Struct G2

pub struct G2 { /* private fields */ }

This is an element of $\mathbb{G}_2$ represented in the projective coordinate space.

Implementations

impl G2Projective

pub fn identity() -> G2Projective

Returns the identity of the group: the point at infinity.

pub fn generator() -> G2Projective

Returns a fixed generator of the group. See notes::design for how this generator is chosen.

pub fn double(&self) -> G2Projective

Computes the doubling of this point.

pub fn add(&self, rhs: &G2Projective) -> G2Projective

Adds this point to another point.

pub fn add_mixed(&self, rhs: &G2Affine) -> G2Projective

Adds this point to another point in the affine model.

pub fn clear_cofactor(&self) -> G2Projective

Clears the cofactor, using Budroni-Pintore. This is equivalent to multiplying by $h_\textrm{eff} = 3(z^2 - 1) \cdot h_2$, where $h_2$ is the cofactor of $\mathbb{G}_2$ and $z$ is the parameter of BLS12-381.

pub fn batch_normalize(p: &[Self], q: &mut [G2Affine])

Converts a batch of G2Projective elements into G2Affine elements. This function will panic if p.len() != q.len().

pub fn is_identity(&self) -> Choice

Returns true if this element is the identity (the point at infinity).

pub fn is_on_curve(&self) -> Choice

Returns true if this point is on the curve. This should always return true unless an “unchecked” API was used.

Trait Implementations

impl<'a, 'b> Add<&'b G2Affine> for &'a G2Projective

type Output = G2Projective

The resulting type after applying the + operator.

fn add(self, rhs: &'b G2Affine) -> G2Projective

Performs the + operation.

impl<'b> Add<&'b G2Affine> for G2Projective

type Output = G2Projective

The resulting type after applying the + operator.

fn add(self, rhs: &'b G2Affine) -> G2Projective

Performs the + operation.

impl<'a, 'b> Add<&'b G2Projective> for &'a G2Affine

type Output = G2Projective

The resulting type after applying the + operator.

fn add(self, rhs: &'b G2Projective) -> G2Projective

Performs the + operation.

impl<'a, 'b> Add<&'b G2Projective> for &'a G2Projective

type Output = G2Projective

The resulting type after applying the + operator.

fn add(self, rhs: &'b G2Projective) -> G2Projective

Performs the + operation.

impl<'b> Add<&'b G2Projective> for G2Affine

type Output = G2Projective

The resulting type after applying the + operator.

fn add(self, rhs: &'b G2Projective) -> G2Projective

Performs the + operation.

impl<'b> Add<&'b G2Projective> for G2Projective

type Output = G2Projective

The resulting type after applying the + operator.

fn add(self, rhs: &'b G2Projective) -> G2Projective

Performs the + operation.

impl<'a> Add<G2Affine> for &'a G2Projective

type Output = G2Projective

The resulting type after applying the + operator.

fn add(self, rhs: G2Affine) -> G2Projective

Performs the + operation.

impl Add<G2Affine> for G2Projective

type Output = G2Projective

The resulting type after applying the + operator.

fn add(self, rhs: G2Affine) -> G2Projective

Performs the + operation.

impl<'a> Add<G2Projective> for &'a G2Affine

type Output = G2Projective

The resulting type after applying the + operator.

fn add(self, rhs: G2Projective) -> G2Projective

Performs the + operation.

impl<'a> Add<G2Projective> for &'a G2Projective

type Output = G2Projective

The resulting type after applying the + operator.

fn add(self, rhs: G2Projective) -> G2Projective

Performs the + operation.

impl Add<G2Projective> for G2Affine

type Output = G2Projective

The resulting type after applying the + operator.

fn add(self, rhs: G2Projective) -> G2Projective

Performs the + operation.

impl Add for G2Projective

type Output = G2Projective

The resulting type after applying the + operator.

fn add(self, rhs: G2Projective) -> G2Projective

Performs the + operation.

impl<'b> AddAssign<&'b G2Affine> for G2Projective

fn add_assign(&mut self, rhs: &'b G2Affine)

Performs the += operation.

impl<'b> AddAssign<&'b G2Projective> for G2Projective

fn add_assign(&mut self, rhs: &'b G2Projective)

Performs the += operation.

impl AddAssign<G2Affine> for G2Projective

fn add_assign(&mut self, rhs: G2Affine)

Performs the += operation.

impl AddAssign for G2Projective

fn add_assign(&mut self, rhs: G2Projective)

Performs the += operation.

impl Clone for G2Projective

fn clone(&self) -> G2Projective

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for G2Projective

fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self

Select a or b according to choice.

fn conditional_assign(&mut self, other: &Self, choice: Choice)

Conditionally assign other to self, according to choice.

fn conditional_swap(a: &mut Self, b: &mut Self, choice: Choice)

