneric(R, P, r);
T R;
T::mulGeneric(R, P, r);
assert(R.isZero());
}
#endif
@ -329,8 +359,8 @@ struct GLV2 {
const size_t maxUnit = 3;
const int splitN = 4;
mpz_class u[splitN];
G2 in[splitN];
G2 tbl[16];
T in[splitN];
T tbl[16];
int bitTbl[splitN]; // bit size of u[i]
Unit w[splitN][maxUnit]; // unit array of u[i]
int maxBit = 0; // max bit of u[i]
@ -348,21 +378,21 @@ struct GLV2 {
}
split(u, x);
in[0] = P;
FrobeniusOnTwist(in[1], in[0]);
FrobeniusOnTwist(in[2], in[1]);
FrobeniusOnTwist(in[3], in[2]);
T::Frobenius(in[1], in[0]);
T::Frobenius(in[2], in[1]);
T::Frobenius(in[3], in[2]);
for (int i = 0; i < splitN; i++) {
if (u[i] < 0) {
u[i] = -u[i];
G2::neg(in[i], in[i]);
T::neg(in[i], in[i]);
}
// in[i].normalize(); // slow
}
#if 0
for (int i = 0; i < splitN; i++) {
G2::mulGeneric(in[i], in[i], u[i]);
T::mulGeneric(in[i], in[i], u[i]);
}
G2::add(Q, in[0], in[1]);
T::add(Q, in[0], in[1]);
Q += in[2];
Q += in[3];
return;
@ -400,7 +430,7 @@ struct GLV2 {
Q.clear();
for (int i = maxN; i >= 0; i--) {
for (int j = m - 1; j >= 0; j--) {
G2::dbl(Q, Q);
T::dbl(Q, Q);
uint32_t b0 = (w[0][i] >> j) & 1;
uint32_t b1 = (w[1][i] >> j) & 1;
uint32_t b2 = (w[2][i] >> j) & 1;
@ -418,119 +448,25 @@ struct GLV2 {
DummyLoop:
if (!constTime) return;
const int limitBit = (int)Fp::getBitSize() / splitN;
G2 D = tbl[0];
T D = tbl[0];
for (int i = maxBit + 1; i < limitBit; i++) {
G2::dbl(D, D);
T::dbl(D, D);
D += tbl[0];
}
}
void mul(G2& Q, const G2& P, mpz_class x, bool constTime = false) const
{
typedef AddFrobenius<G2> G2withF;
G2withF& _Q(static_cast<G2withF&>(Q));
const G2withF& _P(static_cast<const G2withF&>(P));
mul(_Q, _P, x, constTime);
}
void pow(Fp12& z, const Fp12& x, mpz_class y, bool constTime = false) const
{
#if 0 // #ifndef NDEBUG
{
Fp12 t;
Fp12::powGeneric(t, x, r);
assert(t.isZero());
}
#endif
typedef mcl::fp::Unit Unit;
const size_t maxUnit = 3;
const int splitN = 4;
mpz_class u[splitN];
Fp12 in[splitN];
Fp12 tbl[16];
int bitTbl[splitN]; // bit size of u[i]
Unit w[splitN][maxUnit]; // unit array of u[i]
int maxBit = 0; // max bit of u[i]
int maxN = 0;
int m = 0;
y %= r;
if (y == 0) {
z = 1;
if (constTime) goto DummyLoop;
return;
}
if (y < 0) {
y += r;
}
split(u, y);
in[0] = x;
Fp12::Frobenius(in[1], in[0]);
Fp12::Frobenius(in[2], in[1]);
Fp12::Frobenius(in[3], in[2]);
for (int i = 0; i < splitN; i++) {
if (u[i] < 0) {
u[i] = -u[i];
Fp12::unitaryInv(in[i], in[i]);
}
// in[i].normalize(); // slow
}
#if 0
for (int i = 0; i < splitN; i++) {
Fp12::pow(in[i], in[i], u[i]);
}
Fp12::mul(z, in[0], in[1]);
z *= in[2];
z *= in[3];
return;
#else
tbl[0] = in[0];
for (size_t i = 1; i < 16; i++) {
tbl[i] = 1;
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];
}
// tbl[i].normalize();
}
for (int i = 0; i < splitN; i++) {
mcl::gmp::getArray(w[i], maxUnit, u[i]);
bitTbl[i] = (int)mcl::gmp::getBitSize(u[i]);
maxBit = std::max(maxBit, bitTbl[i]);
}
maxBit--;
/*
maxBit = maxN * UnitBitSize + m
0 < m <= UnitBitSize
*/
maxN = maxBit / mcl::fp::UnitBitSize;
m = maxBit % mcl::fp::UnitBitSize;
m++;
z = 1;
for (int i = maxN; i >= 0; i--) {
for (int j = m - 1; j >= 0; j--) {
Fp12::sqr(z, z);
uint32_t b0 = (w[0][i] >> j) & 1;
uint32_t b1 = (w[1][i] >> j) & 1;
uint32_t b2 = (w[2][i] >> j) & 1;
uint32_t b3 = (w[3][i] >> j) & 1;
uint32_t c = b3 * 8 + b2 * 4 + b1 * 2 + b0;
if (c == 0) {
if (constTime) tbl[0] *= tbl[1];
} else {
z *= tbl[c];
}
}
m = (int)mcl::fp::UnitBitSize;
}
#endif
DummyLoop:
if (!constTime) return;
const int limitBit = (int)Fp::getBitSize() / splitN;
Fp12 d = tbl[0];
for (int i = maxBit + 1; i < limitBit; i++) {
Fp12::sqr(d, d);
d *= tbl[0];
}
typedef GroupMtoA<Fp12> AG; // as additive group
AG& _z = static_cast<AG&>(z);
const AG& _x = static_cast<const AG&>(x);
mul(_z, _x, y, constTime);
}
};
@ -627,6 +563,7 @@ struct BNT {
typedef mcl::Fp12T<Fp> Fp12;
typedef mcl::EcT<Fp> G1;
typedef mcl::EcT<Fp2> G2;
typedef AddFrobenius<G2> G2withF;
typedef mcl::Fp2DblT<Fp> Fp2Dbl;
typedef ParamT<Fp> Param;
static Param param;
@ -655,26 +592,10 @@ struct BNT {
{
param.init(cp, mode);
G1::setMulArrayGLV(mulArrayGLV1);
param.glv2.init(param.r, param.z, FrobeniusOnTwist);
param.glv2.init(param.r, param.z);
G2::setMulArrayGLV(mulArrayGLV2);
Fp12::setPowArrayGLV(powArrayGLV2);
}
/*
p mod 6 = 1, w^6 = xi
Frob(x', y') = phi Frob phi^-1(x', y')
= phi Frob (x' w^2, y' w^3)
= phi (x'^p w^2p, y'^p w^3p)
= (F(x') w^2(p - 1), F(y') w^3(p - 1))
= (F(x') g^2, F(y') g^3)
*/
static void FrobeniusOnTwist(G2& D, const G2& S)
{
Fp2::Frobenius(D.x, S.x);
Fp2::Frobenius(D.y, S.y);
Fp2::Frobenius(D.z, S.z);
D.x *= Fp2::get_gTbl()[0];
D.y *= Fp2::get_gTbl()[3];
}
/*
l = (a, b, c) => (a, b * P.y, c * P.x)
*/
@ -1316,8 +1237,8 @@ struct BNT {
}
}
G2 Q1, Q2;
FrobeniusOnTwist(Q1, Q);
FrobeniusOnTwist(Q2, Q1);
G2withF::Frobenius(Q1, Q);
G2withF::Frobenius(Q2, Q1);
G2::neg(Q2, Q2);
if (param.z < 0) {
G2::neg(T, T);
@ -1378,8 +1299,8 @@ struct BNT {
}
}
G2 Q1, Q2;
FrobeniusOnTwist(Q1, Q);
FrobeniusOnTwist(Q2, Q1);
G2withF::Frobenius(Q1, Q);
G2withF::Frobenius(Q2, Q1);
G2::neg(Q2, Q2);
if (param.z < 0) {
G2::neg(T, T);

