Struct Projective

pub struct Projective<P>
where
    P: SWCurveConfig,
{
    pub x: <P as CurveConfig>::BaseField,
    pub y: <P as CurveConfig>::BaseField,
    pub z: <P as CurveConfig>::BaseField,
}

Jacobian coordinates for a point on an elliptic curve in short Weierstrass form, over the base field P::BaseField. This struct implements arithmetic via the Jacobian formulae

Fields

x: <P as CurveConfig>::BaseField

X / Z projection of the affine X

y: <P as CurveConfig>::BaseField

Y / Z projection of the affine Y

z: <P as CurveConfig>::BaseField

Projective multiplicative inverse. Will be 0 only at infinity.

Implementations

impl<P> Projective<P>

where P: SWCurveConfig,

pub const fn new_unchecked( x: <P as CurveConfig>::BaseField, y: <P as CurveConfig>::BaseField, z: <P as CurveConfig>::BaseField, ) -> Projective<P>

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

pub fn new( x: <P as CurveConfig>::BaseField, y: <P as CurveConfig>::BaseField, z: <P as CurveConfig>::BaseField, ) -> Projective<P>

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

Trait Implementations

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

where P: SWCurveConfig,

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> Add<&'a Projective<P>> for Affine<P>

where P: SWCurveConfig,

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> Add<&'a Projective<P>> for Projective<P>

where P: SWCurveConfig,

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

where P: SWCurveConfig,

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> Add<&'a mut Projective<P>> for Projective<P>

where P: SWCurveConfig,

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<'b, P> Add<Projective<P>> for &'b Projective<P>

where P: SWCurveConfig,

type Output = Projective<P>

The resulting type after applying the + operator.

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

Performs the + operation.

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

where P: SWCurveConfig,

type Output = Projective<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<P, T> Add<T> for Projective<P>

where P: SWCurveConfig, T: Borrow<Affine<P>>,

type Output = Projective<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<P> Add for Projective<P>

where P: SWCurveConfig,

type Output = Projective<P>

The resulting type after applying the + operator.

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

Performs the + operation.

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

where P: SWCurveConfig,

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

Performs the += operation.

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

where P: SWCurveConfig,

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

Performs the += operation.

impl<P, T> AddAssign<T> for Projective<P>

where P: SWCurveConfig, T: Borrow<Affine<P>>,

fn add_assign(&mut self, other: T)

Using http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-madd-2007-bl

impl<P> AddAssign for Projective<P>

where P: SWCurveConfig,

fn add_assign(&mut self, other: Projective<P>)

Performs the += operation.

impl<P> AdditiveGroup for Projective<P>

where P: SWCurveConfig,

fn double_in_place(&mut self) -> &mut Projective<P>

Sets self = 2 * self. Note that Jacobian formulae are incomplete, and so doubling cannot be computed as self + self. Instead, this implementation uses the following specialized doubling formulae:

• P::A is zero
• P::A is not zero

const ZERO: Projective<P> = _

The additive identity of the field.

type Scalar = <P as CurveConfig>::ScalarField

fn double(&self) -> Self

Doubles self.

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

Negates self in place.

impl<P> CanonicalDeserialize for Projective<P>

where P: SWCurveConfig,

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

where R: Read,

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> CanonicalSerialize for Projective<P>

where P: SWCurveConfig,

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

where W: Write,

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: SWCurveConfig, <P as CurveConfig>::BaseField: Copy,

fn clone(&self) -> Projective<P>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<P> CurveGroup for Projective<P>

where P: SWCurveConfig,

fn normalize_batch( v: &[Projective<P>], ) -> Vec<<Projective<P> as CurveGroup>::Affine>

Normalizes a slice of projective elements so that conversion to affine is cheap.

In more detail, this method converts a curve point in Jacobian coordinates (x, y, z) into an equivalent representation (x/z^2, y/z^3, 1).

For N = v.len(), this costs 1 inversion + 6N field multiplications + N field squarings.