Conditionally swap self and other if choice == 1; otherwise, reassign both unto themselves.

impl ConstantTimeEq for G2Projective

fn ct_eq(&self, other: &Self) -> Choice

Determine if two items are equal.

fn ct_ne(&self, other: &Self) -> Choice

Determine if two items are NOT equal.

impl Curve for G2Projective

type AffineRepr = G2Affine

The affine representation for this elliptic curve.

fn batch_normalize(p: &[Self], q: &mut [Self::AffineRepr])

Converts a batch of projective elements into affine elements. This function will panic if p.len() != q.len().

fn to_affine(&self) -> Self::AffineRepr

Converts this element into its affine representation.

impl CurveExt for G2Projective

const CURVE_ID: &'static str = "Bls12-381"

CURVE_ID used for hash-to-curve.

type ScalarExt = Scalar

The scalar field of this elliptic curve.

type Base = Fp2

The base field over which this elliptic curve is constructed.

type AffineExt = G2Affine

The affine version of the curve

fn endo(&self) -> Self

Apply the curve endomorphism by multiplying the x-coordinate by an element of multiplicative order 3.

fn jacobian_coordinates(&self) -> (Fp2, Fp2, Fp2)

Return the Jacobian coordinates of this point.

fn hash_to_curve<'a>(domain_prefix: &'a str) -> Box<dyn Fn(&[u8]) -> Self + 'a>

Requests a hasher that accepts messages and returns near-uniformly distributed elements in the group, given domain prefix domain_prefix.

fn is_on_curve(&self) -> Choice

Returns whether or not this element is on the curve; should always be true unless an “unchecked” API was used.

fn b() -> Self::Base

Returns the curve constant b.

fn a() -> Self::Base

Returns the curve constant a.

fn new_jacobian(x: Self::Base, y: Self::Base, z: Self::Base) -> CtOption<Self>

Obtains a point given Jacobian coordinates $X : Y : Z$, failing if the coordinates are not on the curve.

impl Debug for G2Projective

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

Formats the value using the given formatter.

impl Default for G2Projective

fn default() -> G2Projective

Returns the “default value” for a type.

impl Display for G2Projective

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

Formats the value using the given formatter.

impl<'a> From<&'a G2Affine> for G2Projective

fn from(p: &'a G2Affine) -> G2Projective

Converts to this type from the input type.

impl<'a> From<&'a G2Projective> for G2Affine

fn from(p: &'a G2Projective) -> G2Affine

Converts to this type from the input type.

impl From<G2Affine> for G2Projective

fn from(p: G2Affine) -> G2Projective

Converts to this type from the input type.

impl From<G2Projective> for G2Affine

fn from(p: G2Projective) -> G2Affine

Converts to this type from the input type.

impl Group for G2Projective

type Scalar = Scalar

Scalars modulo the order of this group’s scalar field.

fn random(rng: impl RngCore) -> Self

Returns an element chosen uniformly at random from the non-identity elements of this group.

fn identity() -> Self

Returns the additive identity, also known as the “neutral element”.

fn generator() -> Self

Returns a fixed generator of the prime-order subgroup.

fn is_identity(&self) -> Choice

Determines if this point is the identity.

fn double(&self) -> Self

Doubles this element.

impl GroupEncoding for G2Projective

type Repr = G2Compressed

The encoding of group elements.

fn from_bytes(bytes: &Self::Repr) -> CtOption<Self>

Attempts to deserialize a group element from its encoding.

fn from_bytes_unchecked(bytes: &Self::Repr) -> CtOption<Self>

Attempts to deserialize a group element, not checking if the element is valid.

fn to_bytes(&self) -> Self::Repr

Converts this element into its byte encoding. This may or may not support encoding the identity.

impl MapToCurve for G2Projective

type Field = Fp2

The field element type.

fn map_to_curve(u: &Fp2) -> G2Projective

Maps an element of the finite field Self::Field to a point on the curve Self.

fn clear_h(&self) -> Self

Clears the cofactor, sending a point on curve E to the target group (G1/G2).

impl<'a, 'b> Mul<&'b G2Projective> for &'a Scalar

type Output = G2Projective

The resulting type after applying the * operator.

fn mul(self, rhs: &'b G2Projective) -> Self::Output

Performs the * operation.

impl<'b> Mul<&'b G2Projective> for Scalar

type Output = G2Projective

The resulting type after applying the * operator.

fn mul(self, rhs: &'b G2Projective) -> G2Projective

Performs the * operation.

impl<'a, 'b> Mul<&'b Scalar> for &'a G2Projective

type Output = G2Projective

The resulting type after applying the * operator.

fn mul(self, other: &'b Scalar) -> Self::Output

Performs the * operation.

impl<'b> Mul<&'b Scalar> for G2Projective

type Output = G2Projective

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Scalar) -> G2Projective

Performs the * operation.

