feat(point): naive scalar point multiplication

src/ecc/scalar.rs

@@ -1,4 +1,5 @@
 use crate::ecc::field_element::FieldElement;
+use crate::ecc::point::Point;
 use std::ops::Mul;
 
 #[derive(Debug, Clone)]
@@ -31,9 +32,27 @@ impl Mul<FieldElement> for Scalar {
     }
 }
 
+impl Mul<Point> for Scalar {
+    type Output = Result<Point, String>;
+
+    // Naive impl
+    fn mul(self, rhs: Point) -> Self::Output {
+        let mut result = Point::new(rhs.a.clone(), rhs.b.clone(), None, None).unwrap();
+
+        let end = self.value;
+
+        for _ in 0..end {
+            result = (result + rhs.clone())?
+        }
+
+        Ok(result)
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use crate::ecc::field_element::FieldElement;
+    use crate::ecc::point::Point;
     use crate::ecc::scalar::Scalar;
 
     fn new_fe(num: i64, prime: i64) -> FieldElement {
@@ -46,4 +65,24 @@ mod tests {
         let res = Scalar::new(2) * fe;
         assert_eq!(res.unwrap(), new_fe(30, 223))
     }
+
+    #[test]
+    fn scalar_multiplication_point() {
+        let prime = 223;
+        let a = new_fe(0, prime.clone());
+        let b = new_fe(7, prime.clone());
+        let x = new_fe(47, prime.clone());
+        let y = new_fe(71, prime.clone());
+        let p = Point::new(a.clone(), b.clone(), Some(x), Some(y)).unwrap();
+
+        assert_eq!(
+            Scalar::new(10) * p,
+            Point::new(
+                a,
+                b,
+                Some(new_fe(154, prime.clone())),
+                Some(new_fe(150, prime.clone()))
+            )
+        )
+    }
 }