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#pragma once
/**
@file
@brief utility for pairings
@author MITSUNARI Shigeo(@herumi)
@license modified new BSD license
http://opensource.org/licenses/BSD-3-Clause
*/
#include <mcl/fp_tower.hpp>
#include <mcl/ec.hpp>
#include <mcl/curve_type.h>
#include <assert.h>
namespace mcl {
struct CurveParam {
/*
y^2 = x^3 + b
i^2 = -1
xi = xi_a + i
v^3 = xi
w^2 = v
*/
const char *z;
int b; // y^2 = x^3 + b
int xi_a; // xi = xi_a + i
int curveType; // same in bn.h
bool operator==(const CurveParam& rhs) const { return z == rhs.z && b == rhs.b && xi_a == rhs.xi_a; }
bool operator!=(const CurveParam& rhs) const { return !operator==(rhs); }
};
namespace bn {
const CurveParam CurveFp254BNb = { "-0x4080000000000001", 2, 1, mclBn_CurveFp254BNb }; // -(2^62 + 2^55 + 1)
// provisional(experimental) param with maxBitSize = 384
const CurveParam CurveFp382_1 = { "-0x400011000000000000000001", 2, 1, mclBn_CurveFp382_1 }; // -(2^94 + 2^76 + 2^72 + 1) // A Family of Implementation-Friendly BN Elliptic Curves
const CurveParam CurveFp382_2 = { "-0x400040090001000000000001", 2, 1, mclBn_CurveFp382_2 }; // -(2^94 + 2^78 + 2^67 + 2^64 + 2^48 + 1) // used in relic-toolkit
const CurveParam CurveFp462 = { "0x4001fffffffffffffffffffffbfff", 5, 2, mclBn_CurveFp462 }; // 2^114 + 2^101 - 2^14 - 1 // https://eprint.iacr.org/2017/334
const CurveParam CurveSNARK1 = { "4965661367192848881", 3, 9, mclBn_CurveSNARK1 };
} // mcl::bn
namespace bls12 {
const CurveParam CurveFp381 = { "-0xd201000000010000", 4, 1, mclBls12_CurveFp381 };
} // mcl::bls12
inline const CurveParam& getCurveParam(int type)
{
switch (type) {
case mclBn_CurveFp254BNb: return bn::CurveFp254BNb;
case mclBn_CurveFp382_1: return bn::CurveFp382_1;
case mclBn_CurveFp382_2: return bn::CurveFp382_2;
case mclBn_CurveFp462: return bn::CurveFp462;
case mclBn_CurveSNARK1: return bn::CurveSNARK1;
case mclBls12_CurveFp381: return bls12::CurveFp381;
default:
throw cybozu::Exception("getCurveParam:bad type") << type;
}
}
namespace util {
typedef std::vector<int8_t> SignVec;
inline size_t getPrecomputeQcoeffSize(const SignVec& sv)
{
size_t idx = 2 + 2;
for (size_t i = 2; i < sv.size(); i++) {
idx++;
if (sv[i]) idx++;
}
return idx;
}
template<class X, class C, size_t N>
X evalPoly(const X& x, const C (&c)[N])
{
X ret = c[N - 1];
for (size_t i = 1; i < N; i++) {
ret *= x;
ret += c[N - 1 - i];
}
return ret;
}
enum TwistBtype {
tb_generic,
tb_1m1i, // 1 - 1i
tb_1m2i // 1 - 2i
};
template<class _Fp>
struct CommonParamT {
typedef _Fp Fp;
typedef Fp2T<Fp> Fp2;
typedef mcl::EcT<Fp> G1;
typedef mcl::EcT<Fp2> G2;
int curveType;
bool isCurveFp254BNb;
mpz_class z;
mpz_class abs_z;
bool isNegative;
mpz_class p;
mpz_class r;
int b;
/*
BN254, BN381, etc. : Dtype
BLS12-381 : Mtype
*/
bool isMtype;
/*
Dtype twist
(x', y') = phi(x, y) = (x/w^2, y/w^3)
y^2 = x^3 + b
=> (y'w^3)^2 = (x'w^2)^3 + b
=> y'^2 = x'^3 + b / w^6 ; w^6 = xi
=> y'^2 = x'^3 + twist_b;
*/
Fp2 twist_b;
util::TwistBtype twist_b_type;
bool is_b_div_xi_1_m1i;
mpz_class exp_c0;
mpz_class exp_c1;
mpz_class exp_c2;
mpz_class exp_c3;
// Loop parameter for the Miller loop part of opt. ate pairing.
