bn::components Namespace Reference

Functions
void	precomputeG2 (std::vector< Fp6 > &coeff, Fp2 Q[3], const Fp2 inQ[3])
void	millerLoop (Fp12 &f, const std::vector< Fp6 > &Qcoeff, const Fp precP[2])
void	millerLoop2 (Fp12 &f, const std::vector< Fp6 > &Q1coeff, const Fp precP1[2], const std::vector< Fp6 > &Q2coeff, const Fp precP2[2])

Function Documentation

millerLoop()

void bn::components::millerLoop ( Fp12 & f, const std::vector< Fp6 > & Qcoeff, const Fp precP[2] )

inline

Definition at line 3060 of file bn.h.

{
    assert(Param::siTbl[1] == 1);
    size_t idx = 0;
 
    Fp6 d = Qcoeff[idx];
    Fp6::mulFp6_24_Fp_01(d, precP);
    idx++;
 
    Fp6 e = Qcoeff[idx];
    Fp6::mulFp6_24_Fp_01(e, precP);
    Fp12::Dbl::mul_Fp2_024_Fp2_024(f, d, e);
 
    idx++;
    bn::Fp6 l;
    for (size_t i = 2; i < Param::siTbl.size(); i++) {
        l = Qcoeff[idx];
        idx++;
        Fp12::square(f);
        Fp6::mulFp6_24_Fp_01(l, precP);
 
        Fp12::Dbl::mul_Fp2_024(f, l);
 
        if (Param::siTbl[i]) {
            l = Qcoeff[idx];
            idx++;
            Fp6::mulFp6_24_Fp_01(l, precP);
            Fp12::Dbl::mul_Fp2_024(f, l);
        }
    }
 
#ifndef BN_SUPPORT_SNARK
    // @memo z < 0
    Fp6::neg(f.b_, f.b_);
#endif
    Fp12 ft;
 
    d = Qcoeff[idx];
    Fp6::mulFp6_24_Fp_01(d, precP);
    idx++;
 
    e = Qcoeff[idx];
    Fp6::mulFp6_24_Fp_01(e, precP);
 
    Fp12::Dbl::mul_Fp2_024_Fp2_024(ft, d, e);
    Fp12::mul(f, f, ft);
}

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millerLoop2()

void bn::components::millerLoop2 ( Fp12 & f, const std::vector< Fp6 > & Q1coeff, const Fp precP1[2], const std::vector< Fp6 > & Q2coeff, const Fp precP2[2] )

inline

Definition at line 3108 of file bn.h.

{
    assert(Param::siTbl[1] == 1);
    size_t idx = 0;
 
    Fp6 d1 = Q1coeff[idx];
    Fp6::mulFp6_24_Fp_01(d1, precP1);
    Fp6 d2 = Q2coeff[idx];
    Fp6::mulFp6_24_Fp_01(d2, precP2);
    idx++;
 
    Fp12 f1;
    Fp6 e1 = Q1coeff[idx];
    Fp6::mulFp6_24_Fp_01(e1, precP1);
    Fp12::Dbl::mul_Fp2_024_Fp2_024(f1, d1, e1);
 
    Fp12 f2;
    Fp6 e2 = Q2coeff[idx];
    Fp6::mulFp6_24_Fp_01(e2, precP2);
    Fp12::Dbl::mul_Fp2_024_Fp2_024(f2, d2, e2);
    Fp12::mul(f, f1, f2);
 
    idx++;
    bn::Fp6 l1, l2;
    for (size_t i = 2; i < Param::siTbl.size(); i++) {
        l1 = Q1coeff[idx];
        l2 = Q2coeff[idx];
        idx++;
        Fp12::square(f);
 
        Fp6::mulFp6_24_Fp_01(l1, precP1);
        Fp6::mulFp6_24_Fp_01(l2, precP2);
 
        Fp12::Dbl::mul_Fp2_024_Fp2_024(f1, l1, l2);
        Fp12::mul(f, f, f1);
 
        if (Param::siTbl[i]) {
            l1 = Q1coeff[idx];
            l2 = Q2coeff[idx];
            idx++;
            Fp6::mulFp6_24_Fp_01(l1, precP1);
            Fp6::mulFp6_24_Fp_01(l2, precP2);
            Fp12::Dbl::mul_Fp2_024_Fp2_024(f1, l1, l2);
            Fp12::mul(f, f, f1);
        }
    }
 
#ifndef BN_SUPPORT_SNARK
    // @memo z < 0
    Fp6::neg(f.b_, f.b_);
#endif
 
    d1 = Q1coeff[idx];
    Fp6::mulFp6_24_Fp_01(d1, precP1);
 
    d2 = Q2coeff[idx];
    Fp6::mulFp6_24_Fp_01(d2, precP2);
    idx++;
 
    e1 = Q1coeff[idx];
    Fp6::mulFp6_24_Fp_01(e1, precP1);
 
    e2 = Q2coeff[idx];
    Fp6::mulFp6_24_Fp_01(e2, precP2);
 
    Fp12::Dbl::mul_Fp2_024_Fp2_024(f1, d1, e1);
    Fp12::Dbl::mul_Fp2_024_Fp2_024(f2, d2, e2);
    Fp12::mul(f, f, f1);
    Fp12::mul(f, f, f2);
}

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precomputeG2()

void bn::components::precomputeG2 ( std::vector< Fp6 > & coeff, Fp2 Q[3], const Fp2 inQ[3] )

inline

Definition at line 2997 of file bn.h.

{
    coeff.clear();
    bn::ecop::NormalizeJac(Q, inQ);
 
    Fp2 T[3];
    T[0] = Q[0];
    T[1] = Q[1];
    T[2] = Fp2(1);
    Fp2 Qneg[2];
    if (Param::useNAF) {
        Qneg[0] = Q[0];
        Fp2::neg(Qneg[1], Q[1]);
    }
 
    Fp6 d;
    Fp6::pointDblLineEvalWithoutP(d, T);
    coeff.push_back(d);
 
    Fp6 e;
    assert(Param::siTbl[1] == 1);
    Fp6::pointAddLineEvalWithoutP(e, T, Q);
    coeff.push_back(e);
 
    bn::Fp6 l;
    // 844kclk
    for (size_t i = 2; i < Param::siTbl.size(); i++) {
        Fp6::pointDblLineEvalWithoutP(l, T);
        coeff.push_back(l);
 
        if (Param::siTbl[i] > 0) {
            Fp6::pointAddLineEvalWithoutP(l, T, Q);
            coeff.push_back(l);
        }
        else if (Param::siTbl[i] < 0) {
            Fp6::pointAddLineEvalWithoutP(l, T, Qneg);
            coeff.push_back(l);
        }
    }
 
    // addition step
    Fp2 Q1[2];
    bn::ecop::FrobEndOnTwist_1(Q1, Q);
    Fp2 Q2[2];
#ifdef BN_SUPPORT_SNARK
    bn::ecop::FrobEndOnTwist_2(Q2, Q);
    Fp2::neg(Q2[1], Q2[1]);
#else
    // @memo z < 0
    ecop::FrobEndOnTwist_8(Q2, Q);
    Fp2::neg(T[1], T[1]);
#endif
 
    Fp6::pointAddLineEvalWithoutP(d, T, Q1);
    coeff.push_back(d);
 
    Fp6::pointAddLineEvalWithoutP(e, T, Q2);
    coeff.push_back(e);
}

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