(Where batch inversion comprises 3N field multiplications + 1 inversion of these operations)

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 into_affine(self) -> Self::Affine

Converts self into the affine representation.

impl<P> Debug for Projective<P>

where P: SWCurveConfig,

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

Formats the value using the given formatter.

impl<P> Default for Projective<P>

where P: SWCurveConfig,

fn default() -> Projective<P>

Returns the “default value” for a type.

impl<P> Display for Projective<P>

where P: SWCurveConfig,

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

Formats the value using the given formatter.

impl<'a, P> From<&'a Projective<<P as BW6Config>::G1Config>> for G1Prepared<P>

where P: BW6Config,

fn from(q: &'a Projective<<P as BW6Config>::G1Config>) -> G1Prepared<P>

Converts to this type from the input type.

impl<'a, P> From<&'a Projective<<P as BW6Config>::G2Config>> for G2Prepared<P>

where P: BW6Config,

fn from(q: &'a Projective<<P as BW6Config>::G2Config>) -> G2Prepared<P>

Converts to this type from the input type.

impl<'a, P> From<&'a Projective<<P as Bls12Config>::G1Config>> for G1Prepared<P>

where P: Bls12Config,

fn from(q: &'a Projective<<P as Bls12Config>::G1Config>) -> G1Prepared<P>

Converts to this type from the input type.

impl<'a, P> From<&'a Projective<<P as Bls12Config>::G2Config>> for G2Prepared<P>

where P: Bls12Config,

fn from(q: &'a Projective<<P as Bls12Config>::G2Config>) -> G2Prepared<P>

Converts to this type from the input type.

impl<'a, P> From<&'a Projective<<P as BnConfig>::G1Config>> for G1Prepared<P>

where P: BnConfig,

fn from(q: &'a Projective<<P as BnConfig>::G1Config>) -> G1Prepared<P>

Converts to this type from the input type.

impl<'a, P> From<&'a Projective<<P as BnConfig>::G2Config>> for G2Prepared<P>

where P: BnConfig,

fn from(q: &'a Projective<<P as BnConfig>::G2Config>) -> G2Prepared<P>

Converts to this type from the input type.

impl<'a, P> From<&'a Projective<<P as MNT4Config>::G1Config>> for G1Prepared<P>

where P: MNT4Config,

fn from(g1: &'a Projective<<P as MNT4Config>::G1Config>) -> G1Prepared<P>

Converts to this type from the input type.

impl<'a, P> From<&'a Projective<<P as MNT4Config>::G2Config>> for G2Prepared<P>

where P: MNT4Config,

fn from(g2: &'a Projective<<P as MNT4Config>::G2Config>) -> G2Prepared<P>

Converts to this type from the input type.

impl<'a, P> From<&'a Projective<<P as MNT6Config>::G1Config>> for G1Prepared<P>

where P: MNT6Config,

fn from(g1: &'a Projective<<P as MNT6Config>::G1Config>) -> G1Prepared<P>

Converts to this type from the input type.

impl<'a, P> From<&'a Projective<<P as MNT6Config>::G2Config>> for G2Prepared<P>

where P: MNT6Config,

fn from(g2: &'a Projective<<P as MNT6Config>::G2Config>) -> G2Prepared<P>

Converts to this type from the input type.

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

where P: SWCurveConfig,

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

Converts to this type from the input type.

impl<P> From<Projective<<P as BW6Config>::G1Config>> for G1Prepared<P>

where P: BW6Config,

fn from(q: Projective<<P as BW6Config>::G1Config>) -> G1Prepared<P>

Converts to this type from the input type.

impl<P> From<Projective<<P as BW6Config>::G2Config>> for G2Prepared<P>

where P: BW6Config,

fn from(q: Projective<<P as BW6Config>::G2Config>) -> G2Prepared<P>

Converts to this type from the input type.

impl<P> From<Projective<<P as Bls12Config>::G1Config>> for G1Prepared<P>

where P: Bls12Config,

fn from(q: Projective<<P as Bls12Config>::G1Config>) -> G1Prepared<P>

Converts to this type from the input type.