impl<'a> Mul<G2Projective> for &'a Scalar

type Output = G2Projective

The resulting type after applying the * operator.

fn mul(self, rhs: G2Projective) -> G2Projective

Performs the * operation.

impl Mul<G2Projective> for Scalar

type Output = G2Projective

The resulting type after applying the * operator.

fn mul(self, rhs: G2Projective) -> G2Projective

Performs the * operation.

impl<'a> Mul<Scalar> for &'a G2Projective

type Output = G2Projective

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar) -> G2Projective

Performs the * operation.

impl Mul<Scalar> for G2Projective

type Output = G2Projective

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar) -> G2Projective

Performs the * operation.

impl<'b> MulAssign<&'b Scalar> for G2Projective

fn mul_assign(&mut self, rhs: &'b Scalar)

Performs the *= operation.

impl MulAssign<Scalar> for G2Projective

fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation.

impl<'a> Neg for &'a G2Projective

type Output = G2Projective

The resulting type after applying the - operator.

fn neg(self) -> G2Projective

Performs the unary - operation.

impl Neg for G2Projective

type Output = G2Projective

The resulting type after applying the - operator.

fn neg(self) -> G2Projective

Performs the unary - operation.

impl PartialEq for G2Projective

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 PrimeCurve for G2Projective

type Affine = G2Affine

impl<'a, 'b> Sub<&'b G2Affine> for &'a G2Projective

type Output = G2Projective

The resulting type after applying the - operator.

fn sub(self, rhs: &'b G2Affine) -> G2Projective

Performs the - operation.

impl<'b> Sub<&'b G2Affine> for G2Projective

type Output = G2Projective

The resulting type after applying the - operator.

fn sub(self, rhs: &'b G2Affine) -> G2Projective

Performs the - operation.

impl<'a, 'b> Sub<&'b G2Projective> for &'a G2Affine

type Output = G2Projective

The resulting type after applying the - operator.

fn sub(self, rhs: &'b G2Projective) -> G2Projective

Performs the - operation.

impl<'a, 'b> Sub<&'b G2Projective> for &'a G2Projective

type Output = G2Projective

The resulting type after applying the - operator.

fn sub(self, rhs: &'b G2Projective) -> G2Projective

Performs the - operation.

impl<'b> Sub<&'b G2Projective> for G2Affine

type Output = G2Projective

The resulting type after applying the - operator.

fn sub(self, rhs: &'b G2Projective) -> G2Projective

Performs the - operation.

impl<'b> Sub<&'b G2Projective> for G2Projective

type Output = G2Projective

The resulting type after applying the - operator.

fn sub(self, rhs: &'b G2Projective) -> G2Projective

Performs the - operation.

impl<'a> Sub<G2Affine> for &'a G2Projective

type Output = G2Projective

The resulting type after applying the - operator.

fn sub(self, rhs: G2Affine) -> G2Projective

Performs the - operation.

impl Sub<G2Affine> for G2Projective

type Output = G2Projective

The resulting type after applying the - operator.

fn sub(self, rhs: G2Affine) -> G2Projective

Performs the - operation.

impl<'a> Sub<G2Projective> for &'a G2Affine

type Output = G2Projective

The resulting type after applying the - operator.

fn sub(self, rhs: G2Projective) -> G2Projective

Performs the - operation.

impl<'a> Sub<G2Projective> for &'a G2Projective

type Output = G2Projective

The resulting type after applying the - operator.

fn sub(self, rhs: G2Projective) -> G2Projective

Performs the - operation.

impl Sub<G2Projective> for G2Affine

type Output = G2Projective

The resulting type after applying the - operator.

fn sub(self, rhs: G2Projective) -> G2Projective

Performs the - operation.

impl Sub for G2Projective

type Output = G2Projective

The resulting type after applying the - operator.

fn sub(self, rhs: G2Projective) -> G2Projective

Performs the - operation.

impl<'b> SubAssign<&'b G2Affine> for G2Projective

fn sub_assign(&mut self, rhs: &'b G2Affine)

Performs the -= operation.

impl<'b> SubAssign<&'b G2Projective> for G2Projective

fn sub_assign(&mut self, rhs: &'b G2Projective)

Performs the -= operation.

impl SubAssign<G2Affine> for G2Projective

fn sub_assign(&mut self, rhs: G2Affine)

Performs the -= operation.

impl SubAssign for G2Projective

fn sub_assign(&mut self, rhs: G2Projective)

Performs the -= operation.

impl<T> Sum<T> for G2Projective

where T: Borrow<G2Projective>,

fn sum<I>(iter: I) -> Self

where I: Iterator<Item = T>,

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

impl Copy for G2Projective

impl Eq for G2Projective

impl PrimeGroup for G2Projective