Merge pull request #7 from pluto/review_point_addition

Update curve.rs

src/curve.rs

@@ -14,6 +14,7 @@ pub struct Point<F: Field> {
   y: F,
 }
 
+// Since EVERY point is either at "infinity" or not, the coproduct makes sense.
 #[derive(Clone, Copy)]
 pub enum PointOrInfinity<F: Field> {
   Point(Point<F>),
@@ -30,13 +31,15 @@ impl<F: Field> Curve<F> {
     }
   }
 
+  // inverse
   pub fn negate(&self, p: PointOrInfinity<F>) -> PointOrInfinity<F> {
     match p {
       PointOrInfinity::Point(p) => PointOrInfinity::Point(Point { x: p.x, y: -p.y }),
       PointOrInfinity::Infinity => PointOrInfinity::Infinity,
     }
   }
 
+  // outer add does infinitity check
   pub fn add(&self, p: PointOrInfinity<F>, q: PointOrInfinity<F>) -> PointOrInfinity<F> {
     match (p, q) {
       (PointOrInfinity::Infinity, _) => q,
@@ -49,21 +52,24 @@ impl<F: Field> Curve<F> {
   }
 
   fn add_points(&self, p: Point<F>, q: Point<F>) -> Point<F> {
-    let (x1, y1) = (p.x, p.y);
-    let (x2, y2) = (q.x, q.y);
+    // https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplicationcv
+    let (x_p, y_p) = (p.x, p.y);
+    let (x_q, y_q) = (q.x, q.y);
 
-    if x1 == x2 && y1 == -y2 {
+    // check for zero
+    if x_p == x_q && y_p == -y_q {
       return Point { x: F::zero(), y: F::zero() };
     }
 
-    let m = if x1 == x2 && y1 == y2 {
-      (self.three * x1 * x1 + self.a) / (self.two * y1)
+    // Check if point is itself, if it is you double (which is easier)
+    let lamda = if x_p == x_q && y_p == y_q {
+      (self.three * x_p * x_p + self.a) / (self.two * y_p)
     } else {
-      (y2 - y1) / (x2 - x1)
+      (y_q - y_p) / (x_q - x_p)
     };
 
-    let x = m * m - x1 - x2;
-    let y = m * (x1 - x) - y1;
+    let x = lamda * lamda - x_p - x_q;
+    let y = lamda * (x_p - x) - y_p;
 
     Point { x, y }
   }