39
include/mcl/fp_tower.hpp
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@ -1121,5 +1121,44 @@ struct Fp12T : public fp::Operator<Fp12T<Fp> > {
}
};
/*
convert multiplicative group to additive group
*/
template<class T>
struct GroupMtoA : public T {
static T& self(GroupMtoA& x) { return static_cast<T&>(x); }
static const T& self(const GroupMtoA& x) { return static_cast<const T&>(x); }
void clear()
{
self(*this) = 1;
}
static void add(GroupMtoA& z, const GroupMtoA& x, const GroupMtoA& y)
{
T::mul(self(z), self(x), self(y));
}
static void dbl(GroupMtoA& y, const GroupMtoA& x)
{
T::sqr(self(y), self(x));
}
static void neg(GroupMtoA& y, const GroupMtoA& x)
{
// assume Fp12
T::unitaryInv(self(y), self(x));
}
static void Frobenus(GroupMtoA& y, const GroupMtoA& x)
{
T::Frobenius(self(y), self(x));
}
template<class INT>
static void mul(GroupMtoA& z, const GroupMtoA& x, const INT& y)
{
T::pow(self(z), self(x), y);
}
void operator+=(const GroupMtoA& rhs)
{
add(*this, *this, rhs);
}
};
} // mcl

2
test/glv_test.cpp
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@ -161,7 +161,7 @@ void testGLV2()
mpz_class r = BN::param.r;
mpz_class lambda = 6 * z * z;
mcl::bn::GLV2<Fp2> glv2;
glv2.init(r, z, BN::FrobeniusOnTwist);
glv2.init(r, z);
mpz_class u[4];
mpz_class n;
cybozu::XorShift rg;

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