[WIP] weierstrass: initial crate

Implements `AffinePoint` and `ProjectivePoint` generically

Cargo.toml

@@ -6,7 +6,8 @@ members = [
     "k256",
     "p256",
     "p384",
-    "p521"
+    "p521",
+    "weierstrass"
 ]
 
 [profile.dev]

p384/Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name = "p384"
-version = "0.11.1"
+version = "0.12.0-pre"
 description = """
 Pure Rust implementation of the NIST P-384 (a.k.a. secp384r1) elliptic curve
 with support for ECDH, ECDSA signing/verification, and general purpose curve
@@ -18,6 +18,7 @@ rust-version = "1.57"
 
 [dependencies]
 elliptic-curve = { version = "0.12.2", default-features = false, features = ["hazmat", "sec1"] }
+weierstrass = { version = "0", path = "../weierstrass" }
 
 # optional dependencies
 ecdsa-core = { version = "0.14", package = "ecdsa", optional = true, default-features = false, features = ["der"] }

p384/src/arithmetic.rs

@@ -8,25 +8,63 @@
 #[macro_use]
 mod macros;
 
-pub(crate) mod affine;
 pub(crate) mod field;
-pub(crate) mod projective;
 pub(crate) mod scalar;
 
-use self::{
-    affine::AffinePoint,
-    field::{FieldElement, MODULUS},
-    projective::ProjectivePoint,
-    scalar::Scalar,
-};
-
-/// a = -3 (0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffc)
-const CURVE_EQUATION_A: FieldElement = FieldElement::ZERO
-    .sub(&FieldElement::ONE)
-    .sub(&FieldElement::ONE)
-    .sub(&FieldElement::ONE);
-
-/// b = b3312fa7 e23ee7e4 988e056b e3f82d19 181d9c6e fe814112
-///     0314088f 5013875a c656398d 8a2ed19d 2a85c8ed d3ec2aef
-const CURVE_EQUATION_B: FieldElement =
-    FieldElement::from_be_hex("b3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef");
+use self::field::FieldElement;
+use crate::NistP384;
+use elliptic_curve::{AffineArithmetic, PrimeCurveArithmetic, ProjectiveArithmetic};
+use weierstrass::WeierstrassCurve;
+
+/// Elliptic curve point in affine coordinates.
+pub type AffinePoint = weierstrass::AffinePoint<NistP384>;
+
+/// Elliptic curve point in projective coordinates.
+pub type ProjectivePoint = weierstrass::ProjectivePoint<NistP384>;
+
+impl WeierstrassCurve for NistP384 {
+    type FieldElement = FieldElement;
+
+    const ZERO: FieldElement = FieldElement::ZERO;
+    const ONE: FieldElement = FieldElement::ONE;
+
+    /// a = -3 (0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffc)
+    const EQUATION_A: FieldElement = FieldElement::ZERO
+        .sub(&FieldElement::ONE)
+        .sub(&FieldElement::ONE)
+        .sub(&FieldElement::ONE);
+
+    /// b = b3312fa7 e23ee7e4 988e056b e3f82d19 181d9c6e fe814112
+    ///     0314088f 5013875a c656398d 8a2ed19d 2a85c8ed d3ec2aef
+    const EQUATION_B: FieldElement = FieldElement::from_be_hex("b3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef");
+
+    /// Base point of P-384.
+    ///
+    /// Defined in FIPS 186-4 § D.1.2.4:
+    ///
+    /// ```text
+    /// Gₓ = aa87ca22 be8b0537 8eb1c71e f320ad74 6e1d3b62 8ba79b98
+    ///      59f741e0 82542a38 5502f25d bf55296c 3a545e38 72760ab7
+    /// Gᵧ = 3617de4a 96262c6f 5d9e98bf 9292dc29 f8f41dbd 289a147c
+    ///      e9da3113 b5f0b8c0 0a60b1ce 1d7e819d 7a431d7c 90ea0e5f
+    /// ```
+    ///
+    /// NOTE: coordinate field elements have been translated into the Montgomery
+    /// domain.
+    const GENERATOR: (FieldElement, FieldElement) = (
+        FieldElement::from_be_hex("aa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7"),
+        FieldElement::from_be_hex("3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f"),
+    );
+}
+
+impl AffineArithmetic for NistP384 {
+    type AffinePoint = AffinePoint;
+}
+
+impl ProjectiveArithmetic for NistP384 {
+    type ProjectivePoint = ProjectivePoint;
+}
+
+impl PrimeCurveArithmetic for NistP384 {
+    type CurveGroup = ProjectivePoint;
+}