PoS_EVM
/
mcl
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

pairing TBD

Browse Source
dev
MITSUNARI Shigeo 9 years ago
parent d6a0f08f75
commit 987ecf1e73
2 changed files with 194 additions and 41 deletions
Show all changes Ignore whitespace when comparing lines Ignore changes in amount of whitespace Ignore changes in whitespace at EOL
Show Stats Download Patch File Download Diff File
  1. 230
      include/mcl/bn.hpp
  2. 5
      include/mcl/fp_tower.hpp

230
include/mcl/bn.hpp
Unescape View File

@ -148,8 +148,8 @@ struct ParamT {
half = Fp(1) / Fp(2);
Fp2 xi(cp.xi_a, 1);
b_invxi = Fp2(b) / xi;
G1::setParam(0, b);
G2::setParam(0, b_invxi);
G1::setParam(0, b, mcl::ec::Proj);
G2::setParam(0, b_invxi, mcl::ec::Proj);
power(gammar[0], xi, (p - 1) / 6);
for (size_t i = 1; i < gammarN; i++) {
@ -200,58 +200,206 @@ struct BNT {
{
param.init(cp);
}
static void optimalAtePairing(Fp12& f, const G2& Q, const G1& P)
/*
l = (a, b, c) => (a, b * P.y, c * P.x)
*/
static void updateLine(Fp6& l, const G1& P)
{
l.b.a *= P.y;
l.b.b *= P.y;
l.c.a *= P.x;
l.c.b *= P.x;
}
};
template<class Fp>
ParamT<Fp> BNT<Fp>::param;
#if 0
template<class Fp>
struct NaiveT {
typedef mcl::Fp2T<Fp> Fp2;
typedef mcl::Fp6T<Fp> Fp6;
typedef mcl::Fp12T<Fp> Fp12;
typedef mcl::EcT<Fp> G1;
typedef mcl::EcT<Fp2> G2;
typedef ParamT<Fp> Param;
static Param param;
static void init(const mcl::bn::CurveParam& cp)
static void mulB_invxi(Fp2& y, const Fp2& x)
{
param.init(cp);
Fp2::mul(y, x, param.b_invxi); // QQQ
}
/*
v is the line arising in the addition of Q1 and Q2 in G2 evaluated at point P in G1
*/
static void evalLine(Fp12& v, const G2& Q1, const G2& Q2, const G1& P)
static void dblLineWithoutP(Fp6& l, const G2& Q)
{
Fp2 t;
Q1.normalize();
Q2.normalize();
P.normalize();
if (Q1.x == Q2.x) {
t = Q1.x * Q1.x * 3 / (Q1.y + Q1.y);
} else {
t = (Q1.y - Q2.y) / (Q1.x - Q2.x);
}
t *= Fp2(P.x, 0) - Q1.x;
t += Q1.y;
v.clear();
v.a.a = t;
Fp2 A, B, C, D, E, F, X3, G, Y3, H, Z3, I, J;
Fp2::mul(A, Q.x, Q.y);
Fp2::divBy2(A, A);
Fp2::sqr(B, Q.y);
Fp2::sqr(C, Q.z);
Fp2::add(D, C, C); D += C; // D = 3C
mulB_invxi(E, D);
Fp2::sqr(J, Q.x);
Fp2::add(F, E, E); F += E; // F = 3E
Fp2::add(H, Q.y, Q.z);
Fp2::sqr(H, H);
H -= B;
H -= C;
Fp2::sub(Q.x, B, F);
Q.x *= A;
Fp2::add(G, B, F);
Fp2::divBy2(G, G);
Fp2::sqr(Q.y, G); // G^2
F *= E;// F = 3E^2
Q.y -= F;
Fp2::mul(Q.z, B, H);
Fp2::sub(I, E, B);
l.clear();
l.a.a = I.a - I.b;
l.a.b = I.a + I.b;
l.b = -H;
Fp2::add(l.c, J, J);
l.c += J;
}
static void mulOpt1(Fp2& z, const Fp2& x, const Fp2& y)
{
Fp d0;
Fp s, t;
Fp::add(s, x.a, x.b);
Fp::add(t, y.a, y.b);
Fp::mul(d0, x.b, y.b);
Fp::mul(z.a, x.a, y.a);
Fp::mul(z.b, s, t);
z.b -= z.a;
z.b -= d0;
z.a -= d0;
}
static void addLineWithoutP(Fp6& l, G2& R, const G2& Q)
{
#if 1
const Fp2& X1 = R.x;
const Fp2& Y1 = R.y;
const Fp2& Z1 = R.z;
const Fp2& X2 = Q.x;
const Fp2& Y2 = Q.y;
Fp2 theta, lambda;
theta = Y1 - Y2 * Z1;
lambda = X1 - X2 * Z1;
Fp2 lambda2;
Fp2::sqr(lambda2, lambda);
Fp2 t1, t2, t3, t4;
t1 = X1 * lambda2;
t2 = t1 + t1; // 2 X1 lambda^2
t3 = lambda2 * lambda; // lambda^3
