Struct Affine

pub struct Affine<P: TECurveConfig> {
    pub x: P::BaseField,
    pub y: P::BaseField,
}

Affine coordinates for a point on a twisted Edwards curve, over the base field P::BaseField.

Fields

x: P::BaseField

X coordinate of the point represented as a field element

y: P::BaseField

Y coordinate of the point represented as a field element

Implementations

impl<P: TECurveConfig> Affine<P>

pub const fn new_unchecked(x: P::BaseField, y: P::BaseField) -> Self

Construct a new group element without checking whether the coordinates specify a point in the subgroup.

pub fn new(x: P::BaseField, y: P::BaseField) -> Self

Construct a new group element in a way while enforcing that points are in the prime-order subgroup.

pub const fn zero() -> Self

Construct the identity of the group

pub fn is_zero(&self) -> bool

Is this point the identity?

pub fn get_point_from_y_unchecked( y: P::BaseField, greatest: bool, ) -> Option<Self>

Attempts to construct an affine point given an 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 x-coordinate be selected.

a * X^2 + Y^2 = 1 + d * X^2 * Y^2 a * X^2 - d * X^2 * Y^2 = 1 - Y^2 X^2 * (a - d * Y^2) = 1 - Y^2 X^2 = (1 - Y^2) / (a - d * Y^2)

pub fn get_xs_from_y_unchecked( y: P::BaseField, ) -> Option<(P::BaseField, P::BaseField)>

Attempts to recover the x-coordinate given an y-coordinate. The resulting point is not guaranteed to be in the prime order subgroup.

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

a * X^2 + Y^2 = 1 + d * X^2 * Y^2 a * X^2 - d * X^2 * Y^2 = 1 - Y^2 X^2 * (a - d * Y^2) = 1 - Y^2 X^2 = (1 - Y^2) / (a - d * Y^2)

pub fn is_on_curve(&self) -> bool

Checks that the current point is on the elliptic curve.

impl<P: TECurveConfig> Affine<P>

pub fn is_in_correct_subgroup_assuming_on_curve(&self) -> bool

Checks if self is in the subgroup having order equaling that of P::ScalarField given it is on the curve.

Trait Implementations

impl<'a, P: TECurveConfig> Add<&'a Projective<P>> for Affine<P>

type Output = Projective<P>

The resulting type after applying the + operator.

fn add(self, other: &'a Projective<P>) -> Projective<P>

Performs the + operation.

impl<P: TECurveConfig> Add<Projective<P>> for Affine<P>

type Output = Projective<P>

The resulting type after applying the + operator.

fn add(self, other: Projective<P>) -> Projective<P>

Performs the + operation.

impl<P: TECurveConfig, T: Borrow<Self>> Add<T> for Affine<P>

type Output = Projective<P>

The resulting type after applying the + operator.

fn add(self, other: T) -> Self::Output

Performs the + operation.

impl<P: TECurveConfig> AffineRepr for Affine<P>

fn mul_by_cofactor_to_group(&self) -> Self::Group

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

fn clear_cofactor(&self) -> Self

Performs cofactor clearing. The default method is simply to multiply by the cofactor. Some curves can implement a more efficient algorithm.

type Config = P

type BaseField = <P as CurveConfig>::BaseField

The finite field over which this curve is defined.

type ScalarField = <P as CurveConfig>::ScalarField

type Group = Projective<P>

The projective representation of points on this curve.

fn xy(&self) -> Option<(Self::BaseField, Self::BaseField)>

Returns the x and y coordinates of this affine point.

fn generator() -> Self

Returns a fixed generator of unknown exponent.

fn zero() -> Self

Returns the point at infinity.

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_bigint(&self, by: impl AsRef<[u64]>) -> Self::Group

Performs scalar multiplication of this element with mixed addition.

fn x(&self) -> Option<Self::BaseField>

Returns the x coordinate of this affine point.

fn y(&self) -> Option<Self::BaseField>

Returns the y coordinate of this affine point.

fn is_zero(&self) -> bool

Is self the point at infinity?

fn into_group(self) -> Self::Group

Converts self into the projective representation.

fn mul_by_cofactor(&self) -> Self

Multiplies this element by the cofactor.

fn mul_by_cofactor_inv(&self) -> Self

Multiplies this element by the inverse of the cofactor in Self::ScalarField.

impl<P: TECurveConfig> CanonicalDeserialize for Affine<P>

fn deserialize_with_mode<R: Read>( reader: R, compress: Compress, validate: Validate, ) -> Result<Self, SerializationError>

The general deserialize method that takes in customization flags.

