fix: elliptic curve subtraction on proper ec points (#70)

* fix issue on elliptic curve addition with negative points that were not remapped back to a proper curve point

* set back minimum version to go 1.16

go.mod

@@ -13,5 +13,6 @@ require (
 	github.com/twmb/murmur3 v1.1.6
 	github.com/zeebo/blake3 v0.2.0
 	golang.org/x/sync v0.0.0-20210220032951-036812b2e83c
-	golang.org/x/sys v0.0.0-20210823070655-63515b42dcdf // indirect
 )
+
+require golang.org/x/sys v0.0.0-20210823070655-63515b42dcdf // indirect

internal/crypto/point.go

@@ -68,8 +68,13 @@ func (p *Point) ScalarMult(scalar []byte) *Point {
 
 // Sub substracts point p from q
 func (p *Point) Sub(q *Point) *Point {
+	// in order to do point subtraction, we need to make sure
+	// the negative point is still mapped properly in the field elements.
+	negQy := new(big.Int).Neg(q.y)
+	negQy = negQy.Mod(negQy, curve.Params().P) // here P is the order of the curve field
+
 	// p - q = p.x + q.x, p.y - q.y
-	x, y := curve.Add(p.x, p.y, q.x, new(big.Int).Neg(q.y))
+	x, y := curve.Add(p.x, p.y, q.x, negQy)
 	return &Point{x: x, y: y}
 }