Trait CurveAffine

pub trait CurveAffine:
    PrimeCurveAffine<Scalar = Self::ScalarExt, Curve = Self::CurveExt>
    + Default
    + Add<Output = Self::Curve>
    + Sub<Output = Self::Curve>
    + ConditionallySelectable
    + ConstantTimeEq
    + From<Self::Curve> {
    type ScalarExt: WithSmallOrderMulGroup<3> + Ord;
    type Base: WithSmallOrderMulGroup<3> + Ord;
    type CurveExt: CurveExt<AffineExt = Self, ScalarExt = Self::ScalarExt>;

    // Required methods
    fn coordinates(&self) -> CtOption<Coordinates<Self>>;
    fn from_xy(x: Self::Base, y: Self::Base) -> CtOption<Self>;
    fn is_on_curve(&self) -> Choice;
    fn a() -> Self::Base;
    fn b() -> Self::Base;
}

This trait is the affine counterpart to Curve and is used for serialization, storage in memory, and inspection of $x$ and $y$ coordinates.

Requires the alloc feature flag because of hash_to_curve on CurveExt.

Required Associated Types

type ScalarExt: WithSmallOrderMulGroup<3> + Ord

The scalar field of this elliptic curve.

type Base: WithSmallOrderMulGroup<3> + Ord

The base field over which this elliptic curve is constructed.

type CurveExt: CurveExt<AffineExt = Self, ScalarExt = Self::ScalarExt>

The projective form of the curve

Required Methods

fn coordinates(&self) -> CtOption<Coordinates<Self>>

Gets the coordinates of this point.

Returns None if this is the identity.

fn from_xy(x: Self::Base, y: Self::Base) -> CtOption<Self>

Obtains a point given $(x, y)$, failing if it is not on the curve.

fn is_on_curve(&self) -> Choice

Returns whether or not this element is on the curve; should always be true unless an “unchecked” API was used.

fn a() -> Self::Base

Returns the curve constant $a$.

fn b() -> Self::Base

Returns the curve constant $b$.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types

impl CurveAffine for G1Affine

type ScalarExt = Scalar

The scalar field of this elliptic curve.

type Base = Fp

The base field over which this elliptic curve is constructed.

type CurveExt = G1Projective

The projective form of the curve

fn coordinates(&self) -> CtOption<Coordinates<G1Affine>>

Gets the coordinates of this point.

Returns None if this is the identity.

fn from_xy( x: <G1Affine as CurveAffine>::Base, y: <G1Affine as CurveAffine>::Base, ) -> CtOption<G1Affine>

Obtains a point given $(x, y)$, failing if it is not on the curve.

fn is_on_curve(&self) -> Choice

Returns whether or not this element is on the curve; should always be true unless an “unchecked” API was used.

fn a() -> <G1Affine as CurveAffine>::Base

Returns the curve constant $a$.

fn b() -> <G1Affine as CurveAffine>::Base

Returns the curve constant $b$.

impl CurveAffine for G2Affine

type ScalarExt = Scalar

The scalar field of this elliptic curve.

type Base = Fp2

The base field over which this elliptic curve is constructed.

type CurveExt = G2Projective

The projective form of the curve

fn coordinates(&self) -> CtOption<Coordinates<G2Affine>>

Gets the coordinates of this point.

Returns None if this is the identity.

fn from_xy( x: <G2Affine as CurveAffine>::Base, y: <G2Affine as CurveAffine>::Base, ) -> CtOption<G2Affine>

Obtains a point given $(x, y)$, failing if it is not on the curve.

fn is_on_curve(&self) -> Choice

Returns whether or not this element is on the curve; should always be true unless an “unchecked” API was used.

fn a() -> <G2Affine as CurveAffine>::Base

Returns the curve constant $a$.

fn b() -> <G2Affine as CurveAffine>::Base

Returns the curve constant $b$.

impl CurveAffine for G1Affine

type ScalarExt = Fr

type Base = Fq

type CurveExt = G1

fn is_on_curve(&self) -> Choice

fn coordinates(&self) -> CtOption<Coordinates<G1Affine>>

fn from_xy( x: <G1Affine as CurveAffine>::Base, y: <G1Affine as CurveAffine>::Base, ) -> CtOption<G1Affine>

fn a() -> <G1Affine as CurveAffine>::Base

fn b() -> <G1Affine as CurveAffine>::Base

impl CurveAffine for G2Affine

type ScalarExt = Fr

type Base = Fq2

type CurveExt = G2

fn is_on_curve(&self) -> Choice

fn coordinates(&self) -> CtOption<Coordinates<G2Affine>>

fn from_xy( x: <G2Affine as CurveAffine>::Base, y: <G2Affine as CurveAffine>::Base, ) -> CtOption<G2Affine>

