Struct ark_ec::models::twisted_edwards::Projective

pub struct Projective<P: TECurveConfig> {
    pub x: P::BaseField,
    pub y: P::BaseField,
    pub t: P::BaseField,
    pub z: P::BaseField,
}

Projective implements Extended Twisted Edwards Coordinates as described in [HKCD08].

This implementation uses the unified addition formulae from that paper (see Section 3.1).

Fields

x: P::BaseField

y: P::BaseField

t: P::BaseField

z: P::BaseField

Implementations

impl<P: TECurveConfig> Projective<P>

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

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

Trait Implementations

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

type Output = Projective<P>

The resulting type after applying the + operator.

fn add(self, other: &'a Self) -> Self

Performs the + operation.

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

type Output = Projective<P>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Projective<P>

The resulting type after applying the + operator.

fn add(self, other: &'a mut Self) -> Self

Performs the + operation.

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

type Output = Projective<P>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Projective<P>

The resulting type after applying the + operator.

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

Performs the + operation.

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

fn add_assign(&mut self, other: &'a Self)

Performs the += operation.

impl<'a, P: TECurveConfig> AddAssign<&'a mut Projective<P>> for Projective<P>

fn add_assign(&mut self, other: &'a mut Self)

Performs the += operation.

impl<P: TECurveConfig> AddAssign<Projective<P>> for Projective<P>

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl<P: TECurveConfig, T: Borrow<Affine<P>>> AddAssign<T> for Projective<P>

fn add_assign(&mut self, other: T)

Performs the += operation.

impl<P: TECurveConfig> CanonicalDeserialize for Projective<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 Projective<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> Clone for Projective<P>where
    P: TECurveConfig,

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> CurveGroup for Projective<P>

type Config = P

type BaseField = <P as CurveConfig>::BaseField

The field over which this curve is defined.

type Affine = Affine<P>

The affine representation of this element.

type FullGroup = Affine<P>

Type representing an element of the full elliptic curve group, not just the prime order subgroup.

fn normalize_batch(v: &[Self]) -> Vec<Self::Affine>

Normalizes a slice of group elements into affine.

fn into_affine(self) -> Self::Affine

Converts self into the affine representation.

impl<P> Debug for Projective<P>where
    P: TECurveConfig,

fn fmt(&self, __f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

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

fn default() -> Self

Returns the “default value” for a type.

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

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

Formats the value using the given formatter.

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

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

type ScalarField = <P as CurveConfig>::ScalarField

The scalar field F_r, where r is the order of this group.

fn generator() -> Self

Returns a fixed generator of this group.

fn double_in_place(&mut self) -> &mut Self

Double self in place.

fn mul_bigint(&self, other: impl AsRef<[u64]>) -> Self

Performs scalar multiplication of this element.

fn double(&self) -> Self

Doubles self.

fn mul_bits_be(&self, other: impl Iterator<Item = bool>) -> Self

Computes other * self, where other is a big-endian bit representation of some integer.

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

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 Projective<P>

type Output = Projective<P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<P: TECurveConfig, T: Borrow<P::ScalarField>> MulAssign<T> for Projective<P>

fn mul_assign(&mut self, other: T)

Performs the *= operation.

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

type Output = Projective<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

This method tests for self and other values to be equal, and is used by ==.

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

This method 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

This method tests for self and other values to be equal, and is used by ==.

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

This method 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 Projective<P>

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

This method tests for self and other values to be equal, and is used by ==.

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

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

impl<P: TECurveConfig> ScalarMul for Projective<P>

type MulBase = Affine<P>

const NEGATION_IS_CHEAP: bool = true

fn batch_convert_to_mul_base(bases: &[Self]) -> Vec<Self::MulBase>

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

type Output = Projective<P>

The resulting type after applying the - operator.

fn sub(self, other: &'a Self) -> Self

Performs the - operation.

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

type Output = Projective<P>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Projective<P>

The resulting type after applying the - operator.

fn sub(self, other: &'a mut Self) -> Self

Performs the - operation.

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

type Output = Projective<P>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Projective<P>

The resulting type after applying the - operator.

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

Performs the - operation.

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

fn sub_assign(&mut self, other: &'a Self)

Performs the -= operation.

impl<'a, P: TECurveConfig> SubAssign<&'a mut Projective<P>> for Projective<P>

fn sub_assign(&mut self, other: &'a mut Self)

Performs the -= operation.

impl<P: TECurveConfig> SubAssign<Projective<P>> for Projective<P>

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

impl<P: TECurveConfig, T: Borrow<Affine<P>>> SubAssign<T> for Projective<P>

fn sub_assign(&mut self, other: T)

Performs the -= operation.

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

fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<P: TECurveConfig> Sum<Projective<P>> for Projective<P>

fn sum<I: Iterator<Item = Self>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<P: TECurveConfig, T: Borrow<Affine<P>>> Sum<T> for Projective<P>

fn sum<I>(iter: I) -> Selfwhere
    I: Iterator<Item = T>,

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<M: TECurveConfig, ConstraintF: Field> ToConstraintField<ConstraintF> for Projective<M>where
    M::BaseField: ToConstraintField<ConstraintF>,

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

impl<P: TECurveConfig> Valid for Projective<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> VariableBaseMSM for Projective<P>

fn msm(
    bases: &[Self::MulBase],
    bigints: &[Self::ScalarField]
) -> Result<Self, usize>

Performs multi-scalar multiplication, without checking that bases.len() == scalars.len().

fn msm_unchecked(bases: &[Self::MulBase], scalars: &[Self::ScalarField]) -> Self

Computes an inner product between the PrimeField elements in scalars and the corresponding group elements in bases.

fn msm_bigint(
    bases: &[Self::MulBase],
    bigints: &[<Self::ScalarField as PrimeField>::BigInt]
) -> Self

Optimized implementation of multi-scalar multiplication.

fn msm_chunks<I, J>(bases_stream: &J, scalars_stream: &I) -> Selfwhere
    I: Iterable + ?Sized,
    I::Item: Borrow<Self::ScalarField>,
    J: Iterable,
    J::Item: Borrow<Self::MulBase>,

Streaming multi-scalar multiplication algorithm with hard-coded chunk size.

impl<P: TECurveConfig> Zero for Projective<P>

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl<P: TECurveConfig> Zeroize for Projective<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> Copy for Projective<P>where
    P: TECurveConfig,

impl<P> Eq for Projective<P>where
    P: TECurveConfig,