primeorder: use FieldArithmetic trait (#1833)

Uses the new `hazmat` trait added to `elliptic-curve` in
RustCrypto/traits#2458 to define the associated `FieldElement` type for
a given curve.

Author: tarcieri

Cargo.lock

@@ -8,13 +8,12 @@
 pub(crate) mod field;
 pub(crate) mod scalar;
 
-pub use self::scalar::Scalar;
+pub use self::{field::FieldElement, scalar::Scalar};
+pub use elliptic_curve::{CurveArithmetic, PrimeCurveArithmetic, hazmat::FieldArithmetic};
+pub use primeorder::{PrimeCurveParams, point_arithmetic};
 
-pub use self::field::FieldElement;
 use crate::BignP256;
-pub use elliptic_curve::{CurveArithmetic, PrimeCurveArithmetic};
 use primeorder::backend;
-pub use primeorder::{PrimeCurveParams, point_arithmetic};
 
 /// Elliptic curve point in affine coordinates.
 pub type AffinePoint = primeorder::AffinePoint<BignP256>;
@@ -28,12 +27,15 @@ impl CurveArithmetic for BignP256 {
     type Scalar = Scalar;
 }
 
+impl FieldArithmetic for BignP256 {
+    type FieldElement = FieldElement;
+}
+
 impl PrimeCurveArithmetic for BignP256 {
     type CurveGroup = ProjectivePoint;
 }
 
 impl PrimeCurveParams for BignP256 {
-    type FieldElement = FieldElement;
     type PointArithmetic = point_arithmetic::EquationAIsGeneric;
     type Backend = backend::VariableOnly;
 

bignp256/src/arithmetic.rs

@@ -2,9 +2,9 @@
 
 use bp256::BrainpoolP256r1;
 use criterion::{criterion_group, criterion_main};
-use primeorder::PrimeCurveParams;
+use elliptic_curve::hazmat::FieldArithmetic;
 
-type FieldElement = <BrainpoolP256r1 as PrimeCurveParams>::FieldElement;
+type FieldElement = <BrainpoolP256r1 as FieldArithmetic>::FieldElement;
 
 const FE_A: FieldElement = FieldElement::from_hex_vartime(
     "8bd2aeb9cb7e57cb2c4b482ffc81b7afb9de27e1e3bd23c23a4453bd9ace3262",

bp256/benches/field.rs

@@ -2,7 +2,7 @@
 
 use super::BrainpoolP256r1;
 use crate::{FieldElement, Scalar};
-use elliptic_curve::{CurveArithmetic, PrimeCurveArithmetic};
+use elliptic_curve::{CurveArithmetic, PrimeCurveArithmetic, hazmat::FieldArithmetic};
 use primeorder::{PrimeCurveParams, backend, point_arithmetic};
 
 /// Elliptic curve point in affine coordinates.
@@ -23,12 +23,15 @@ impl CurveArithmetic for BrainpoolP256r1 {
     type Scalar = Scalar;
 }
 
+impl FieldArithmetic for BrainpoolP256r1 {
+    type FieldElement = FieldElement;
+}
+
 impl PrimeCurveArithmetic for BrainpoolP256r1 {
     type CurveGroup = ProjectivePoint;
 }
 
 impl PrimeCurveParams for BrainpoolP256r1 {
-    type FieldElement = FieldElement;
     type PointArithmetic = point_arithmetic::EquationAIsGeneric;
     type Backend = backend::VariableOnly;
 

bp256/src/r1/arithmetic.rs

@@ -2,7 +2,7 @@
 
 use super::BrainpoolP256t1;
 use crate::{FieldElement, Scalar};
-use elliptic_curve::{CurveArithmetic, PrimeCurveArithmetic};
+use elliptic_curve::{CurveArithmetic, PrimeCurveArithmetic, hazmat::FieldArithmetic};
 use primeorder::{PrimeCurveParams, backend, point_arithmetic};
 
 /// Elliptic curve point in affine coordinates.
@@ -27,8 +27,11 @@ impl PrimeCurveArithmetic for BrainpoolP256t1 {
     type CurveGroup = ProjectivePoint;
 }
 
-impl PrimeCurveParams for BrainpoolP256t1 {
+impl FieldArithmetic for BrainpoolP256t1 {
     type FieldElement = FieldElement;
+}
+
+impl PrimeCurveParams for BrainpoolP256t1 {
     type PointArithmetic = point_arithmetic::EquationAIsGeneric;
     type Backend = backend::VariableOnly;
 

bp256/src/t1/arithmetic.rs

@@ -2,9 +2,9 @@
 
 use bp384::BrainpoolP384r1;
 use criterion::{criterion_group, criterion_main};
-use primeorder::PrimeCurveParams;
+use elliptic_curve::hazmat::FieldArithmetic;
 