fn a() -> <G2Affine as CurveAffine>::Base

fn b() -> <G2Affine as CurveAffine>::Base

impl CurveAffine for Ed25519Affine

type ScalarExt = Fr

type Base = Fq

type CurveExt = Ed25519

fn is_on_curve(&self) -> Choice

fn coordinates(&self) -> CtOption<Coordinates<Ed25519Affine>>

fn from_xy( x: <Ed25519Affine as CurveAffine>::Base, y: <Ed25519Affine as CurveAffine>::Base, ) -> CtOption<Ed25519Affine>

fn a() -> <Ed25519Affine as CurveAffine>::Base

fn b() -> <Ed25519Affine as CurveAffine>::Base

impl CurveAffine for G1Affine

type ScalarExt = Fq

type Base = Fr

type CurveExt = G1

fn is_on_curve(&self) -> Choice

fn coordinates(&self) -> CtOption<Coordinates<G1Affine>>

fn from_xy( x: <G1Affine as CurveAffine>::Base, y: <G1Affine as CurveAffine>::Base, ) -> CtOption<G1Affine>

fn a() -> <G1Affine as CurveAffine>::Base

fn b() -> <G1Affine as CurveAffine>::Base

impl CurveAffine for ErisAffine

type ScalarExt = Fp

type Base = Fq

type CurveExt = Eris

fn is_on_curve(&self) -> Choice

fn coordinates(&self) -> CtOption<Coordinates<ErisAffine>>

fn from_xy( x: <ErisAffine as CurveAffine>::Base, y: <ErisAffine as CurveAffine>::Base, ) -> CtOption<ErisAffine>

fn a() -> <ErisAffine as CurveAffine>::Base

fn b() -> <ErisAffine as CurveAffine>::Base

impl CurveAffine for G1Affine

type ScalarExt = Fq

type Base = Fp

type CurveExt = G1

fn is_on_curve(&self) -> Choice

fn coordinates(&self) -> CtOption<Coordinates<G1Affine>>

fn from_xy( x: <G1Affine as CurveAffine>::Base, y: <G1Affine as CurveAffine>::Base, ) -> CtOption<G1Affine>

fn a() -> <G1Affine as CurveAffine>::Base

fn b() -> <G1Affine as CurveAffine>::Base

impl CurveAffine for G2Affine

type ScalarExt = Fq

type Base = Fp2

type CurveExt = G2

fn is_on_curve(&self) -> Choice

fn coordinates(&self) -> CtOption<Coordinates<G2Affine>>

fn from_xy( x: <G2Affine as CurveAffine>::Base, y: <G2Affine as CurveAffine>::Base, ) -> CtOption<G2Affine>

fn a() -> <G2Affine as CurveAffine>::Base

fn b() -> <G2Affine as CurveAffine>::Base

impl CurveAffine for Secp256k1Affine

type ScalarExt = Fq

type Base = Fp

type CurveExt = Secp256k1

fn is_on_curve(&self) -> Choice

fn coordinates(&self) -> CtOption<Coordinates<Secp256k1Affine>>

fn from_xy( x: <Secp256k1Affine as CurveAffine>::Base, y: <Secp256k1Affine as CurveAffine>::Base, ) -> CtOption<Secp256k1Affine>

fn a() -> <Secp256k1Affine as CurveAffine>::Base

fn b() -> <Secp256k1Affine as CurveAffine>::Base

impl CurveAffine for Secp256r1Affine

type ScalarExt = Fq

type Base = Fp

type CurveExt = Secp256r1

fn is_on_curve(&self) -> Choice

fn coordinates(&self) -> CtOption<Coordinates<Secp256r1Affine>>

fn from_xy( x: <Secp256r1Affine as CurveAffine>::Base, y: <Secp256r1Affine as CurveAffine>::Base, ) -> CtOption<Secp256r1Affine>

fn a() -> <Secp256r1Affine as CurveAffine>::Base

fn b() -> <Secp256r1Affine as CurveAffine>::Base

impl CurveAffine for Secq256k1Affine

type ScalarExt = Fp

type Base = Fq

type CurveExt = Secq256k1

fn is_on_curve(&self) -> Choice

fn coordinates(&self) -> CtOption<Coordinates<Secq256k1Affine>>

fn from_xy( x: <Secq256k1Affine as CurveAffine>::Base, y: <Secq256k1Affine as CurveAffine>::Base, ) -> CtOption<Secq256k1Affine>

fn a() -> <Secq256k1Affine as CurveAffine>::Base

fn b() -> <Secq256k1Affine as CurveAffine>::Base

Implementors

impl CurveAffine for EpAffine

type ScalarExt = Fq

type Base = Fp

type CurveExt = Ep

impl CurveAffine for EqAffine

type ScalarExt = Fp

type Base = Fq

type CurveExt = Eq