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BLS12 final exponentiation (eprint 2020/875) #29

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Jan 28, 2021
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BLS12 final exponentiation (eprint 2020/875) #29

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4717936
bls381: final exp hard part eprint 2020/875
yelhousni Jan 28, 2021
13a0751
bls377: final exp hard part eprint 2020/875
yelhousni Jan 28, 2021
aa71ad3
bls12/: fmt
yelhousni Jan 28, 2021
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51 changes: 21 additions & 30 deletions bls377/pairing.go
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Original file line number Diff line number Diff line change
Expand Up @@ -61,7 +61,7 @@ func FinalExponentiation(z *GT, _z ...*GT) GT {
}

// https://eprint.iacr.org/2016/130.pdf
var t [6]GT
var t [3]GT

// easy part
t[0].Conjugate(&result)
Expand All @@ -71,36 +71,27 @@ func FinalExponentiation(z *GT, _z ...*GT) GT {
Mul(&result, &t[0])

// hard part (up to permutation)
t[0].InverseUnitary(&result).Square(&t[0])
t[5].Expt(&result)
t[1].CyclotomicSquare(&t[5])
t[3].Mul(&t[0], &t[5])

t[0].Expt(&t[3])
// Daiki Hayashida and Kenichiro Hayasaka
// and Tadanori Teruya
// https://eprint.iacr.org/2020/875.pdf
t[0].CyclotomicSquare(&result)
t[1].Expt(&result)
t[2].InverseUnitary(&result)
t[1].Mul(&t[1], &t[2])
t[2].Expt(&t[1])
t[1].InverseUnitary(&t[1])
t[1].Mul(&t[1], &t[2])
t[2].Expt(&t[1])
t[1].Frobenius(&t[1])
t[1].Mul(&t[1], &t[2])
result.Mul(&result, &t[0])
t[0].Expt(&t[1])
t[2].Expt(&t[0])
t[4].Expt(&t[2])

t[4].Mul(&t[1], &t[4])
t[1].Expt(&t[4])
t[3].InverseUnitary(&t[3])
t[1].Mul(&t[3], &t[1])
t[1].Mul(&t[1], &result)

t[0].Mul(&t[0], &result)
t[0].FrobeniusCube(&t[0])

t[3].InverseUnitary(&result)
t[4].Mul(&t[3], &t[4])
t[4].Frobenius(&t[4])

t[5].Mul(&t[2], &t[5])
t[5].FrobeniusSquare(&t[5])

t[5].Mul(&t[5], &t[0])
t[5].Mul(&t[5], &t[4])
t[5].Mul(&t[5], &t[1])

result.Set(&t[5])
t[0].FrobeniusSquare(&t[1])
t[1].InverseUnitary(&t[1])
t[1].Mul(&t[1], &t[2])
t[1].Mul(&t[1], &t[0])
result.Mul(&result, &t[1])

return result
}
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33 changes: 15 additions & 18 deletions bls381/pairing.go
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Original file line number Diff line number Diff line change
Expand Up @@ -58,7 +58,7 @@ func FinalExponentiation(z *GT, _z ...*GT) GT {
result.Mul(&result, e)
}

var t [4]GT
var t [3]GT

// easy part
t[0].Conjugate(&result)
Expand All @@ -68,30 +68,27 @@ func FinalExponentiation(z *GT, _z ...*GT) GT {
Mul(&result, &t[0])

// hard part (up to permutation)
// Alg.2 from https://eprint.iacr.org/2016/130.pdf
// Daiki Hayashida and Kenichiro Hayasaka
// and Tadanori Teruya
// https://eprint.iacr.org/2020/875.pdf
t[0].CyclotomicSquare(&result)
t[1].Expt(&t[0])
t[2].ExptHalf(&t[1])
t[3].InverseUnitary(&result)
t[1].Mul(&t[1], &t[3])
t[1].InverseUnitary(&t[1])
t[1].ExptHalf(&t[0])
t[2].InverseUnitary(&result)
t[1].Mul(&t[1], &t[2])
t[2].Expt(&t[1])
t[3].Expt(&t[2])
t[1].InverseUnitary(&t[1])
t[3].Mul(&t[1], &t[3])
t[1].InverseUnitary(&t[1])
t[1].FrobeniusCube(&t[1])
t[2].FrobeniusSquare(&t[2])
t[1].Mul(&t[1], &t[2])
t[2].Expt(&t[3])
t[2].Mul(&t[2], &t[0])
t[2].Mul(&t[2], &result)
t[2].Expt(&t[1])
t[1].Frobenius(&t[1])
t[1].Mul(&t[1], &t[2])
t[2].Frobenius(&t[3])
result.Mul(&result, &t[0])
t[0].Expt(&t[1])
t[2].Expt(&t[0])
t[0].FrobeniusSquare(&t[1])
t[1].InverseUnitary(&t[1])
t[1].Mul(&t[1], &t[2])

result.Set(&t[1])
t[1].Mul(&t[1], &t[0])
result.Mul(&result, &t[1])

return result
}
Expand Down