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Refactor identity methods into Identity trait #42

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Refactor identity methods into Identity trait #42

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42f58a0
Refactor identity methods into `Identity` trait
daxpedda Dec 20, 2022
9b570d4
Use an associated constant instead of `identity()`
daxpedda Dec 20, 2022
73d7bdf
Address review
daxpedda Aug 8, 2023
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9 changes: 2 additions & 7 deletions src/cofactor.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -3,6 +3,7 @@ use core::ops::{Mul, Neg};
use ff::PrimeField;
use subtle::{Choice, CtOption};

use crate::Identity;
use crate::{prime::PrimeGroup, Curve, Group, GroupEncoding, GroupOps, GroupOpsOwned};

/// This trait represents an element of a cryptographic group with a large prime-order
Expand Down Expand Up @@ -66,6 +67,7 @@ pub trait CofactorCurve:
/// in the correct prime order subgroup.
pub trait CofactorCurveAffine:
GroupEncoding
+ Identity
+ Copy
+ Clone
+ Sized
Expand All @@ -85,16 +87,9 @@ pub trait CofactorCurveAffine:
type Scalar: PrimeField;
type Curve: CofactorCurve<Affine = Self, Scalar = Self::Scalar>;

/// Returns the additive identity.
fn identity() -> Self;

/// Returns a fixed generator of unknown exponent.
fn generator() -> Self;

/// Determines if this point represents the point at infinity; the
/// additive identity.
fn is_identity(&self) -> Choice;

/// Converts this element to its curve representation.
fn to_curve(&self) -> Self::Curve;
}
19 changes: 12 additions & 7 deletions src/lib.rs
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Expand Up @@ -53,7 +53,8 @@ impl<T, Rhs, Output> ScalarMulOwned<Rhs, Output> for T where T: for<'r> ScalarMu

/// This trait represents an element of a cryptographic group.
pub trait Group:
Clone
Identity
+ Clone
+ Copy
+ fmt::Debug
+ Eq
Expand All @@ -78,15 +79,9 @@ pub trait Group:
/// This function is non-deterministic, and samples from the user-provided RNG.
fn random(rng: impl RngCore) -> Self;

/// Returns the additive identity, also known as the "neutral element".
fn identity() -> Self;

/// Returns a fixed generator of the prime-order subgroup.
fn generator() -> Self;

/// Determines if this point is the identity.
fn is_identity(&self) -> Choice;

/// Doubles this element.
#[must_use]
fn double(&self) -> Self;
Expand Down Expand Up @@ -172,3 +167,13 @@ pub trait UncompressedEncoding: Sized {
/// the point at infinity.
fn to_uncompressed(&self) -> Self::Uncompressed;
}

/// Obtain or determine the identity point.

@str4d str4d Jul 29, 2023

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Same issue ("point" instead of "element").

I don't know how to describe this trait, which is concerning. It's not an extension trait because it's being added as a required bound. But the constant and method it defines do not make sense in a vacuum; they need to be in the context of a group.

This makes me question the premise of the PR: what is the motivating use case for generalising over both the affine and efficient forms of a curve point, such that a shared trait is needed?

@daxpedda daxpedda Aug 8, 2023

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Apologies for the delay.

The original motivation was RustCrypto/traits#1170. We currently use Default to obtain the identity element, which isn't ideal and doesn't support const.

Unfortunately this was a long time ago and I don't have all the details in my head anymore, but I assume these sort of requirements will keep popping up in elliptic-curve because of it's nature: it introduces types that are generic over many different things, so it requires traits that are equally generic to support this idea.

Maybe @tarcieri has more to say on this topic.

@tarcieri tarcieri Aug 8, 2023

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I can't think of a use case for such a generalization

pub trait Identity: Sized {
/// Returns the additive identity.
const IDENTITY: Self;

/// Determines if this point represents the point at infinity; the
/// additive identity.
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fn is_identity(&self) -> Choice;
}
11 changes: 2 additions & 9 deletions src/prime.rs
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@@ -1,9 +1,8 @@
use core::fmt;
use core::ops::{Mul, Neg};
use ff::PrimeField;
use subtle::Choice;

use crate::{Curve, Group, GroupEncoding};
use crate::{Curve, Group, GroupEncoding, Identity};

/// This trait represents an element of a prime-order cryptographic group.
pub trait PrimeGroup: Group + GroupEncoding {}
Expand All @@ -19,6 +18,7 @@ pub trait PrimeCurve: Curve<AffineRepr = <Self as PrimeCurve>::Affine> + PrimeGr
/// Affine representation of an elliptic curve point guaranteed to be
/// in the correct prime order subgroup.
pub trait PrimeCurveAffine: GroupEncoding
+ Identity
+ Copy
+ Clone
+ Sized
Expand All @@ -35,16 +35,9 @@ pub trait PrimeCurveAffine: GroupEncoding
type Scalar: PrimeField;
type Curve: PrimeCurve<Affine = Self, Scalar = Self::Scalar>;

/// Returns the additive identity.
fn identity() -> Self;

/// Returns a fixed generator of unknown exponent.
fn generator() -> Self;

/// Determines if this point represents the point at infinity; the
/// additive identity.
fn is_identity(&self) -> Choice;

/// Converts this element to its curve representation.
fn to_curve(&self) -> Self::Curve;
}
2 changes: 1 addition & 1 deletion src/tests/mod.rs
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Expand Up @@ -7,7 +7,7 @@ use rand_xorshift::XorShiftRng;
use crate::{
prime::{PrimeCurve, PrimeCurveAffine},
wnaf::WnafGroup,
GroupEncoding, UncompressedEncoding,
GroupEncoding, Identity, UncompressedEncoding,
};

pub fn curve_tests<G: PrimeCurve>() {
Expand Down