impl<P> From<Projective<<P as Bls12Config>::G2Config>> for G2Prepared<P>

where P: Bls12Config,

fn from(q: Projective<<P as Bls12Config>::G2Config>) -> G2Prepared<P>

Converts to this type from the input type.

impl<P> From<Projective<<P as BnConfig>::G1Config>> for G1Prepared<P>

where P: BnConfig,

fn from(q: Projective<<P as BnConfig>::G1Config>) -> G1Prepared<P>

Converts to this type from the input type.

impl<P> From<Projective<<P as BnConfig>::G2Config>> for G2Prepared<P>

where P: BnConfig,

fn from(q: Projective<<P as BnConfig>::G2Config>) -> G2Prepared<P>

Converts to this type from the input type.

impl<P> From<Projective<<P as MNT4Config>::G1Config>> for G1Prepared<P>

where P: MNT4Config,

fn from(g1: Projective<<P as MNT4Config>::G1Config>) -> G1Prepared<P>

Converts to this type from the input type.

impl<P> From<Projective<<P as MNT4Config>::G2Config>> for G2Prepared<P>

where P: MNT4Config,

fn from(g2: Projective<<P as MNT4Config>::G2Config>) -> G2Prepared<P>

Converts to this type from the input type.

impl<P> From<Projective<<P as MNT6Config>::G1Config>> for G1Prepared<P>

where P: MNT6Config,

fn from(g1: Projective<<P as MNT6Config>::G1Config>) -> G1Prepared<P>

Converts to this type from the input type.

impl<P> From<Projective<<P as MNT6Config>::G2Config>> for G2Prepared<P>

where P: MNT6Config,

fn from(g2: Projective<<P as MNT6Config>::G2Config>) -> G2Prepared<P>

Converts to this type from the input type.

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

where P: SWCurveConfig,

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

Converts to this type from the input type.

impl<P> Hash for Projective<P>

where P: SWCurveConfig,

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

where H: Hasher,

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> MapToCurve<Projective<P>> for SWUMap<P>

where P: SWUConfig,

fn check_parameters() -> Result<(), HashToCurveError>

Checks if P represents a valid map.

fn map_to_curve( element: <P as CurveConfig>::BaseField, ) -> Result<Affine<P>, HashToCurveError>

Map an arbitrary base field element to a curve point. Based on https://github.com/zcash/pasta_curves/blob/main/src/hashtocurve.rs.

impl<P> MapToCurve<Projective<P>> for WBMap<P>

where P: WBConfig,

fn check_parameters() -> Result<(), HashToCurveError>

Checks if P represents a valid map.

fn map_to_curve( element: <Affine<P> as AffineRepr>::BaseField, ) -> Result<Affine<P>, HashToCurveError>

Map random field point to a random curve point inspired from https://github.com/zcash/pasta_curves/blob/main/src/hashtocurve.rs

impl<P, T> Mul<T> for Projective<P>

where P: SWCurveConfig, T: Borrow<<P as CurveConfig>::ScalarField>,

type Output = Projective<P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<P, T> MulAssign<T> for Projective<P>

where P: SWCurveConfig, T: Borrow<<P as CurveConfig>::ScalarField>,

fn mul_assign(&mut self, other: T)

Performs the *= operation.

impl<P> Neg for Projective<P>

where P: SWCurveConfig,

type Output = Projective<P>

The resulting type after applying the - operator.

fn neg(self) -> Projective<P>

Performs the unary - operation.

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

where P: SWCurveConfig,

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> PartialEq<Projective<P>> for Affine<P>

where P: SWCurveConfig,

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> PartialEq for Projective<P>

where P: SWCurveConfig,

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> PrimeGroup for Projective<P>

where P: SWCurveConfig,

type ScalarField = <P as CurveConfig>::ScalarField

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

fn generator() -> Projective<P>

Returns a fixed generator of this group.

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

Performs scalar multiplication of this element.

