curve + point structs (#5)

* curve + point structs

* Squashed commit of the following:

commit 7a7a0db
Author: Thor 🪁 <[email protected]>
Date:   Wed May 1 12:00:43 2024 -0700

    plonky3 deps added (#4)

    * dependencies added

    * cargo fmt

commit 307e995
Merge: d8f688b 344c2bd
Author: Thor 🪁 <[email protected]>
Date:   Wed May 1 11:52:54 2024 -0700

    Merge pull request #2 from pluto/dependabot/github_actions/dependabot/fetch-metadata-2

    Bump dependabot/fetch-metadata from 1 to 2

commit 344c2bd
Author: dependabot[bot] <49699333+dependabot[bot]@users.noreply.github.com>
Date:   Wed May 1 18:29:21 2024 +0000

    Bump dependabot/fetch-metadata from 1 to 2

    Bumps [dependabot/fetch-metadata](https://github.com/dependabot/fetch-metadata) from 1 to 2.
    - [Release notes](https://github.com/dependabot/fetch-metadata/releases)
    - [Commits](dependabot/fetch-metadata@v1...v2)

    ---
    updated-dependencies:
    - dependency-name: dependabot/fetch-metadata
      dependency-type: direct:production
      update-type: version-update:semver-major
    ...

    Signed-off-by: dependabot[bot] <[email protected]>

---------

Co-authored-by: Thor Kampefner <[email protected]>

Cargo.toml

@@ -1,8 +1,4 @@
 [workspace]
-resolver = "2"
+resolver="2"
 
-members = [
-    "ronkathon",
-    "field",
-    "util"
-]
+members=["ronkathon", "field", "util"]

ronkathon/src/curve.rs

@@ -0,0 +1,70 @@
+use p3_field::{AbstractField, Field};
+
+/// Elliptic curve in Weierstrass form: y^2 = x^3 + ax + b
+pub struct Curve<F: Field> {
+  pub a: F,
+  pub b: F,
+  three: F,
+  two:   F,
+}
+
+#[derive(Clone, Copy)]
+pub struct Point<F: Field> {
+  x: F,
+  y: F,
+}
+
+#[derive(Clone, Copy)]
+pub enum PointOrInfinity<F: Field> {
+  Point(Point<F>),
+  Infinity,
+}
+
+impl<F: Field> Curve<F> {
+  pub fn new(a: F, b: F) -> Self {
+    Self {
+      a,
+      b,
+      three: <F as AbstractField>::from_canonical_u8(3),
+      two: <F as AbstractField>::from_canonical_u8(2),
+    }
+  }
+
+  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,
+    }
+  }
+
+  pub fn add(&self, p: PointOrInfinity<F>, q: PointOrInfinity<F>) -> PointOrInfinity<F> {
+    match (p, q) {
+      (PointOrInfinity::Infinity, _) => q,
+      (_, PointOrInfinity::Infinity) => p,
+      (PointOrInfinity::Point(p), PointOrInfinity::Point(q)) => {
+        let r = self.add_points(p, q);
+        PointOrInfinity::Point(Point { x: r.x, y: r.y })
+      },
+    }
+  }
+
+  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);
+
+    if x1 == x2 && y1 == -y2 {
+      return Point { x: F::zero(), y: F::zero() };
+    }
+
+    let m = if x1 == x2 && y1 == y2 {
+      (self.three * x1 * x1 + self.a) / (self.two * y1)
+    } else {
+      (y2 - y1) / (x2 - x1)
+    };
+
+    let x = m * m - x1 - x2;
+    let y = m * (x1 - x) - y1;
+
+    Point { x, y }
+  }
+}

ronkathon/src/lib.rs

@@ -5,3 +5,5 @@
 #![allow(non_snake_case)]
 #![allow(clippy::clone_on_copy)]
 #![allow(unused_mut)]
+
+pub mod curve;