Struct G2Projective 

pub struct G2Projective { /* private fields */ }

Available on crate feature groups only.

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

Implementations

impl G2Projective

pub const COMPRESSED_BYTES: usize = 96

Bytes to represent this point compressed

pub const UNCOMPRESSED_BYTES: usize = 192

Bytes to represent this point uncompressed

pub const IDENTITY: Self

The identity of the group: the point at infinity.

pub const GENERATOR: Self

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

pub fn to_compressed(&self) -> [u8; 96]

Serializes this element into compressed form.

pub fn to_uncompressed(&self) -> [u8; 192]

Serializes this element into uncompressed form.

pub fn from_uncompressed(bytes: &[u8; 192]) -> CtOption<Self>

Attempts to deserialize an uncompressed element.

pub fn from_uncompressed_unchecked(bytes: &[u8; 192]) -> CtOption<Self>

Attempts to deserialize an uncompressed element, not checking if the element is on the curve and not checking if it is in the correct subgroup.

This is dangerous to call unless you trust the bytes you are reading; otherwise, API invariants may be broken. Please consider using from_uncompressed() instead.

pub fn from_compressed(bytes: &[u8; 96]) -> CtOption<Self>

Attempts to deserialize a compressed element.

pub fn from_compressed_unchecked(bytes: &[u8; 96]) -> CtOption<Self>

Attempts to deserialize an uncompressed element, not checking if the element is in the correct subgroup.

This is dangerous to call unless you trust the bytes you are reading; otherwise, API invariants may be broken. Please consider using from_compressed() instead.

pub fn identity() -> G2Projective

👎Deprecated since 0.5.5:

Use IDENTITY instead.

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

pub fn generator() -> G2Projective

👎Deprecated since 0.5.5:

Use GENERATOR instead.

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 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.

pub fn hash<X>(msg: &[u8], dst: &[u8]) -> Self

where X: for<'a> ExpandMsg<'a>,

Use a random oracle to map a value to a curve point

pub fn encode<X>(msg: &[u8], dst: &[u8]) -> Self

where X: for<'a> ExpandMsg<'a>,

Use injective encoding to map a value to a curve point

pub fn sum_of_products(points: &[Self], scalars: &[Scalar]) -> Self

Available on crate feature alloc only.

Use pippenger multi-exponentiation method to compute the sum of multiple points raise to scalars. This is constant time with respect to the scalars.

pub fn sum_of_products_vartime(points: &[Self], scalars: &[Scalar]) -> Self

Available on crate feature alloc only.

Use variable-time multi-exponentiation to compute the sum of multiple points raised to scalars.

This is faster than Self::sum_of_products but may leak scalar information through memory access patterns. Use only when every scalar is public.

pub fn sum_of_products_in_place(points: &[Self], scalars: &mut [Scalar]) -> Self

Use pippenger multi-exponentiation method to compute the sum of multiple points raise to scalars. This uses a fixed window of 4 to be constant time The scalars are used as place holders for temporary computations

Trait Implementations

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> 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<'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<'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 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<'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 Add<G2Projective> for 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 AddAssign for G2Projective

fn add_assign(&mut self, rhs: 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 Clone for G2Projective

fn clone(&self) -> G2Projective

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl CofactorGroup for G2Projective

fn clear_cofactor(&self) -> Self::Subgroup

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.

type Subgroup = G2Projective

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

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 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 Copy for G2Projective

impl Curve for G2Projective

type Affine = G2Affine

The affine representation for this elliptic curve.

fn batch_normalize(points: &[Self], out: &mut [Self::Affine])

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

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

Converts this element into its affine representation.

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 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 DefaultIsZeroes for G2Projective

impl<'de> Deserialize<'de> for G2Projective

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

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for G2Projective

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

Formats the value using the given formatter.

impl Eq for G2Projective

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<&G2Projective> for Vec<u8>

Available on crate feature alloc only.

fn from(value: &G2Projective) -> Self

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 From<G2Projective> for Vec<u8>

Available on crate feature alloc only.

fn from(value: G2Projective) -> Self

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 try_random<R: TryRng + ?Sized>(rng: &mut R) -> Result<Self, R::Error>

Returns an element chosen uniformly at random from the non-identity elements of this group using a user-provided fallible RNG.

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.

fn random<R>(rng: &mut R) -> Self

where R: Rng + ?Sized,

Returns an element chosen uniformly at random from the non-identity elements of this group using a user-provided infallible RNG.

fn mul_by_generator(scalar: &Self::Scalar) -> Self

Multiply by the generator of the prime-order subgroup.

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 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 Hash for G2Projective

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 LinearCombination for G2Projective

fn lincomb(x: &Self, k: &Self::Scalar, y: &Self, l: &Self::Scalar) -> Self

Calculates x * k + y * l.

impl LowerHex for G2Projective

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

Formats the value using the given formatter.

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

fn mul_by_generator(scalar: &Self::Scalar) -> Self

Multiply by the generator of the prime-order subgroup.

impl Neg for &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

Equality operator ==.

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

Inequality operator !=.

impl PrimeCurve for G2Projective

impl PrimeCurve for G2Projective

type Affine = G2Affine

impl PrimeGroup for G2Projective

impl PrimeGroup for G2Projective

impl Serialize for G2Projective

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

where S: Serializer,

Serialize this value into the given Serde serializer.

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> 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<'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<'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 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<'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 Sub<G2Projective> for 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 SubAssign for G2Projective

fn sub_assign(&mut self, rhs: 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<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 TryFrom<&Vec<u8>> for G2Projective

Available on crate feature alloc only.

type Error = String

The type returned in the event of a conversion error.

fn try_from(value: &Vec<u8>) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<&[u8]> for G2Projective

Available on crate feature alloc only.

type Error = String

The type returned in the event of a conversion error.

fn try_from(value: &[u8]) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<Box<[u8]>> for G2Projective

Available on crate feature alloc only.

type Error = String

The type returned in the event of a conversion error.

fn try_from(value: Box<[u8]>) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<Vec<u8>> for G2Projective

Available on crate feature alloc only.

type Error = String

The type returned in the event of a conversion error.

fn try_from(value: Vec<u8>) -> Result<Self, Self::Error>

Performs the conversion.

impl UpperHex for G2Projective

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

Formats the value using the given formatter.

impl WnafGroup for G2Projective

Available on crate feature alloc only.

fn recommended_wnaf_for_num_scalars(num_scalars: usize) -> usize

Recommends a wNAF window size given the number of scalars you intend to multiply a base by. Always returns a number between 2 and 22, inclusive.

impl WnafGroup for G2Projective

Available on crate feature alloc only.

fn recommended_wnaf_for_num_scalars(num_scalars: usize) -> usize

Recommends a wNAF window size given the number of scalars you intend to multiply a base by. Always returns a number between 2 and 22, inclusive.