Struct Projective

pub struct Projective<P: SWCurveConfig> {
    pub x: P::BaseField,
    pub y: P::BaseField,
    pub z: P::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::BaseField

X / Z projection of the affine X

y: P::BaseField

Y / Z projection of the affine Y

z: P::BaseField

Projective multiplicative inverse. Will be 0 only at infinity.

Implementations

impl<P: SWCurveConfig> Projective<P>

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

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

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

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

Trait Implementations

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

type Output = Projective<P>

The resulting type after applying the + operator.

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

Performs the + operation.

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

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

Performs the += operation.

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

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

Performs the += operation.

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

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl<P: SWCurveConfig> AdditiveGroup for Projective<P>

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

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: Self = _

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: SWCurveConfig> 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: SWCurveConfig> 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: SWCurveConfig> Clone for Projective<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: SWCurveConfig> CurveGroup for Projective<P>

fn normalize_batch(v: &[Self]) -> Vec<Self::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: SWCurveConfig> Debug for Projective<P>

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

Formats the value using the given formatter.

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

fn default() -> Self

Returns the “default value” for a type.

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

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

Formats the value using the given formatter.

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

fn from(q: &'a G1Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(q: &'a G2Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(q: &'a G1Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(q: &'a G2Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(q: &'a G1Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(q: &'a G2Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(g1: &'a G1Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(g2: &'a G2Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(g1: &'a G1Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(g2: &'a G2Projective<P>) -> Self

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

fn from(q: G1Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(q: G2Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(q: G1Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(q: G2Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(q: G1Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(q: G2Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(g1: G1Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(g2: G2Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(g1: G1Projective<P>) -> Self

Converts to this type from the input type.

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

fn from(g2: G2Projective<P>) -> Self

Converts to this type from the input type.

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

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

Converts to this type from the input type.

impl<P: SWCurveConfig> 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: SWUConfig> MapToCurve<Projective<P>> for SWUMap<P>

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

Checks if P represents a valid map.

fn map_to_curve(element: P::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: WBConfig> MapToCurve<Projective<P>> for WBMap<P>

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: SWCurveConfig, 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: SWCurveConfig, T: Borrow<P::ScalarField>> MulAssign<T> for Projective<P>

fn mul_assign(&mut self, other: T)

Performs the *= operation.

impl<P: SWCurveConfig> 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: SWCurveConfig> 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: SWCurveConfig> 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: SWCurveConfig> PartialEq for Projective<P>

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

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: SWCurveConfig> ScalarMul for Projective<P>

const NEGATION_IS_CHEAP: bool = true

type MulBase = Affine<P>

fn batch_convert_to_mul_base(bases: &[Self]) -> Vec<Self::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: SWCurveConfig> 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: SWCurveConfig> 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<'a, P: SWCurveConfig> 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: SWCurveConfig> 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: SWCurveConfig> 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: SWCurveConfig> 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: SWCurveConfig> 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: SWCurveConfig, 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<P: SWCurveConfig> Sub for Projective<P>

type Output = Projective<P>

The resulting type after applying the - operator.

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

Performs the - operation.

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

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

Performs the -= operation.

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

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

Performs the -= operation.

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

fn sub_assign(&mut self, other: T)

Performs the -= operation.

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

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

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

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

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

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

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

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

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

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

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

impl<M: SWCurveConfig, ConstraintF: Field> ToConstraintField<ConstraintF> for Projective<M>

where M::BaseField: ToConstraintField<ConstraintF>,

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

impl<P: SWCurveConfig> 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: SWCurveConfig> VariableBaseMSM for Projective<P>

fn msm( bases: &[Self::MulBase], bigints: &[Self::ScalarField], ) -> Result<Self, 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::Item: Borrow<Self::ScalarField>, J: Iterable, J::Item: Borrow<Self::MulBase>,

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

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

fn zero() -> Self

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: SWCurveConfig> 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: SWCurveConfig> Copy for Projective<P>

where P::BaseField: Copy,

impl<P: SWCurveConfig> Eq for Projective<P>