Fp2::sqr(t4, theta);
t4 *= Z1; // t4 = Z1 theta^2
R.x = lambda * (t3 + t4 - t2);
R.y = theta * (t2 + t1 - t3 - t4) - Y1 * t3;
R.z = Z1 * t3;
l.a = theta * X2 - lambda * Y2;
Fp2::mulXi(l.a, l.a);
l.b = lambda;
l.c = -theta;
#else
Fp2 t1, t2, t3, t4, T1, T2;
Fp2::mul(t1, R.z, Q.x);
Fp2::mul(t2, R.z, Q.y);
Fp2::sub(t1, R.x, t1);
Fp2::sub(t2, R.y, t2);
Fp2::sqr(t3, t1);
Fp2::mul(R.x, t3, R.x);
Fp2::sqr(t4, t2);
t3 *= t1;
t4 *= R.z;
t4 += t3;
t4 -= R.x;
t4 -= R.x;
R.x -= t4;
mulOpt1(T1, t2, R.x);
mulOpt1(T2, t3, R.y);
Fp2::sub(R.y, T1, T2);
Fp2::mul(R.x, t1, t4);
Fp2::mul(R.z, t3, R.z);
Fp2::neg(l.c, t2);
mulOpt1(T1, t2, Q.x);
mulOpt1(T2, t1, Q.y);
Fp2::sub(t2, T1, T2);
Fp2::mulXi(l.a, t2);
l.b = t1;
#endif
}
static void dblLine(Fp6& l, G2& Q, const G1& P)
{
dblLineWithoutP(l, Q);
updateLine(l, P);
}
static void addLine(Fp6& l, G2& R, const G2& Q, const G1& P)
{
addLineWithoutP(l, R, Q);
updateLine(l, P);
}
static void convertFp6toFp12(Fp12& y, const Fp6& x)
{
y.clear();
y.a.a = x.a;
y.a.c = x.c;
y.b.b = x.b;
}
static void mul_024(Fp12&y, const Fp6& x)
{
Fp12 t;
convertFp6toFp12(t, x);
y *= t;
}
static void mul_024_024(Fp12& z, const Fp6& x, const Fp6& y)
{
Fp12 x2, y2;
convertFp6toFp12(x2, x);
convertFp6toFp12(y2, y);
Fp12::mul(z, x2, y2);
}
static void optimalAtePairing(Fp12& f, const G2& Q, const G1& P)
{
#if 1
P.normalize();
Q.normalize();
const mpz_class& p = param.p;
Fp6 l;
G2 T = Q;
f = 1;
G2 negQ;
G2::neg(negQ, Q);
Fp6 d;
dblLine(d, T, P);
Fp6 e;
assert(param.siTbl[1] == 1);
addLine(e, T, Q, P);
mul_024_024(f, d, e);
for (size_t i = 2; i < param.siTbl.size(); i++) {
dblLine(l, T, P);
Fp12::sqr(f, f);
mul_024(f, l);
if (param.siTbl[i] > 0) {
addLine(l, T, Q, P);
mul_024(f, l);
} else if (param.siTbl[i] < 0) {
addLine(l, T, negQ, P);
mul_024(f, l);
}
}
G2 Q1, Q2;
Frobenius(Q1, Q, p);
Frobenius(Q2, Q1, p);
if (param.z < 0) {
G2::neg(T, T);
Fp12::inv(f, f);
}
addLine(l, T, Q1, P);
mul_024(f, l);
T += Q1;
addLine(l, T, -Q2, P);
mul_024(f, l);
mpz_class a = p * p * p;
a *= a;
a *= a;
a = (a - 1) / param.r;
Fp12::power(f, f, a);
#else
P.normalize();
const mpz_class& p = param.p;
const mpz_class s = abs(6 * param.z + 2);
G2 T = Q;
Fp12 t;
Fp6 l;
f = 1;
const int c = (int)mcl::gmp::getBitSize(s);
for (int i = c - 2; i >= 0; i--) {
Fp12::sqr(f, f);
evalLine(t, T, T, P);
dblLine(l, T, P);
mul(f, t);
f *= t;
G2::dbl(T, T);
if (mcl::gmp::testBit(s, i)) {
@ -277,12 +425,12 @@ struct NaiveT {
a *= a;
a = (a - 1) / param.r;
Fp12::power(f, f, a);
#endif
}
};
template<class Fp>
ParamT<Fp> NaiveT<Fp>::param;
#endif
ParamT<Fp> BNT<Fp>::param;
} } // mcl::bn

5
include/mcl/fp_tower.hpp
Unescape View File

@ -83,6 +83,11 @@ public:
static inline void neg(Fp2T& y, const Fp2T& x) { Fp::op_.fp2_neg(y.a.v_, x.a.v_); }
static inline void sqr(Fp2T& y, const Fp2T& x) { Fp::op_.fp2_sqr(y.a.v_, x.a.v_); }
static inline void mulXi(Fp2T& y, const Fp2T& x) { Fp::op_.fp2_mulXi(y.a.v_, x.a.v_); }
static inline void divBy2(Fp2T& y, const Fp2T& x)
{
Fp::divBy2(y.a, x.a);
Fp::divBy2(y.b, x.b);
}
/*
Fp2T = <a> + ' ' + <b>
*/

Write Preview
Loading…
Cancel
Save