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update Fp12::inv

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update-fork
MITSUNARI Shigeo 4 years ago
parent 0d01560a14
commit 5d703a98a8
1 changed files with 45 additions and 40 deletions
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  1. 85
      include/mcl/fp_tower.hpp

85
include/mcl/fp_tower.hpp
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@ -866,38 +866,11 @@ struct Fp6T : public fp::Serializable<Fp6T<_Fp>,
Fp2::mul2(y.b, x.b);
Fp2::mul2(y.c, x.c);
}
/*
x = a + bv + cv^2, v^3 = xi
x^2 = (a^2 + 2bc xi) + (c^2 xi + 2ab)v + (b^2 + 2ac)v^2
b^2 + 2ac = (a + b + c)^2 - a^2 - 2bc - c^2 - 2ab
*/
static void sqr(Fp6T& y, const Fp6T& x)
{
const Fp2& a = x.a;
const Fp2& b = x.b;
const Fp2& c = x.c;
Fp2 t;
Fp2Dbl BC2, AB2, AA, CC, T;
Fp2::mul2(t, b);
Fp2Dbl::mulPre(BC2, t, c); // 2bc
Fp2Dbl::mulPre(AB2, t, a); // 2ab
Fp2Dbl::sqrPre(AA, a);
Fp2Dbl::sqrPre(CC, c);
Fp2::add(t, a, b);
Fp2::add(t, t, c);
Fp2Dbl::sqrPre(T, t); // (a + b + c)^2
Fp2Dbl::sub(T, T, AA);
Fp2Dbl::sub(T, T, BC2);
Fp2Dbl::sub(T, T, CC);
Fp2Dbl::sub(T, T, AB2);
Fp2Dbl::mod(y.c, T);
Fp2Dbl::mul_xi(BC2, BC2);
Fp2Dbl::add(AA, AA, BC2);
Fp2Dbl::mod(y.a, AA);
Fp2Dbl::mul_xi(CC, CC);
Fp2Dbl::add(CC, CC, AB2);
Fp2Dbl::mod(y.b, CC);
Fp6Dbl XX;
Fp6Dbl::sqrPre(XX, x);
Fp6Dbl::mod(y, XX);
}
static inline void mul(Fp6T& z, const Fp6T& x, const Fp6T& y);
/*
@ -1015,6 +988,36 @@ struct Fp6DblT {
Fp2Dbl::add(ZB, ZB, CF);
Fp2Dbl::add(ZC, ZC, BE);
}
/*
x = a + bv + cv^2, v^3 = xi
x^2 = (a^2 + 2bc xi) + (c^2 xi + 2ab)v + (b^2 + 2ac)v^2
b^2 + 2ac = (a + b + c)^2 - a^2 - 2bc - c^2 - 2ab
*/
static void sqrPre(Fp6DblT& y, const Fp6& x)
{
const Fp2& a = x.a;
const Fp2& b = x.b;
const Fp2& c = x.c;
Fp2 t;
Fp2Dbl BC2, AB2, AA, CC, T;
Fp2::mul2(t, b);
Fp2Dbl::mulPre(BC2, t, c); // 2bc
Fp2Dbl::mulPre(AB2, t, a); // 2ab
Fp2Dbl::sqrPre(AA, a);
Fp2Dbl::sqrPre(CC, c);
Fp2::add(t, a, b);
Fp2::add(t, t, c);
Fp2Dbl::sqrPre(T, t); // (a + b + c)^2
Fp2Dbl::sub(T, T, AA);
Fp2Dbl::sub(T, T, BC2);
Fp2Dbl::sub(T, T, CC);
Fp2Dbl::sub(y.c, T, AB2);
Fp2Dbl::mul_xi(BC2, BC2);
Fp2Dbl::add(y.a, AA, BC2);
Fp2Dbl::mul_xi(CC, CC);
Fp2Dbl::add(y.b, CC, AB2);
}
static void mod(Fp6& y, const Fp6Dbl& x)
{
Fp2Dbl::mod(y.a, x.a);
@ -1169,16 +1172,18 @@ struct Fp12T : public fp::Serializable<Fp12T<Fp>,
{
const Fp6& a = x.a;
const Fp6& b = x.b;
Fp6 t0, t1;
Fp6::sqr(t0, a);
Fp6::sqr(t1, b);
Fp2::mul_xi(t1.c, t1.c);
t0.a -= t1.c;
t0.b -= t1.a;
t0.c -= t1.b; // t0 = a^2 - b^2v
Fp6::inv(t0, t0);
Fp6::mul(y.a, x.a, t0);
Fp6::mul(y.b, x.b, t0);
Fp6Dbl AA, BB;
Fp6Dbl::sqrPre(AA, a);
Fp6Dbl::sqrPre(BB, b);
Fp2Dbl::mul_xi(BB.c, BB.c);
Fp2Dbl::sub(AA.a, AA.a, BB.c);
Fp2Dbl::sub(AA.b, AA.b, BB.a);
Fp2Dbl::sub(AA.c, AA.c, BB.b); // a^2 - b^2 v
Fp6 t;
Fp6Dbl::mod(t, AA);
Fp6::inv(t, t);
Fp6::mul(y.a, x.a, t);
Fp6::mul(y.b, x.b, t);
Fp6::neg(y.b, y.b);
}
/*

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