build: rebase on develop

internal/generator/tower/template/fq12over6over2/fq12.go.tmpl

@@ -680,4 +680,96 @@ func (z *E12) IsInSubGroup() bool {
 	{{$.To}}.SetBytes(e[{{$.OffSet}}:{{$.OffSet}} + fp.Bytes])
 {{end}}
 
+// CompressTorus GT/E12 element to half its size
+// z must be in the cyclotomic subgroup
+// i.e. z^(p^4-p^2+1)=1
+// e.g. GT
+// "COMPRESSION IN FINITE FIELDS AND TORUS-BASED CRYPTOGRAPHY", K. RUBIN AND A. SILVERBERG
+// z.C1 == 0 only when z \in {-1,1}
+func (z *E12) CompressTorus() (E6, error) {
+
+	if z.C1.IsZero() {
+		return E6{}, errors.New("invalid input")
+	}
+
+	var res, tmp, one E6
+	one.SetOne()
+	tmp.Inverse(&z.C1)
+	res.Add(&z.C0, &one).
+		Mul(&res, &tmp)
+
+	return res, nil
+}
+
+// BatchCompressTorus GT/E12 elements to half their size
+// using a batch inversion
+func BatchCompressTorus(x []E12) ([]E6, error) {
+
+	n := len(x)
+	if n == 0 {
+		return []E6{}, errors.New("invalid input size")
+	}
+
+	var one E6
+	one.SetOne()
+	res := make([]E6, n)
+
+	for i := 0; i < n; i++ {
+		res[i].Set(&x[i].C1)
+	}
+
+	t := BatchInvertE6(res) // costs 1 inverse
+
+	for i := 0; i < n; i++ {
+		res[i].Add(&x[i].C0, &one).
+			Mul(&res[i], &t[i])
+	}
+
+	return res, nil
+}
+
+// DecompressTorus GT/E12 a compressed element
+// element must be in the cyclotomic subgroup
+// "COMPRESSION IN FINITE FIELDS AND TORUS-BASED CRYPTOGRAPHY", K. RUBIN AND A. SILVERBERG
+func (z *E6) DecompressTorus() E12 {
+
+	var res, num, denum E12
+	num.C0.Set(z)
+	num.C1.SetOne()
+	denum.C0.Set(z)
+	denum.C1.SetOne().Neg(&denum.C1)
+	res.Inverse(&denum).
+		Mul(&res, &num)
+
+	return res
+}
+
+// BatchDecompressTorus GT/E12 compressed elements
+// using a batch inversion
+func BatchDecompressTorus(x []E6) ([]E12, error) {
+
+	n := len(x)
+	if n == 0 {
+		return []E12{}, errors.New("invalid input size")
+	}
+
+	res := make([]E12, n)
+	num := make([]E12, n)
+	denum := make([]E12, n)
+
+	for i := 0; i < n; i++ {
+		num[i].C0.Set(&x[i])
+		num[i].C1.SetOne()
+		denum[i].C0.Set(&x[i])
+		denum[i].C1.SetOne().Neg(&denum[i].C1)
+	}
+
+	denum = BatchInvertE12(denum) // costs 1 inverse
+
+	for i := 0; i < n; i++ {
+		res[i].Mul(&num[i], &denum[i])
+	}
+
+	return res, nil
+}
 {{ template "base" .}}