Struct G1Affine

pub struct G1Affine {
    pub x: Fp,
    pub y: Fp,
    /* private fields */
}

This is an element of $\mathbb{G}_1$ represented in the affine coordinate space. It is ideal to keep elements in this representation to reduce memory usage and improve performance through the use of mixed curve model arithmetic.

Values of G1Affine are guaranteed to be in the $q$-order subgroup unless an “unchecked” API was misused.

Fields

x: Fp

y: Fp

Implementations

impl G1Affine

pub fn identity() -> G1Affine

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

pub fn random(rng: impl RngCore) -> Self

pub fn generator() -> G1Affine

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

pub fn to_compressed_be(&self) -> [u8; 48]

Serializes this element into compressed form. See notes::serialization for details about how group elements are serialized.

pub fn to_compressed_le(&self) -> [u8; 48]

Serializes this element into compressed form in little-endian.

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

Serializes this element into uncompressed form. See notes::serialization for details about how group elements are serialized.

NOTE: this function used in UncompressedEncoding::to_uncompressed.

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

Serializes this element into uncompressed form in little-endian.

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

Attempts to deserialize an uncompressed element. See notes::serialization for details about how group elements are serialized.

pub fn from_uncompressed_unchecked_be(bytes: &[u8; 96]) -> 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_be(bytes: &[u8; 48]) -> CtOption<Self>

Attempts to deserialize a compressed element from big-endian bytes. See notes::serialization for details about how group elements are serialized.

NOTE: this function used in CompressedEncoding::from_compressed.

pub fn from_compressed_unchecked_be(bytes: &[u8; 48]) -> CtOption<Self>

Attempts to deserialize an uncompressed element from big-endian bytes, 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 from_uncompressed_le(bytes: &[u8; 96]) -> CtOption<Self>

Attempts to deserialize an uncompressed element. See notes::serialization for details about how group elements are serialized.

pub fn from_uncompressed_unchecked_le(bytes: &[u8; 96]) -> 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_unchecked_le(bytes: &[u8; 48]) -> CtOption<Self>

Attempts to deserialize an uncompressed element from little-endian bytes, not checking if the element is in the correct subgroup.

pub fn from_compressed_le(bytes: &[u8; 48]) -> CtOption<Self>

Attempts to deserialize a compressed element from little-endian bytes.

pub fn is_identity(&self) -> Choice

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

pub fn is_torsion_free(&self) -> Choice

Returns true if this point is free of an $h$-torsion component, and so it exists within the $q$-order subgroup $\mathbb{G}_1$. This should always return true unless an “unchecked” API was used.

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 G1Affine> for &'a G1Projective

type Output = G1Projective

The resulting type after applying the + operator.

fn add(self, rhs: &'b G1Affine) -> G1Projective

Performs the + operation.

impl<'b> Add<&'b G1Affine> for G1Projective

type Output = G1Projective

The resulting type after applying the + operator.

fn add(self, rhs: &'b G1Affine) -> G1Projective

Performs the + operation.

impl<'a, 'b> Add<&'b G1Projective> for &'a G1Affine

type Output = G1Projective

The resulting type after applying the + operator.

fn add(self, rhs: &'b G1Projective) -> G1Projective

Performs the + operation.

impl<'b> Add<&'b G1Projective> for G1Affine

type Output = G1Projective

The resulting type after applying the + operator.

fn add(self, rhs: &'b G1Projective) -> G1Projective

Performs the + operation.

impl<'a> Add<G1Affine> for &'a G1Projective

type Output = G1Projective

The resulting type after applying the + operator.

fn add(self, rhs: G1Affine) -> G1Projective

Performs the + operation.

impl Add<G1Affine> for G1Projective

type Output = G1Projective

The resulting type after applying the + operator.

fn add(self, rhs: G1Affine) -> G1Projective

Performs the + operation.

impl<'a> Add<G1Projective> for &'a G1Affine

type Output = G1Projective

The resulting type after applying the + operator.

fn add(self, rhs: G1Projective) -> G1Projective

Performs the + operation.

impl Add<G1Projective> for G1Affine

type Output = G1Projective

The resulting type after applying the + operator.

fn add(self, rhs: G1Projective) -> G1Projective

Performs the + operation.

impl Add for G1Affine

type Output = G1Projective

The resulting type after applying the + operator.

fn add(self, rhs: G1Affine) -> Self::Output

Performs the + operation.

impl<'b> AddAssign<&'b G1Affine> for G1Projective

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

Performs the += operation.

impl AddAssign<G1Affine> for G1Projective

fn add_assign(&mut self, rhs: G1Affine)

Performs the += operation.

impl Clone for G1Affine

fn clone(&self) -> G1Affine

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ConditionallySelectable for G1Affine

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 G1Affine

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 CurveAffine for G1Affine

type ScalarExt = Scalar

The scalar field of this elliptic curve.

type Base = Fp

The base field over which this elliptic curve is constructed.

type CurveExt = G1Projective

The projective form of the curve

fn coordinates(&self) -> CtOption<Coordinates<Self>>

Gets the coordinates of this point.

Returns None if this is the identity.

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

Obtains a point given $(x, y)$, failing if it is not on the curve.

