Generic arithmetic for Weierstrass curves

Cargo.toml

@@ -3,4 +3,5 @@ members = [
     "k256",
     "p256",
     "p384",
+    "weierstrass",
 ]

weierstrass/Cargo.toml

@@ -0,0 +1,12 @@
+[package]
+name = "weierstrass"
+version = "0.1.0"
+authors = ["RustCrypto Developers"]
+edition = "2018"
+
+[dependencies]
+generic-array = "0.14"
+subtle = "2.3"
+rand_core = "0.5"
+biguint-literal = { git = "https://github.com/RustCrypto/utils", branch = "biguint" }
+hex-literal = "0.3"

weierstrass/src/affine.rs

@@ -0,0 +1,173 @@
+use core::ops::{Mul, Neg};
+use generic_array::{ArrayLength, typenum::U1};
+use subtle::{Choice, ConditionallySelectable, ConstantTimeEq};
+use core::ops::Add;
+
+use crate::{
+    WeirstrassCurve, Word, 
+    Words, WordsLen,
+    WideWordsLen,
+    WordsBytesLen,
+    WordsP1Len,
+};
+use crate::scalar::Scalar;
+use crate::projective::ProjectivePoint;
+use crate::field::FieldElement;
+
+#[derive(Clone, Copy)]
+pub struct AffinePoint<C>
+    where
+        C: WeirstrassCurve,
+        WordsLen<C>: ArrayLength<Word> + Add<U1>,
+        WideWordsLen<C>: ArrayLength<Word>,
+        WordsP1Len<C>: ArrayLength<Word>,
+        WordsBytesLen<C>: ArrayLength<u8>,
+        Words<C>: Copy,
+{
+    pub x: FieldElement<C>,
+    pub y: FieldElement<C>,
+    pub infinity: Choice,
+}
+
+impl<C> AffinePoint<C>
+    where
+        C: WeirstrassCurve,
+        WordsLen<C>: ArrayLength<Word> + Add<U1>,
+        WideWordsLen<C>: ArrayLength<Word>,
+        WordsP1Len<C>: ArrayLength<Word>,
+        WordsBytesLen<C>: ArrayLength<u8>,
+        Words<C>: Copy,
+{
+    /// Returns the base point
+    pub fn generator() -> Self {
+        Self {
+            x: C::GENERATOR_X,
+            y: C::GENERATOR_Y,
+            infinity: Choice::from(0),
+        }
+    }
+
+    /// Returns the identity of the group: the point at infinity.
+    pub fn identity() -> Self {
+        Self {
+            x: FieldElement::zero(),
+            y: FieldElement::zero(),
+            infinity: Choice::from(1),
+        }
+    }
+
+    /// Is this point the identity point?
+    pub fn is_identity(&self) -> Choice {
+        self.infinity
+    }
+}
+
+impl<C> ConditionallySelectable for AffinePoint<C>
+    where
+        C: WeirstrassCurve,
+        WordsLen<C>: ArrayLength<Word> + Add<U1>,
+        WideWordsLen<C>: ArrayLength<Word>,
+        WordsP1Len<C>: ArrayLength<Word>,
+        WordsBytesLen<C>: ArrayLength<u8>,
+        Words<C>: Copy,
+{
+    fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
+        AffinePoint {
+            x: FieldElement::conditional_select(&a.x, &b.x, choice),
+            y: FieldElement::conditional_select(&a.y, &b.y, choice),
+            infinity: Choice::conditional_select(&a.infinity, &b.infinity, choice),
+        }
+    }
+}
+
+impl<C> ConstantTimeEq for AffinePoint<C>
+    where
+        C: WeirstrassCurve,
+        WordsLen<C>: ArrayLength<Word> + Add<U1>,
+        WideWordsLen<C>: ArrayLength<Word>,
+        WordsP1Len<C>: ArrayLength<Word>,
+        WordsBytesLen<C>: ArrayLength<u8>,
+        Words<C>: Copy,
+{
+    fn ct_eq(&self, other: &Self) -> Choice {
+        self.x.ct_eq(&other.x)
+            & self.y.ct_eq(&other.y)
+            & self.infinity.ct_eq(&other.infinity)
+    }
+}
+
+impl<C> PartialEq for AffinePoint<C>
+    where
+        C: WeirstrassCurve,
+        WordsLen<C>: ArrayLength<Word> + Add<U1>,
+        WideWordsLen<C>: ArrayLength<Word>,
+        WordsP1Len<C>: ArrayLength<Word>,
+        WordsBytesLen<C>: ArrayLength<u8>,
+        Words<C>: Copy,
+{
+    fn eq(&self, other: &Self) -> bool {
+        self.ct_eq(other).into()
+    }
+}
+
+impl<C> Eq for AffinePoint<C>
+    where
+        C: WeirstrassCurve,
+        WordsLen<C>: ArrayLength<Word> + Add<U1>,
+        WideWordsLen<C>: ArrayLength<Word>,
+        WordsP1Len<C>: ArrayLength<Word>,
+        WordsBytesLen<C>: ArrayLength<u8>,
+        Words<C>: Copy,
+{}
+
+impl<C> Mul<Scalar<C>> for AffinePoint<C>
+    where
+        C: WeirstrassCurve,
+        WordsLen<C>: ArrayLength<Word> + Add<U1>,
+        WideWordsLen<C>: ArrayLength<Word>,
+        WordsP1Len<C>: ArrayLength<Word>,
+        WordsBytesLen<C>: ArrayLength<u8>,
+        Words<C>: Copy,
+{
+    type Output = Self;
+
+    fn mul(self, scalar: Scalar<C>) -> Self {
+        (ProjectivePoint::from(self) * scalar).to_affine()
+    }
+}
+
+impl<C> Neg for AffinePoint<C>
+    where
+        C: WeirstrassCurve,
+        WordsLen<C>: ArrayLength<Word> + Add<U1>,
+        WideWordsLen<C>: ArrayLength<Word>,
+        WordsP1Len<C>: ArrayLength<Word>,
+        WordsBytesLen<C>: ArrayLength<u8>,
+        Words<C>: Copy,
+{
+    type Output = Self;
+
+    fn neg(self) -> Self::Output {
+        AffinePoint {
+            x: self.x,
+            y: -self.y,
+            infinity: self.infinity,
+        }
+    }
+}
+
+#[cfg(feature = "zeroize")]
+impl<C> Zeroize for AffinePoint<C>
+    where
+        C: WeirstrassCurve,
+        WordsLen<C>: ArrayLength<Word> + Add<U1>,
+        WideWordsLen<C>: ArrayLength<Word>,
+        WordsP1Len<C>: ArrayLength<Word>,
+        WordsBytesLen<C>: ArrayLength<u8>,
+        Words<C>: Copy,
+{
+    fn zeroize(&mut self) {
+        self.x.zeroize();
+        self.y.zeroize();
+    }
+}