Trait AffineCurve

pub trait AffineCurve:
    Sized
    + CanonicalSerialize
    + CanonicalDeserialize
    + Copy
    + Clone
    + Debug
    + Display
    + Default
    + FromBytes
    + Send
    + Sync
    + 'static
    + Eq
    + Hash
    + Neg<Output = Self>
    + Uniform
    + PartialEq<Self::Projective>
    + Mul<Self::ScalarField, Output = Self::Projective>
    + Serialize
    + DeserializeOwned
    + ToBytes
    + From<Self::Projective>
    + Zero {
    type Projective: ProjectiveCurve<Affine = Self, ScalarField = Self::ScalarField> + From<Self> + Into<Self>;
    type BaseField: Field + SquareRootField;
    type ScalarField: PrimeField + SquareRootField + Into<<Self::ScalarField as PrimeField>::BigInteger>;
    type Coordinates;

    // Required methods
    fn from_coordinates(coordinates: Self::Coordinates) -> Option<Self>;
    fn from_coordinates_unchecked(coordinates: Self::Coordinates) -> Self;
    fn cofactor() -> &'static [u64];
    fn prime_subgroup_generator() -> Self;
    fn from_x_coordinate(x: Self::BaseField, greatest: bool) -> Option<Self>;
    fn pair_from_x_coordinate(x: Self::BaseField) -> Option<(Self, Self)>;
    fn from_y_coordinate(y: Self::BaseField, greatest: bool) -> Option<Self>;
    fn mul_by_cofactor_to_projective(&self) -> Self::Projective;
    fn to_projective(&self) -> Self::Projective;
    fn from_random_bytes(bytes: &[u8]) -> Option<Self>;
    fn mul_bits(&self, bits: impl Iterator<Item = bool>) -> Self::Projective;
    fn mul_by_cofactor_inv(&self) -> Self;
    fn is_in_correct_subgroup_assuming_on_curve(&self) -> bool;
    fn to_x_coordinate(&self) -> Self::BaseField;
    fn to_y_coordinate(&self) -> Self::BaseField;
    fn is_on_curve(&self) -> bool;
    fn batch_add_loop_1(
        a: &mut Self,
        b: &mut Self,
        half: &Self::BaseField,
        inversion_tmp: &mut Self::BaseField,
    );
    fn batch_add_loop_2(
        a: &mut Self,
        b: Self,
        inversion_tmp: &mut Self::BaseField,
    );

    // Provided method
    fn mul_by_cofactor(&self) -> Self { ... }
}

Affine representation of an elliptic curve point guaranteed to be in the correct prime order subgroup.

Required Associated Types

type Projective: ProjectiveCurve<Affine = Self, ScalarField = Self::ScalarField> + From<Self> + Into<Self>

type BaseField: Field + SquareRootField

type ScalarField: PrimeField + SquareRootField + Into<<Self::ScalarField as PrimeField>::BigInteger>

type Coordinates

Required Methods

fn from_coordinates(coordinates: Self::Coordinates) -> Option<Self>

Initializes a new affine group element from the given coordinates.

fn from_coordinates_unchecked(coordinates: Self::Coordinates) -> Self

Initializes a new affine group element from the given coordinates. Note: The resulting point is not enforced to be on the curve or in the correct subgroup.

fn cofactor() -> &'static [u64]

Returns the cofactor of the curve.

fn prime_subgroup_generator() -> Self

Returns a fixed generator of unknown exponent.

fn from_x_coordinate(x: Self::BaseField, greatest: bool) -> Option<Self>

Attempts to construct an affine point given an x-coordinate. The point is not guaranteed to be in the prime order subgroup.

If and only if greatest is set will the lexicographically largest y-coordinate be selected.

fn pair_from_x_coordinate(x: Self::BaseField) -> Option<(Self, Self)>

Attempts to construct both possible affine points given an x-coordinate. Points are not guaranteed to be in the prime order subgroup.

The affine points returned should be in lexicographically growing order.

Calling this should be equivalent (but likely more performant) to (AffineCurve::from_x_coordinate(x, false), AffineCurve::from_x_coordinate(x, true)).

fn from_y_coordinate(y: Self::BaseField, greatest: bool) -> Option<Self>

Attempts to construct an affine point given a y-coordinate. The point is not guaranteed to be in the prime order subgroup.

If and only if greatest is set will the lexicographically largest y-coordinate be selected.

fn mul_by_cofactor_to_projective(&self) -> Self::Projective

Multiply this element by the cofactor and output the resulting projective element.

fn to_projective(&self) -> Self::Projective

Converts this element into its projective representation.

fn from_random_bytes(bytes: &[u8]) -> Option<Self>

Returns a group element if the set of bytes forms a valid group element, otherwise returns None. This function is primarily intended for sampling random group elements from a hash-function or RNG output.

fn mul_bits(&self, bits: impl Iterator<Item = bool>) -> Self::Projective

Multiply this element by a big-endian boolean representation of an integer.

fn mul_by_cofactor_inv(&self) -> Self

Multiply this element by the inverse of the cofactor modulo the size of Self::ScalarField.

fn is_in_correct_subgroup_assuming_on_curve(&self) -> bool

Checks that the point is in the prime order subgroup given the point on the curve.

fn to_x_coordinate(&self) -> Self::BaseField

Returns the x-coordinate of the point.

fn to_y_coordinate(&self) -> Self::BaseField

Returns the y-coordinate of the point.

fn is_on_curve(&self) -> bool

Checks that the current point is on the elliptic curve.

fn batch_add_loop_1( a: &mut Self, b: &mut Self, half: &Self::BaseField, inversion_tmp: &mut Self::BaseField, )

Performs the first half of batch addition in-place.

fn batch_add_loop_2(a: &mut Self, b: Self, inversion_tmp: &mut Self::BaseField)

Performs the second half of batch addition in-place.

Provided Methods

fn mul_by_cofactor(&self) -> Self

Multiply this element by the cofactor.

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.

Implementors

impl<P> AffineCurve for snarkvm_curves::templates::short_weierstrass_jacobian::affine::Affine<P>

where P: ShortWeierstrassParameters,

type BaseField = <P as ModelParameters>::BaseField

type Coordinates = (<Affine<P> as AffineCurve>::BaseField, <Affine<P> as AffineCurve>::BaseField, bool)

type Projective = Projective<P>

type ScalarField = <P as ModelParameters>::ScalarField

impl<P> AffineCurve for snarkvm_curves::templates::twisted_edwards_extended::affine::Affine<P>

where P: TwistedEdwardsParameters,

type BaseField = <P as ModelParameters>::BaseField

type Coordinates = (<Affine<P> as AffineCurve>::BaseField, <Affine<P> as AffineCurve>::BaseField)

type Projective = Projective<P>

type ScalarField = <P as ModelParameters>::ScalarField