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 a() -> Self::Base

Returns the curve constant $a$.

fn b() -> Self::Base

Returns the curve constant $b$.

impl CurveAffineExt for G1Affine

fn into_coordinates(self) -> (Self::Base, Self::Base)

Unlike the Coordinates trait, this just returns the raw affine coordinates without checking is_on_curve

impl Debug for G1Affine

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

Formats the value using the given formatter.

impl Default for G1Affine

fn default() -> G1Affine

Returns the “default value” for a type.

impl Display for G1Affine

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

Formats the value using the given formatter.

impl<'a> From<&'a G1Affine> for G1Projective

fn from(p: &'a G1Affine) -> G1Projective

Converts to this type from the input type.

impl<'a> From<&'a G1Projective> for G1Affine

fn from(p: &'a G1Projective) -> G1Affine

Converts to this type from the input type.

impl From<G1Affine> for G1Projective

fn from(p: G1Affine) -> G1Projective

Converts to this type from the input type.

impl From<G1Projective> for G1Affine

fn from(p: G1Projective) -> G1Affine

Converts to this type from the input type.

impl GroupEncoding for G1Affine

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 G1Affine> for &'a Scalar

type Output = G1Projective

The resulting type after applying the * operator.

fn mul(self, rhs: &'b G1Affine) -> Self::Output

Performs the * operation.

impl<'b> Mul<&'b G1Affine> for Scalar

type Output = G1Projective

The resulting type after applying the * operator.

fn mul(self, rhs: &'b G1Affine) -> G1Projective

Performs the * operation.

impl<'a, 'b> Mul<&'b Scalar> for &'a G1Affine

type Output = G1Projective

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b> Mul<&'b Scalar> for G1Affine

type Output = G1Projective

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Scalar) -> G1Projective

Performs the * operation.

impl<'a> Mul<G1Affine> for &'a Scalar

type Output = G1Projective

The resulting type after applying the * operator.

fn mul(self, rhs: G1Affine) -> G1Projective

Performs the * operation.

impl Mul<G1Affine> for Scalar

type Output = G1Projective

The resulting type after applying the * operator.

fn mul(self, rhs: G1Affine) -> G1Projective

Performs the * operation.

impl<'a> Mul<Scalar> for &'a G1Affine

type Output = G1Projective

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar) -> G1Projective

Performs the * operation.

impl Mul<Scalar> for G1Affine

type Output = G1Projective

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar) -> G1Projective

Performs the * operation.

impl<'a> Neg for &'a G1Affine

type Output = G1Affine

The resulting type after applying the - operator.

fn neg(self) -> G1Affine

Performs the unary - operation.

impl Neg for G1Affine

type Output = G1Affine

The resulting type after applying the - operator.

fn neg(self) -> G1Affine

Performs the unary - operation.

impl PairingCurveAffine for G1Affine

type Pair = G2Affine

type PairingResult = Gt

fn pairing_with(&self, other: &Self::Pair) -> Self::PairingResult

Perform a pairing

impl PartialEq for G1Affine

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 PrimeCurveAffine for G1Affine

type Scalar = Scalar

type Curve = G1Projective

fn identity() -> Self

Returns the additive identity.

fn generator() -> Self

Returns a fixed generator of unknown exponent.

fn is_identity(&self) -> Choice

Determines if this point represents the point at infinity; the additive identity.

fn to_curve(&self) -> Self::Curve

Converts this element to its curve representation.

impl<'a, 'b> Sub<&'b G1Affine> for &'a G1Projective

type Output = G1Projective

The resulting type after applying the - operator.

fn sub(self, rhs: &'b G1Affine) -> G1Projective

Performs the - operation.

impl<'b> Sub<&'b G1Affine> for G1Projective

type Output = G1Projective

The resulting type after applying the - operator.

fn sub(self, rhs: &'b G1Affine) -> G1Projective

Performs the - operation.

impl<'a, 'b> Sub<&'b G1Projective> for &'a G1Affine

type Output = G1Projective

The resulting type after applying the - operator.

fn sub(self, rhs: &'b G1Projective) -> G1Projective

Performs the - operation.

impl<'b> Sub<&'b G1Projective> for G1Affine

type Output = G1Projective

The resulting type after applying the - operator.

fn sub(self, rhs: &'b G1Projective) -> G1Projective

Performs the - operation.

impl<'a> Sub<G1Affine> for &'a G1Projective

type Output = G1Projective

The resulting type after applying the - operator.

fn sub(self, rhs: G1Affine) -> G1Projective

Performs the - operation.

impl Sub<G1Affine> for G1Projective

type Output = G1Projective

The resulting type after applying the - operator.

fn sub(self, rhs: G1Affine) -> G1Projective

Performs the - operation.

impl<'a> Sub<G1Projective> for &'a G1Affine

type Output = G1Projective

The resulting type after applying the - operator.

fn sub(self, rhs: G1Projective) -> G1Projective

Performs the - operation.

impl Sub<G1Projective> for G1Affine

type Output = G1Projective

The resulting type after applying the - operator.

fn sub(self, rhs: G1Projective) -> G1Projective

Performs the - operation.

impl Sub for G1Affine

type Output = G1Projective

The resulting type after applying the - operator.

fn sub(self, rhs: G1Affine) -> Self::Output

Performs the - operation.

impl<'b> SubAssign<&'b G1Affine> for G1Projective

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

Performs the -= operation.

impl SubAssign<G1Affine> for G1Projective

fn sub_assign(&mut self, rhs: G1Affine)

Performs the -= operation.

impl UncompressedEncoding for G1Affine

Allows to de/encode G1 points from uncompressed bytes in little endian.

type Uncompressed = G1Uncompressed

fn from_uncompressed(bytes: &Self::Uncompressed) -> CtOption<Self>

Attempts to deserialize an element from its uncompressed encoding.

fn from_uncompressed_unchecked(bytes: &Self::Uncompressed) -> CtOption<Self>

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

fn to_uncompressed(&self) -> Self::Uncompressed

Converts this element into its uncompressed encoding, so long as it’s not the point at infinity.

impl Copy for G1Affine

impl Eq for G1Affine