Struct G1

pub struct G1 {
    pub x: Fq,
    pub y: Fq,
    pub z: Fq,
}

Fields

x: Fq

y: Fq

z: Fq

Implementations

impl G1

pub fn generator() -> Self

Trait Implementations

impl<'a, 'b> Add<&'a G1> for &'b G1

type Output = G1

The resulting type after applying the + operator.

fn add(self, rhs: &'a G1) -> G1

Performs the + operation.

impl<'a, 'b> Add<&'a G1> for &'b G1Affine

type Output = G1

The resulting type after applying the + operator.

fn add(self, rhs: &'a G1) -> G1

Performs the + operation.

impl<'b> Add<&'b G1> for G1

type Output = G1

The resulting type after applying the + operator.

fn add(self, rhs: &'b G1) -> G1

Performs the + operation.

impl<'b> Add<&'b G1> for G1Affine

type Output = G1

The resulting type after applying the + operator.

fn add(self, rhs: &'b G1) -> G1

Performs the + operation.

impl<'a, 'b> Add<&'a G1Affine> for &'b G1

type Output = G1

The resulting type after applying the + operator.

fn add(self, rhs: &'a G1Affine) -> G1

Performs the + operation.

impl<'b> Add<&'b G1Affine> for G1

type Output = G1

The resulting type after applying the + operator.

fn add(self, rhs: &'b G1Affine) -> G1

Performs the + operation.

impl<'a> Add<G1> for &'a G1

type Output = G1

The resulting type after applying the + operator.

fn add(self, rhs: G1) -> G1

Performs the + operation.

impl<'a> Add<G1> for &'a G1Affine

type Output = G1

The resulting type after applying the + operator.

fn add(self, rhs: G1) -> G1

Performs the + operation.

impl Add<G1> for G1Affine

type Output = G1

The resulting type after applying the + operator.

fn add(self, rhs: G1) -> G1

Performs the + operation.

impl<'a> Add<G1Affine> for &'a G1

type Output = G1

The resulting type after applying the + operator.

fn add(self, rhs: G1Affine) -> G1

Performs the + operation.

impl Add<G1Affine> for G1

type Output = G1

The resulting type after applying the + operator.

fn add(self, rhs: G1Affine) -> G1

Performs the + operation.

impl Add for G1

type Output = G1

The resulting type after applying the + operator.

fn add(self, rhs: G1) -> G1

Performs the + operation.

impl<'b> AddAssign<&'b G1> for G1

fn add_assign(&mut self, rhs: &'b G1)

Performs the += operation.

impl<'b> AddAssign<&'b G1Affine> for G1

fn add_assign(&mut self, rhs: &'b G1Affine)

Performs the += operation.

impl AddAssign<G1Affine> for G1

fn add_assign(&mut self, rhs: G1Affine)

Performs the += operation.

impl AddAssign for G1

fn add_assign(&mut self, rhs: G1)

Performs the += operation.

impl Clone for G1

fn clone(&self) -> G1

Returns a copy of the value.

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

Performs copy-assignment from source.

impl CofactorCurve for G1

type Affine = G1Affine

impl CofactorGroup for G1

type Subgroup = G1

The large prime-order subgroup in which cryptographic operations are performed. If Self implements PrimeGroup, then Self::Subgroup may be Self.

fn clear_cofactor(&self) -> Self

Maps self to the prime-order subgroup by multiplying this element by some k-multiple of the cofactor.

fn into_subgroup(self) -> CtOption<Self::Subgroup>

Returns self if it is contained in the prime-order subgroup.

fn is_torsion_free(&self) -> Choice

Determines if this element is “torsion free”, i.e., is contained in the prime-order subgroup.

fn is_small_order(&self) -> Choice

Determines if this element is of small order.

impl ConditionallySelectable for G1

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 G1

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 G1

type AffineRepr = G1Affine

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 G1

const CURVE_ID: &'static str = "bn256_g1"

CURVE_ID used for hash-to-curve.

type ScalarExt = Fr

The scalar field of this elliptic curve.

type Base = Fq

The base field over which this elliptic curve is constructed.

type AffineExt = G1Affine

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) -> (Fq, Fq, Fq)

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 G1

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

Formats the value using the given formatter.

impl Default for G1

fn default() -> G1

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for G1

fn deserialize<D: Deserializer<'de>>(deserializer: D) -> Result<Self, D::Error>

Deserialize this value from the given Serde deserializer.

impl<'a> From<&'a G1> for G1Affine

fn from(p: &'a G1) -> G1Affine

Converts to this type from the input type.

impl<'a> From<&'a G1Affine> for G1

fn from(p: &'a G1Affine) -> G1

Converts to this type from the input type.

impl From<G1> for G1Affine

fn from(p: G1) -> G1Affine

Converts to this type from the input type.

impl From<G1Affine> for G1

fn from(p: G1Affine) -> G1

Converts to this type from the input type.

impl Group for G1

type Scalar = Fr

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 double(&self) -> Self

Doubles this element.

fn generator() -> Self

Returns a fixed generator of the prime-order subgroup.

fn identity() -> Self

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

fn is_identity(&self) -> Choice

Determines if this point is the identity.

