p256+p384: define CurveEquationAProperties

Author: tarcieri

p256/src/arithmetic.rs

@@ -11,7 +11,7 @@ use crate::NistP256;
 use elliptic_curve::{
     AffineArithmetic, PrimeCurveArithmetic, ProjectiveArithmetic, ScalarArithmetic,
 };
-use primeorder::PrimeCurveParams;
+use primeorder::{CurveEquationAIsMinusThree, PrimeCurveParams};
 
 /// Elliptic curve point in affine coordinates.
 pub type AffinePoint = primeorder::AffinePoint<NistP256>;
@@ -21,6 +21,7 @@ pub type ProjectivePoint = primeorder::ProjectivePoint<NistP256>;
 
 impl PrimeCurveParams for NistP256 {
     type FieldElement = FieldElement;
+    type CurveEquationAProperties = CurveEquationAIsMinusThree;
 
     const ZERO: FieldElement = FieldElement::ZERO;
     const ONE: FieldElement = FieldElement::ONE;

p256/tests/projective.rs

@@ -8,6 +8,7 @@ use elliptic_curve::{
 };
 use p256::test_vectors::group::{ADD_TEST_VECTORS, MUL_TEST_VECTORS};
 use p256::{AffinePoint, ProjectivePoint, Scalar};
+use primeorder::Double;
 
 /// Assert that the provided projective point matches the given test vector.
 // TODO(tarcieri): use coordinate APIs. See zkcrypto/group#30

p384/src/arithmetic.rs

@@ -16,7 +16,7 @@ use crate::NistP384;
 use elliptic_curve::{
     AffineArithmetic, PrimeCurveArithmetic, ProjectiveArithmetic, ScalarArithmetic,
 };
-use primeorder::PrimeCurveParams;
+use primeorder::{CurveEquationAIsMinusThree, PrimeCurveParams};
 
 /// Elliptic curve point in affine coordinates.
 pub type AffinePoint = primeorder::AffinePoint<NistP384>;
@@ -26,6 +26,7 @@ pub type ProjectivePoint = primeorder::ProjectivePoint<NistP384>;
 
 impl PrimeCurveParams for NistP384 {
     type FieldElement = FieldElement;
+    type CurveEquationAProperties = CurveEquationAIsMinusThree;
 
     const ZERO: FieldElement = FieldElement::ZERO;
     const ONE: FieldElement = FieldElement::ONE;

p384/tests/projective.rs

@@ -10,6 +10,7 @@ use p384::{
     test_vectors::group::{ADD_TEST_VECTORS, MUL_TEST_VECTORS},
     AffinePoint, ProjectivePoint, Scalar,
 };
+use primeorder::Double;
 
 /// Assert that the provided projective point matches the given test vector.
 // TODO(tarcieri): use coordinate APIs. See zkcrypto/group#30

primeorder/src/projective.rs

@@ -205,9 +205,10 @@ impl<C> Double for ProjectivePoint<C>
 where
     C: PrimeCurveParams<CurveEquationAProperties = CurveEquationAIsMinusThree>,
 {
-    /// We implement the exception-free point doubling formula from
-    /// Renes-Costello-Batina 2015 (Algorithm 6), for prime order short
-    /// Weierstrass curves `y² = x³ + ax + b` where `a = -3`.
+    /// Adapted from Renes-Costello-Batina 2015 (Algorithm 6)
+    ///
+    /// Exception-free point doubling formula for prime order short Weierstrass
+    /// curves `y² = x³ + ax + b` where `a = -3`.
     ///
     /// The comments after each lines indicate which algorithm steps
     /// are being performed.