util::SignVec siTbl;
size_t precomputedQcoeffSize;
bool useNAF;
util::SignVec zReplTbl;
void initCommonParam(const CurveParam& cp, fp::Mode mode, bool isBLS12)
{
curveType = cp.curveType;
z = mpz_class(cp.z);
isCurveFp254BNb = cp == bn::CurveFp254BNb;
isMtype = isBLS12 ? true : false; // ad hoc
isNegative = z < 0;
if (isNegative) {
abs_z = -z;
} else {
abs_z = z;
}
if (isBLS12) {
mpz_class z2 = z * z;
mpz_class z4 = z2 * z2;
r = z4 - z2 + 1;
p = z - 1;
p = p * p * r / 3 + z;
} else {
const int pCoff[] = { 1, 6, 24, 36, 36 };
const int rCoff[] = { 1, 6, 18, 36, 36 };
p = util::evalPoly(z, pCoff);
assert((p % 6) == 1);
r = util::evalPoly(z, rCoff);
}
Fp::init(p, mode);
Fp2::init(cp.xi_a);
b = cp.b;
Fp2 xi(cp.xi_a, 1);
if (isMtype) {
twist_b = Fp2(b) * xi;
} else {
twist_b = Fp2(b) / xi;
}
if (twist_b == Fp2(1, -1)) {
twist_b_type = tb_1m1i;
} else if (twist_b == Fp2(1, -2)) {
twist_b_type = tb_1m2i;
} else {
twist_b_type = tb_generic;
}
G1::init(0, b, mcl::ec::Proj);
G2::init(0, twist_b, mcl::ec::Proj);
G2::setOrder(r);
const mpz_class largest_c = isBLS12 ? abs_z : gmp::abs(z * 6 + 2);
useNAF = gmp::getNAF(siTbl, largest_c);
precomputedQcoeffSize = util::getPrecomputeQcoeffSize(siTbl);
gmp::getNAF(zReplTbl, gmp::abs(z));
if (isBLS12) {
mpz_class z2 = z * z;
mpz_class z3 = z2 * z;
mpz_class z4 = z3 * z;
mpz_class z5 = z4 * z;
exp_c0 = z5 - 2 * z4 + 2 * z2 - z + 3;
exp_c1 = z4 - 2 * z3 + 2 * z - 1;
exp_c2 = z3 - 2 * z2 + z;
exp_c3 = z2 - 2 * z + 1;
} else {
exp_c0 = -2 + z * (-18 + z * (-30 - 36 * z));
exp_c1 = 1 + z * (-12 + z * (-18 - 36 * z));
exp_c2 = 6 * z * z + 1;
}
}
};
/*
l = (a, b, c) => (a, b * P.y, c * P.x)
*/
template<class Fp6, class G1>
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 Fp12, class Fp6>
void convertFp6toFp12(Fp12& y, const Fp6& x)
{
y.clear();
#ifdef MCL_DEV
y.a.a = x.b;
y.b.a = x.c;
y.b.b = x.a;
#else
y.a.a = x.a;
y.a.c = x.c;
y.b.b = x.b;
#endif
}
template<class Param, class Fp2>
void mul_b_div_xi(const Param& param, Fp2& y, const Fp2& x)
{
typedef typename Fp2::BaseFp Fp;
switch (param.twist_b_type) {
case util::tb_1m1i:
/*
b / xi = 1 - 1i
(a + bi)(1 - 1i) = (a + b) + (b - a)i
*/
{
Fp t;
Fp::add(t, x.a, x.b);
Fp::sub(y.b, x.b, x.a);
y.a = t;
}
return;
case util::tb_1m2i:
/*
b / xi = 1 - 2i
(a + bi)(1 - 2i) = (a + 2b) + (b - 2a)i
*/
{
Fp t;
Fp::sub(t, x.b, x.a);
t -= x.a;
Fp::add(y.a, x.a, x.b);
y.a += x.b;
y.b = t;
}
return;
case util::tb_generic:
Fp2::mul(y, x, param.twist_b);
return;
}
}
} // mcl::util
} // mcl
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