bn128_ate_G2_precomp bn128_ate_precompute_G2(const bn128_G2& Q)
{
enter_block("Call to bn128_ate_precompute_G2");
bn128_ate_G2_precomp result;
bn::ecop::NormalizeJac(result.Q, Q.coord);
Fp2 T[3];
T[0] = result.Q[0];
T[1] = result.Q[1];
T[2] = Fp2(1);
Fp6 d;
doubling_step_for_flipped_miller_loop(T, d);
result.coeffs.emplace_back(d);
Fp6 e;
assert(Param::siTbl[1] == 1);
mixed_addition_step_for_flipped_miller_loop(result.Q, T, e);
result.coeffs.emplace_back(e);
bn::Fp6 l;
// 844kclk
for (size_t i = 2; i < Param::siTblNum; i++) {
doubling_step_for_flipped_miller_loop(T, l);
result.coeffs.emplace_back(l);
if (Param::siTbl[i]) {
mixed_addition_step_for_flipped_miller_loop(result.Q, T, l);
result.coeffs.emplace_back(l);
}
}
// addition step
Fp2 Q1[2];
bn::ecop::FrobEndOnTwist_1(Q1, result.Q);
Fp2 Q2[2];
bn::ecop::FrobEndOnTwist_2(Q2, result.Q);
Fp2::neg(Q2[1], Q2[1]);
// @memo z < 0
if (0)
{
bn::Fp2::neg(T[1], T[1]);
}
mixed_addition_step_for_flipped_miller_loop(Q1, T, d);
result.coeffs.emplace_back(d);
mixed_addition_step_for_flipped_miller_loop(Q2, T, e);
result.coeffs.emplace_back(e);
leave_block("Call to bn128_ate_precompute_G2");
return result;
}
void bench_graphe_grille(Pt2di sz,TGr41 & gr)
{
TPtSubGr41 GrAll;
TPart41 Part;
all_face_trigo
(
gr,
(TSubGr41 &) GrAll,
Part
);
ElFifo <Pt2dr> Fp2(2,true);
BENCH_ASSERT(Part.nb() == ((sz.x-1)*(sz.y-1) +1));
INT nb4 =0;
INT perim_th = (sz.x-1 + sz.y-1) * 2;
for (INT f=0; f< Part.nb() ; f++)
{
INT nbf = Part[f].nb();
BENCH_ASSERT((nbf == 4) || (nbf==perim_th));
copy_on(Fp2,Part[f],PtArc41);
REAL surf = surf_or_poly(Fp2);
Pt2dr cdg = barrycentre(Fp2);
if (nbf == 4)
{
nb4 ++;
BENCH_ASSERT (std::abs(std::abs(surf)-1.0) < epsilon);
REAL x = cdg.x - round_down(cdg.x);
REAL y = cdg.y - round_down(cdg.y);
BENCH_ASSERT
(
(std::abs(x-0.5) < epsilon)
&& (std::abs(y-0.5) < epsilon)
);
}
else
{
BENCH_ASSERT (std::abs(surf-(sz.x-1)*(sz.y-1))< epsilon);
BENCH_ASSERT(euclid(cdg,(Pt2dr(sz)-Pt2dr(1,1))/2.0) < epsilon);
}
}
BENCH_ASSERT(Part.nb() == nb4+1);
TSubGr41_xy2 Gr_xy2;
all_face_trigo
(
gr,
(TSubGr41 &) Gr_xy2,
Part
);
BENCH_ASSERT(Part.nb() == (((sz.x-1)/2)*((sz.y-1)/2) +1));
TSubGr41_xeg Gr_xeq;
all_face_trigo
(
gr,
(TSubGr41 &) Gr_xeq,
Part
);
BENCH_ASSERT(Part.nb() == sz.x);
TSubGr41_xeg_y0 Gr_xeq_y0;
all_face_trigo
(
gr,
(TSubGr41 &) Gr_xeq_y0,
Part
);
BENCH_ASSERT(Part.nb() == 1);
}
int main()
{
SystemInit();
const Ec1 g1(-1, 1);
const Ec2 g2(
Fp2(Fp(g2c.aa), Fp(g2c.ab)),
Fp2(Fp(g2c.ba), Fp(g2c.bb))
);
// assertBool g2 and g1 on curve
assertBool("g1 is on EC", g1.isValid());
assertBool("g2 is on twist EC", g2.isValid());
puts("order of group");
const Mpz& r = GetParamR();
PUT(r);
{
Ec1 t = g1;
t.mul(r);
assertBool("orgder of g1 == r", t.isZero());
}
{
Ec2 t = g2;
t.mul(r);
assertBool("order of g2 == r", t.isZero());
}
const Mpz a("123456789012345");
const Mpz b("998752342342342342424242421");
// scalar-multiplication sample
{
Mpz c = a;
c.add(b);
Ec1 Pa = g1; Pa.mul(a);
Ec1 Pb = g1; Pb.mul(b);
Ec1 Pc = g1; Pc.mul(c);
Ec1 out = Pa;
out.add(Pb);
assertEqual("check g1 * c = g1 * a + g1 * b", Pc, out);
}
Fp12 e;
// calc e : G2 x G1 -> G3 pairing
e.pairing(g2, g1); // e = e(g2, g1)
PUT(e);
{
Fp12 t = e;
t.power(r);
assertEqual("order of e == r", t, Fp12(1));
}
Ec2 g2a = g2;
g2a.mul(a);
Fp12 ea1;
ea1.pairing(g2a, g1);
Fp12 ea2 = e;
ea2.power(a); // ea2 = e^a
assertEqual("e(g2 * a, g1) = e(g2, g1)^a", ea1, ea2);
Ec1 g1b = g1;
g1b.mul(b);
Fp12 eb1;
eb1.pairing(g2, g1b); // eb1 = e(g2, g1b)
Fp12 eb2 = e;
eb2.power(b); // eb2 = e^b
assertEqual("e(g2a, g1 * b) = e(g2, g1)^b", eb1, eb2);
Ec1 q1 = g1;
q1.mul(12345);
assertBool("q1 is on EC", q1.isValid());
Fp12 e1, e2;
e1.pairing(g2, g1); // e1 = e(g2, g1)
e2.pairing(g2, q1); // e2 = e(g2, q1)
Ec1 q2 = g1;
q2.add(q1);
e.pairing(g2, q2); // e = e(g2, q2)
e1.mul(e2);
assertEqual("e = e1 * e2", e, e1);
/*
reduce one copy as the following
*/
g2a = g2;
g2a.mul(a);
g1b = g1;
g1b.mul(b);
Ec2 g2at = g2; g2at.mul(a);
Ec1 g1bt = g1; g1bt.mul(b);
assertEqual("g2a == g2 * a", g2a, g2at);
assertEqual("g1b == g1 * b", g1b, g1bt);
printf("errNum = %d\n", errNum);
}