-type FieldElement = <BrainpoolP384r1 as PrimeCurveParams>::FieldElement;
+type FieldElement = <BrainpoolP384r1 as FieldArithmetic>::FieldElement;
 
 const FE_A: FieldElement = FieldElement::from_hex_vartime(
     "1d1c64f068cf45ffa2a63a81b7c13f6b8847a3e77ef14fe3db7fcafe0cbd10e8e826e03436d646aaef87b2e247d4af1e",

bp384/benches/field.rs

@@ -2,7 +2,7 @@
 
 use super::BrainpoolP384r1;
 use crate::{FieldElement, Scalar};
-use elliptic_curve::{CurveArithmetic, PrimeCurveArithmetic};
+use elliptic_curve::{CurveArithmetic, PrimeCurveArithmetic, hazmat::FieldArithmetic};
 use primeorder::{PrimeCurveParams, backend, point_arithmetic};
 
 /// Elliptic curve point in affine coordinates.
@@ -23,12 +23,15 @@ impl CurveArithmetic for BrainpoolP384r1 {
     type Scalar = Scalar;
 }
 
+impl FieldArithmetic for BrainpoolP384r1 {
+    type FieldElement = FieldElement;
+}
+
 impl PrimeCurveArithmetic for BrainpoolP384r1 {
     type CurveGroup = ProjectivePoint;
 }
 
 impl PrimeCurveParams for BrainpoolP384r1 {
-    type FieldElement = FieldElement;
     type PointArithmetic = point_arithmetic::EquationAIsGeneric;
     type Backend = backend::VariableOnly;
 

bp384/src/r1/arithmetic.rs

@@ -2,7 +2,7 @@
 
 use super::BrainpoolP384t1;
 use crate::{FieldElement, Scalar};
-use elliptic_curve::{CurveArithmetic, PrimeCurveArithmetic};
+use elliptic_curve::{CurveArithmetic, PrimeCurveArithmetic, hazmat::FieldArithmetic};
 use primeorder::{PrimeCurveParams, backend, point_arithmetic};
 
 /// Elliptic curve point in affine coordinates.
@@ -23,12 +23,15 @@ impl CurveArithmetic for BrainpoolP384t1 {
     type Scalar = Scalar;
 }
 
+impl FieldArithmetic for BrainpoolP384t1 {
+    type FieldElement = FieldElement;
+}
+
 impl PrimeCurveArithmetic for BrainpoolP384t1 {
     type CurveGroup = ProjectivePoint;
 }
 
 impl PrimeCurveParams for BrainpoolP384t1 {
-    type FieldElement = FieldElement;
     type PointArithmetic = point_arithmetic::EquationAIsGeneric;
     type Backend = backend::VariableOnly;
 

bp384/src/t1/arithmetic.rs

@@ -17,14 +17,18 @@ pub use field::FieldElement;
 
 use self::{affine::AffinePoint, projective::ProjectivePoint, scalar::Scalar};
 use crate::Secp256k1;
-use elliptic_curve::CurveArithmetic;
+use elliptic_curve::{CurveArithmetic, hazmat::FieldArithmetic};
 
 impl CurveArithmetic for Secp256k1 {
     type AffinePoint = AffinePoint;
     type ProjectivePoint = ProjectivePoint;
     type Scalar = Scalar;
 }
 
+impl FieldArithmetic for Secp256k1 {
+    type FieldElement = FieldElement;
+}
+
 const CURVE_EQUATION_B_SINGLE: u32 = 7u32;
 
 #[rustfmt::skip]

k256/src/arithmetic.rs

@@ -42,6 +42,14 @@ use num_bigint::{BigUint, ToBigUint};
 const MODULUS_HEX: &str = "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f";
 
 /// An element in the finite field used for curve coordinates.
+///
+/// <div class="warning">
+/// <b>Security Warning</b>
+///
+/// This type implements lazy normalization. Failure to use it correctly can lead to miscomputation!
+/// Please be extremely sure you understand how this normalization works before you do ANYTHING
+/// with this type.
+/// </div>
 #[derive(Clone, Copy, Debug)]
 pub struct FieldElement(FieldElementImpl);