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pairing TBD

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MITSUNARI Shigeo 9 years ago
parent d6a0f08f75
commit 987ecf1e73
2 changed files with 194 additions and 41 deletions
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  1. 228
      include/mcl/bn.hpp
  2. 5
      include/mcl/fp_tower.hpp

228
include/mcl/bn.hpp
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@ -148,8 +148,8 @@ struct ParamT {
half = Fp(1) / Fp(2); half = Fp(1) / Fp(2);
Fp2 xi(cp.xi_a, 1); Fp2 xi(cp.xi_a, 1);
b_invxi = Fp2(b) / xi; b_invxi = Fp2(b) / xi;
G1::setParam(0, b); G1::setParam(0, b, mcl::ec::Proj);
G2::setParam(0, b_invxi); G2::setParam(0, b_invxi, mcl::ec::Proj);
power(gammar[0], xi, (p - 1) / 6); power(gammar[0], xi, (p - 1) / 6);
for (size_t i = 1; i < gammarN; i++) { for (size_t i = 1; i < gammarN; i++) {
@ -200,58 +200,206 @@ struct BNT {
{ {
param.init(cp); 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;
} }
}; static void mulB_invxi(Fp2& y, const Fp2& 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)
{ {
param.init(cp); Fp2::mul(y, x, param.b_invxi); // QQQ
} }
/* static void dblLineWithoutP(Fp6& l, const G2& Q)
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)
{ {
Fp2 t; Fp2 A, B, C, D, E, F, X3, G, Y3, H, Z3, I, J;
Q1.normalize(); Fp2::mul(A, Q.x, Q.y);
Q2.normalize(); Fp2::divBy2(A, A);
P.normalize(); Fp2::sqr(B, Q.y);
if (Q1.x == Q2.x) { Fp2::sqr(C, Q.z);
t = Q1.x * Q1.x * 3 / (Q1.y + Q1.y); Fp2::add(D, C, C); D += C; // D = 3C
} else { mulB_invxi(E, D);
t = (Q1.y - Q2.y) / (Q1.x - Q2.x); 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;
} }
t *= Fp2(P.x, 0) - Q1.x; static void mulOpt1(Fp2& z, const Fp2& x, const Fp2& y)
t += Q1.y; {
v.clear(); Fp d0;
v.a.a = t; 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) 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& p = param.p;
const mpz_class s = abs(6 * param.z + 2); const mpz_class s = abs(6 * param.z + 2);
G2 T = Q; G2 T = Q;
Fp12 t; Fp6 l;
f = 1; f = 1;
const int c = (int)mcl::gmp::getBitSize(s); const int c = (int)mcl::gmp::getBitSize(s);
for (int i = c - 2; i >= 0; i--) { for (int i = c - 2; i >= 0; i--) {
Fp12::sqr(f, f); Fp12::sqr(f, f);
evalLine(t, T, T, P); dblLine(l, T, P);
mul(f, t);
f *= t; f *= t;
G2::dbl(T, T); G2::dbl(T, T);
if (mcl::gmp::testBit(s, i)) { if (mcl::gmp::testBit(s, i)) {
@ -277,12 +425,12 @@ struct NaiveT {
a *= a; a *= a;
a = (a - 1) / param.r; a = (a - 1) / param.r;
Fp12::power(f, f, a); Fp12::power(f, f, a);
#endif
} }
}; };
template<class Fp> template<class Fp>
ParamT<Fp> NaiveT<Fp>::param; ParamT<Fp> BNT<Fp>::param;
#endif
} } // mcl::bn } } // mcl::bn

5
include/mcl/fp_tower.hpp
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@ -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 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 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 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> Fp2T = <a> + ' ' + <b>
*/ */

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