Fix handling of prime/composite-order curves within short-weierstrass

crypto/evrf/embedwards25519/src/lib.rs

@@ -67,6 +67,10 @@ impl ShortWeierstrass for Embedwards25519 {
 
     (repr, odd_y)
   }
+  // No points have a torsion element as this a prime-order curve
+  fn has_torsion_element(_point: Projective<Self>) -> Choice {
+    0.into()
+  }
 }
 
 pub type Point = Projective<Embedwards25519>;

crypto/short-weierstrass/src/affine.rs

@@ -79,8 +79,8 @@ impl<C: ShortWeierstrass> Affine<C> {
   /// Create an affine point from `x, y` coordinates, without performing any checks.
   ///
   /// This should NOT be used. It is solely intended for trusted data at compile-time. It MUST NOT
-  /// be used with any untrusted/unvalidated data. Providing any off-curve point may produce
-  /// completely undefined behavior.
+  /// be used with any untrusted/unvalidated data. Providing any point not within the largest
+  /// prime-order subgroup has completely undefined behavior.
   pub const fn from_xy_unchecked(x: C::FieldElement, y: C::FieldElement) -> Self {
     Self { x, y }
   }

crypto/short-weierstrass/src/lib.rs

@@ -15,10 +15,6 @@ mod projective;
 pub use projective::Projective;
 
 /// An elliptic curve represented in short Weierstrass form, with equation `y^2 = x^3 + A x + B`.
-///
-/// This elliptic curve is expected to be of prime order. If a generator of the elliptic curve has
-/// a composite order, the elliptic curve is defined solely as its largest odd-prime-order
-/// subgroup, further considered the entire group/elliptic curve.
 pub trait ShortWeierstrass: 'static + Sized + Debug {
   /// The field the elliptic curve is defined over.
   type FieldElement: Zeroize + PrimeField;
@@ -26,9 +22,9 @@ pub trait ShortWeierstrass: 'static + Sized + Debug {
   const A: Self::FieldElement;
   /// The constant `B` from the curve equation.
   const B: Self::FieldElement;
-  /// A generator of this elliptic curve.
+  /// A generator of this elliptic curve's largest prime-order subgroup.
   const GENERATOR: Affine<Self>;
-  /// The scalar type.
+  /// The scalar type for the elliptic curve's largest prime-order subgroup.
   ///
   /// This may be omitted by specifying `()`.
   type Scalar;
@@ -45,4 +41,9 @@ pub trait ShortWeierstrass: 'static + Sized + Debug {
   ///
   /// This is expected to return the `x` coordinate and if the `y` coordinate is odd.
   fn decode_compressed(bytes: &Self::Repr) -> (<Self::FieldElement as PrimeField>::Repr, Choice);
+
+  /// If the point is outside the largest prime-order subgroup and isn't the identity point.
+  ///
+  /// This may immediately return `Choice::new(0)` for curves of prime order.
+  fn has_torsion_element(point: Projective<Self>) -> Choice;
 }

crypto/short-weierstrass/src/projective.rs

@@ -308,12 +308,20 @@ impl<C: ShortWeierstrass> GroupEncoding for Projective<C> {
 
     let (x, odd_y) = C::decode_compressed(bytes);
 
-    // Parse x, recover y, return the result
-    C::FieldElement::from_repr(x).and_then(|x| {
+    let result = C::FieldElement::from_repr(x).and_then(|x| {
+      // Parse x and recover y
       let non_identity_on_curve_point = Affine::decompress(x, odd_y).map(Projective::from);
+      // Set the identity, if the identity
       let identity = CtOption::new(Projective::IDENTITY, identity);
       non_identity_on_curve_point.or_else(|| identity)
-    })
+    });
+
+    let mut result_is_valid = result.is_some();
+    let result = result.unwrap_or(Projective::IDENTITY);
+    // Constrain points to the prime-order subgroup
+    result_is_valid &= !C::has_torsion_element(result);
+
+    CtOption::new(result, result_is_valid)
   }
   fn from_bytes_unchecked(bytes: &C::Repr) -> CtOption<Self> {
     Self::from_bytes(bytes)
@@ -341,6 +349,7 @@ impl<C: ShortWeierstrass> GroupEncoding for Projective<C> {
   }
 }
 
+/// We implement `PrimeGroup` due to constraining to a prime-order subgroup
 impl<C: ShortWeierstrass<Scalar: PrimeFieldBits>> PrimeGroup for Projective<C> {}
 
 #[cfg(feature = "alloc")]