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fp12: improved cyclotomicSquare #25

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Jan 7, 2021
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fp12: improved cyclotomicSquare #25

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44 changes: 23 additions & 21 deletions bls377/internal/fptower/e12.go
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44 changes: 23 additions & 21 deletions bls381/internal/fptower/e12.go
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44 changes: 23 additions & 21 deletions bn256/internal/fptower/e12.go
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47 changes: 24 additions & 23 deletions internal/templates/fq12over6over2/fq12.go.tmpl
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Original file line number Diff line number Diff line change
Expand Up @@ -116,46 +116,47 @@ func (z *E12) Square(x *E12) *E12 {

return z
}

// squares an element a+by interpreted as an Fp4 elmt, where y**2= non_residue_e2
func fp4Square(a, b, c, d *E2) {
var tmp E2
c.Square(a)
tmp.Square(b).MulByNonResidue(&tmp)
tmp.Square(b)
d.Add(a, b).Square(d).Sub(d, c).Sub(d, &tmp)
tmp.MulByNonResidue(&tmp)
c.Add(c, &tmp)
}

func fp4SquareS(a, b, c, d *E2) {
var tmp E2
c.Square(a)
tmp.Square(b)
d.Add(a, b).Square(d).Sub(d, c).Sub(d, &tmp)
c.MulByNonResidue(c)
c.Add(c, &tmp)
d.Mul(a, b).Double(d)
}

// CyclotomicSquare https://eprint.iacr.org/2009/565.pdf, 3.2
func (z *E12) CyclotomicSquare(x *E12) *E12 {
var t [6]E2

var rc0, bc0, rc1, bc1 E6
rc0 = x.C0
rc1 = x.C1
fp4Square(&x.C0.B0, &x.C1.B1, &t[0], &t[1])
fp4Square(&x.C0.B1, &x.C1.B2, &t[2], &t[3])
fp4SquareS(&x.C0.B2, &x.C1.B0, &t[4], &t[5])

fp4Square(&rc0.B0, &rc1.B1, &bc0.B0, &bc1.B1)
fp4Square(&rc0.B1, &rc1.B2, &bc0.B2, &bc1.B0)
bc1.B0.MulByNonResidue(&bc1.B0)

{
var tmp E2
tmp.MulByNonResidueInv(&rc1.B0)
fp4Square(&rc0.B2, &tmp, &bc0.B1, &bc1.B2)
}

bc0.B1.MulByNonResidue(&bc0.B1)
bc1.B2.MulByNonResidue(&bc1.B2)
t[3].MulByNonResidue(&t[3])


rc1.Add(&bc1, &rc1).Double(&rc1)
z.C1.Add(&rc1, &bc1)
rc0.Sub(&bc0, &rc0).Double(&rc0)
z.C0.Add(&rc0, &bc0)
z.C0.B0.Sub(&t[0], &x.C0.B0).Double(&z.C0.B0).Add(&z.C0.B0, &t[0])
z.C0.B1.Sub(&t[4], &x.C0.B1).Double(&z.C0.B1).Add(&z.C0.B1, &t[4])
z.C0.B2.Sub(&t[2], &x.C0.B2).Double(&z.C0.B2).Add(&z.C0.B2, &t[2])
z.C1.B0.Add(&t[3], &x.C1.B0).Double(&z.C1.B0).Add(&z.C1.B0, &t[3])
z.C1.B1.Add(&t[1], &x.C1.B1).Double(&z.C1.B1).Add(&z.C1.B1, &t[1])
z.C1.B2.Add(&t[5], &x.C1.B2).Double(&z.C1.B2).Add(&z.C1.B2, &t[5])

return z
}



// Inverse set z to the inverse of x in E12 and return z
func (z *E12) Inverse(x *E12) *E12 {
// Algorithm 23 from https://eprint.iacr.org/2010/354.pdf
Expand Down