internal/ed25519: add tests for multi-model point types.

internal/edwards25519/edwards25519.go

@@ -107,6 +107,14 @@ func (v *ProjP3) FromP1xP1(p *ProjP1xP1) *ProjP3 {
 	return v
 }
 
+func (v *ProjP3) FromP2(p *ProjP2) *ProjP3 {
+	v.X.Mul(&p.X, &p.Z)
+	v.Y.Mul(&p.Y, &p.Z)
+	v.Z.Square(&p.Z)
+	v.T.Mul(&p.X, &p.Y)
+	return v
+}
+
 func (v *ProjCached) FromP3(p *ProjP3) *ProjCached {
 	v.YplusX.Add(&p.Y, &p.X)
 	v.YminusX.Sub(&p.Y, &p.X)
@@ -232,6 +240,26 @@ func (v *ProjP1xP1) Double(p *ProjP2) *ProjP1xP1 {
 	return v
 }
 
+func (v *ProjP3) Neg(p *ProjP3) *ProjP3 {
+	v.X.Neg(&p.X)
+	v.Y.Set(&p.Y)
+	v.Z.Set(&p.Z)
+	v.T.Neg(&p.T)
+	return v
+}
+
+// by @ebfull
+// https://github.com/dalek-cryptography/curve25519-dalek/pull/226/files
+func (v *ProjP3) Equal(u *ProjP3) int {
+	var t1, t2, t3, t4 radix51.FieldElement
+	t1.Mul(&v.X, &u.Z)
+	t2.Mul(&u.X, &v.Z)
+	t3.Mul(&v.Y, &u.Z)
+	t4.Mul(&u.Y, &v.Z)
+
+	return t1.Equal(&t2) & t3.Equal(&t4)
+}
+
 // From EFD https://hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
 // An elliptic curve in twisted Edwards form has parameters a, d and coordinates
 // x, y satisfying the following equations:

internal/edwards25519/edwards25519_test.go

@@ -36,3 +36,49 @@ func TestAddSubNegOnBasePoint(t *testing.T) {
 		t.Error("B + (-B) != 0")
 	}
 }
+
+func TestAddSubNegOnBasePoint2(t *testing.T) {
+
+	var B, Bneg ProjP3
+	var tmpP2 ProjP2
+	var tmpP1xP1 ProjP1xP1
+	var tmpCached ProjCached
+
+	B = ProjP3{
+		X: radix51.FieldElement([5]uint64{426475514619346, 2063872706840040, 14628272888959, 107677749330612, 288339085807592}),
+		Y: radix51.FieldElement([5]uint64{1934594822876571, 2049809580636559, 1991994783322914, 1758681962032007, 380046701118659}),
+		Z: radix51.FieldElement([5]uint64{1, 0, 0, 0, 0}),
+		T: radix51.FieldElement([5]uint64{410445769351754, 2235400917701188, 1495825632738689, 1351628537510093, 430502003771208}),
+	}
+
+	Bneg.Neg(&B)
+
+	var checkLhs, checkRhs, zero ProjP3
+	zero.Zero()
+
+	tmpCached.FromP3(&B)
+	tmpP1xP1.Add(&B, &tmpCached)
+	checkLhs.FromP1xP1(&tmpP1xP1)
+	tmpP2.FromP3(&B)
+	tmpP1xP1.Double(&tmpP2)
+	checkRhs.FromP1xP1(&tmpP1xP1)
+	if checkLhs.Equal(&checkRhs) != 1 {
+		t.Error("B + B != [2]B")
+	}
+
+	tmpCached.FromP3(&B)
+	tmpP1xP1.Sub(&B, &tmpCached)
+	checkLhs.FromP1xP1(&tmpP1xP1)
+	tmpCached.FromP3(&Bneg)
+	tmpP1xP1.Add(&B, &tmpCached)
+	checkRhs.FromP1xP1(&tmpP1xP1)
+	if checkLhs.Equal(&checkRhs) != 1 {
+		t.Error("B - B != B + (-B)")
+	}
+	if zero.Equal(&checkLhs) != 1 {
+		t.Error("B - B != 0")
+	}
+	if zero.Equal(&checkRhs) != 1 {
+		t.Error("B + (-B) != 0")
+	}
+}