fn deserialize_compressed<R>(reader: R) -> Result<Self, SerializationError>

where R: Read,

fn deserialize_compressed_unchecked<R>( reader: R, ) -> Result<Self, SerializationError>

where R: Read,

fn deserialize_uncompressed<R>(reader: R) -> Result<Self, SerializationError>

where R: Read,

fn deserialize_uncompressed_unchecked<R>( reader: R, ) -> Result<Self, SerializationError>

where R: Read,

impl<P: TECurveConfig> CanonicalSerialize for Affine<P>

fn serialize_with_mode<W: Write>( &self, writer: W, compress: Compress, ) -> Result<(), SerializationError>

The general serialize method that takes in customization flags.

fn serialized_size(&self, compress: Compress) -> usize

fn serialize_compressed<W>(&self, writer: W) -> Result<(), SerializationError>

where W: Write,

fn compressed_size(&self) -> usize

fn serialize_uncompressed<W>(&self, writer: W) -> Result<(), SerializationError>

where W: Write,

fn uncompressed_size(&self) -> usize

impl<P: TECurveConfig> Clone for Affine<P>

where P::BaseField: Copy,

fn clone(&self) -> Self

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<P: TECurveConfig> Debug for Affine<P>

fn fmt(&self, f: &mut Formatter<'_>) -> FmtResult

Formats the value using the given formatter.

impl<P: TECurveConfig> Default for Affine<P>

fn default() -> Self

Returns the “default value” for a type.

impl<P: TECurveConfig> Display for Affine<P>

fn fmt(&self, f: &mut Formatter<'_>) -> FmtResult

Formats the value using the given formatter.

impl<P: TECurveConfig> Distribution<Affine<P>> for Standard

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Affine<P>

Generates a uniformly random instance of the curve.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<P: TECurveConfig> From<Affine<P>> for Projective<P>

fn from(p: Affine<P>) -> Projective<P>

Converts to this type from the input type.

impl<P: TECurveConfig> From<Projective<P>> for Affine<P>

fn from(p: Projective<P>) -> Affine<P>

Converts to this type from the input type.

impl<P: TECurveConfig> Hash for Affine<P>

where P::BaseField: Hash,

fn hash<H: Hasher>(&self, state: &mut H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<P: TECurveConfig, T: Borrow<P::ScalarField>> Mul<T> for Affine<P>

type Output = Projective<P>

The resulting type after applying the * operator.

fn mul(self, other: T) -> Self::Output

Performs the * operation.

impl<P: TECurveConfig> Neg for Affine<P>

type Output = Affine<P>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<P: TECurveConfig> PartialEq<Affine<P>> for Projective<P>

fn eq(&self, other: &Affine<P>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<P: TECurveConfig> PartialEq<Projective<P>> for Affine<P>

fn eq(&self, other: &Projective<P>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<P: TECurveConfig> PartialEq for Affine<P>

where P::BaseField: PartialEq,

fn eq(&self, other: &Self) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<'a, P: TECurveConfig> Sub<&'a Projective<P>> for Affine<P>

type Output = Projective<P>

The resulting type after applying the - operator.

fn sub(self, other: &'a Projective<P>) -> Projective<P>

Performs the - operation.

impl<P: TECurveConfig> Sub<Projective<P>> for Affine<P>

type Output = Projective<P>

The resulting type after applying the - operator.

fn sub(self, other: Projective<P>) -> Projective<P>

Performs the - operation.

impl<P: TECurveConfig, T: Borrow<Self>> Sub<T> for Affine<P>

type Output = Projective<P>

The resulting type after applying the - operator.

fn sub(self, other: T) -> Self::Output

Performs the - operation.

impl<M: TECurveConfig, ConstraintF: Field> ToConstraintField<ConstraintF> for Affine<M>

where M::BaseField: ToConstraintField<ConstraintF>,

fn to_field_elements(&self) -> Option<Vec<ConstraintF>>

impl<P: TECurveConfig> Valid for Affine<P>

fn check(&self) -> Result<(), SerializationError>

fn batch_check<'a>( batch: impl Iterator<Item = &'a Self> + Send, ) -> Result<(), SerializationError>

where Self: 'a,

impl<P: TECurveConfig> Zeroize for Affine<P>

fn zeroize(&mut self)

Zero out this object from memory using Rust intrinsics which ensure the zeroization operation is not “optimized away” by the compiler.

impl<P: TECurveConfig> Copy for Affine<P>

where P::BaseField: Copy,

impl<P: TECurveConfig> Eq for Affine<P>

where P::BaseField: PartialEq,