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> ScalarMul for Projective<P>

where P: SWCurveConfig,

const NEGATION_IS_CHEAP: bool = true

type MulBase = Affine<P>

fn batch_convert_to_mul_base( bases: &[Projective<P>], ) -> Vec<<Projective<P> as ScalarMul>::MulBase>

fn batch_mul(self, v: &[Self::ScalarField]) -> Vec<Self::MulBase>

Compute the vector v[0].G, v[1].G, …, v[n-1].G, given:

fn batch_mul_with_preprocessing( table: &BatchMulPreprocessing<Self>, v: &[Self::ScalarField], ) -> Vec<Self::MulBase>

Compute the vector v[0].G, v[1].G, …, v[n-1].G, given:

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

where P: SWCurveConfig,

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> Sub<&'a Projective<P>> for Affine<P>

where P: SWCurveConfig,

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> Sub<&'a Projective<P>> for Projective<P>

where P: SWCurveConfig,

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

where P: SWCurveConfig,

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> Sub<&'a mut Projective<P>> for Projective<P>

where P: SWCurveConfig,

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<'b, P> Sub<Projective<P>> for &'b Projective<P>

where P: SWCurveConfig,

type Output = Projective<P>

The resulting type after applying the - operator.

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

Performs the - operation.

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

where P: SWCurveConfig,

type Output = Projective<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<P, T> Sub<T> for Projective<P>

where P: SWCurveConfig, T: Borrow<Affine<P>>,

type Output = Projective<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<P> Sub for Projective<P>

where P: SWCurveConfig,

type Output = Projective<P>

The resulting type after applying the - operator.

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

Performs the - operation.

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

where P: SWCurveConfig,

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

Performs the -= operation.

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

where P: SWCurveConfig,

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

Performs the -= operation.

impl<P, T> SubAssign<T> for Projective<P>

where P: SWCurveConfig, T: Borrow<Affine<P>>,

fn sub_assign(&mut self, other: T)

Performs the -= operation.

impl<P> SubAssign for Projective<P>

where P: SWCurveConfig,

fn sub_assign(&mut self, other: Projective<P>)

Performs the -= operation.

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

where P: SWCurveConfig,

fn sum<I>(iter: I) -> Projective<P>

where I: Iterator<Item = &'a Projective<P>>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<P, T> Sum<T> for Projective<P>

where P: SWCurveConfig, T: Borrow<Affine<P>>,

fn sum<I>(iter: I) -> Projective<P>

where I: Iterator<Item = T>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<P> Sum for Projective<P>

where P: SWCurveConfig,

fn sum<I>(iter: I) -> Projective<P>

where I: Iterator<Item = Projective<P>>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<M, ConstraintF> ToConstraintField<ConstraintF> for Projective<M>

where M: SWCurveConfig, ConstraintF: Field, <M as CurveConfig>::BaseField: ToConstraintField<ConstraintF>,

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

impl<P> Valid for Projective<P>

where P: SWCurveConfig,

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

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

where Projective<P>: 'a,

impl<P> VariableBaseMSM for Projective<P>

where P: SWCurveConfig,

fn msm( bases: &[<Projective<P> as ScalarMul>::MulBase], bigints: &[<Projective<P> as PrimeGroup>::ScalarField], ) -> Result<Projective<P>, usize>

Performs multi-scalar multiplication.

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) -> Self

where I: Iterable + ?Sized, <I as Iterable>::Item: Borrow<Self::ScalarField>, J: Iterable, <J as Iterable>::Item: Borrow<Self::MulBase>,

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

impl<P> Zero for Projective<P>

where P: SWCurveConfig,

fn zero() -> Projective<P>

Returns the point at infinity, which always has Z = 0.

fn is_zero(&self) -> bool

Checks whether self.z.is_zero().

fn set_zero(&mut self)

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

impl<P> Zeroize for Projective<P>

where P: SWCurveConfig,

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: SWCurveConfig, <P as CurveConfig>::BaseField: Copy,

impl<P> Eq for Projective<P>

where P: SWCurveConfig,