impl GroupEncoding for G1

type Repr = G1Compressed

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<'a, 'b> Mul<&'b Fr> for &'a G1

type Output = G1

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b> Mul<&'b Fr> for G1

type Output = G1

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Fr) -> G1

Performs the * operation.

impl<'a> Mul<Fr> for &'a G1

type Output = G1

The resulting type after applying the * operator.

fn mul(self, rhs: Fr) -> G1

Performs the * operation.

impl Mul<Fr> for G1

type Output = G1

The resulting type after applying the * operator.

fn mul(self, rhs: Fr) -> G1

Performs the * operation.

impl<'b> MulAssign<&'b Fr> for G1

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

Performs the *= operation.

impl MulAssign<Fr> for G1

fn mul_assign(&mut self, rhs: Fr)

Performs the *= operation.

impl<'a> Neg for &'a G1

type Output = G1

The resulting type after applying the - operator.

fn neg(self) -> G1

Performs the unary - operation.

impl Neg for G1

type Output = G1

The resulting type after applying the - operator.

fn neg(self) -> G1

Performs the unary - operation.

impl PartialEq for G1

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 G1

type Affine = G1Affine

impl SerdeObject for G1

fn from_raw_bytes_unchecked(bytes: &[u8]) -> Self

The purpose of unchecked functions is to read the internal memory representation of a type from bytes as quickly as possible. No sanitization checks are performed to ensure the bytes represent a valid object. As such this function should only be used internally as an extension of machine memory. It should not be used to deserialize externally provided data.

fn from_raw_bytes(bytes: &[u8]) -> Option<Self>

fn to_raw_bytes(&self) -> Vec<u8>

fn read_raw_unchecked<R: Read>(reader: &mut R) -> Self

The purpose of unchecked functions is to read the internal memory representation of a type from disk as quickly as possible. No sanitization checks are performed to ensure the bytes represent a valid object. This function should only be used internally when some machine state cannot be kept in memory (e.g., between runs) and needs to be reloaded as quickly as possible.

fn read_raw<R: Read>(reader: &mut R) -> Result<Self>

fn write_raw<W: Write>(&self, writer: &mut W) -> Result<()>

impl Serialize for G1

fn serialize<S: Serializer>(&self, serializer: S) -> Result<S::Ok, S::Error>

Serialize this value into the given Serde serializer.

impl<'a, 'b> Sub<&'a G1> for &'b G1

type Output = G1

The resulting type after applying the - operator.

fn sub(self, other: &'a G1) -> G1

Performs the - operation.

impl<'a, 'b> Sub<&'a G1> for &'b G1Affine

type Output = G1

The resulting type after applying the - operator.

fn sub(self, other: &'a G1) -> G1

Performs the - operation.

impl<'b> Sub<&'b G1> for G1

type Output = G1

The resulting type after applying the - operator.

fn sub(self, rhs: &'b G1) -> G1

Performs the - operation.

impl<'b> Sub<&'b G1> for G1Affine

type Output = G1

The resulting type after applying the - operator.

fn sub(self, rhs: &'b G1) -> G1

Performs the - operation.

impl<'a, 'b> Sub<&'a G1Affine> for &'b G1

type Output = G1

The resulting type after applying the - operator.

fn sub(self, other: &'a G1Affine) -> G1

Performs the - operation.

impl<'b> Sub<&'b G1Affine> for G1

type Output = G1

The resulting type after applying the - operator.

fn sub(self, rhs: &'b G1Affine) -> G1

Performs the - operation.

impl<'a> Sub<G1> for &'a G1

type Output = G1

The resulting type after applying the - operator.

fn sub(self, rhs: G1) -> G1

Performs the - operation.

impl<'a> Sub<G1> for &'a G1Affine

type Output = G1

The resulting type after applying the - operator.

fn sub(self, rhs: G1) -> G1

Performs the - operation.

impl Sub<G1> for G1Affine

type Output = G1

The resulting type after applying the - operator.

fn sub(self, rhs: G1) -> G1

Performs the - operation.

impl<'a> Sub<G1Affine> for &'a G1

type Output = G1

The resulting type after applying the - operator.

fn sub(self, rhs: G1Affine) -> G1

Performs the - operation.

impl Sub<G1Affine> for G1

type Output = G1

The resulting type after applying the - operator.

fn sub(self, rhs: G1Affine) -> G1

Performs the - operation.

impl Sub for G1

type Output = G1

The resulting type after applying the - operator.

fn sub(self, rhs: G1) -> G1

Performs the - operation.

impl<'b> SubAssign<&'b G1> for G1

fn sub_assign(&mut self, rhs: &'b G1)

Performs the -= operation.

impl<'b> SubAssign<&'b G1Affine> for G1

fn sub_assign(&mut self, rhs: &'b G1Affine)

Performs the -= operation.

impl SubAssign<G1Affine> for G1

fn sub_assign(&mut self, rhs: G1Affine)

Performs the -= operation.

impl SubAssign for G1

fn sub_assign(&mut self, rhs: G1)

Performs the -= operation.

impl<T> Sum<T> for G1

where T: Borrow<G1>,

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 G1

impl Eq for G1

impl PrimeGroup for G1