Struct Affine 

pub struct Affine<P: TECurveConfig> {
    pub x: P::BaseField,
    pub y: P::BaseField,
}

Affine coordinates for a point on a twisted Edwards curve, over the base field P::BaseField.

Fields

x: P::BaseField

X coordinate of the point represented as a field element

y: P::BaseField

Y coordinate of the point represented as a field element

Implementations

impl<P: TECurveConfig> Affine<P>

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

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

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

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

Panics

• If point is not on curve.
• If point is not in the prime-order subgroup.

pub const fn zero() -> Self

Construct the identity of the group.

pub fn is_zero(&self) -> bool

Is this point the identity?

pub fn is_on_curve(&self) -> bool

Checks that the current point is on the elliptic curve.

impl<P: TECurveConfig> Affine<P>

pub fn is_in_prime_order_subgroup(&self) -> bool

Checks if this point is in the prime-order subgroup.

This assumes the point is already on the curve and verifies it belongs to the subgroup with order equal to P::ScalarField.

Trait Implementations

impl<'a, P: TECurveConfig> 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<P: TECurveConfig> 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: TECurveConfig, T: Borrow<Self>> Add<T> for Affine<P>

type Output = Projective<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<P: TECurveConfig> AffineRepr for Affine<P>

fn mul_by_cofactor_to_group(&self) -> Self::Group

Multiplies this element by the cofactor and output the resulting projective element.

fn clear_cofactor(&self) -> Self

Performs cofactor clearing. The default method is simply to multiply by the cofactor. Some curves can implement a more efficient algorithm.

type BaseField = <P as CurveConfig>::BaseField

Base field that the curve is defined over.

type Config = P

Associated configuration for this curve.

type Group = Projective<P>

The projective representation of points on this curve.

type ScalarField = <P as CurveConfig>::ScalarField

Finite prime field corresponding to an appropriate prime-order subgroup of the curve group.

fn xy(&self) -> Option<(Self::BaseField, Self::BaseField)>

Returns the x and y coordinates of this affine point.

fn generator() -> Self

Returns a fixed generator of unknown exponent.

fn zero() -> Self

Returns the point at infinity.

fn mul_bigint(&self, by: impl BitIteratorBE) -> Self::Group

Performs scalar multiplication of this element with mixed addition.

fn x(&self) -> Option<Self::BaseField>

Returns the x coordinate of this affine point.

fn y(&self) -> Option<Self::BaseField>

Returns the y coordinate of this affine point.

fn is_zero(&self) -> bool

Is self the point at infinity?

fn into_group(self) -> Self::Group

Converts self into the projective representation.

fn mul_by_cofactor(&self) -> Self

Multiplies this element by the cofactor.

fn mul_by_cofactor_inv(&self) -> Self

Multiplies this element by the inverse of the cofactor in Self::ScalarField.

impl<P: TECurveConfig> Clone for Affine<P>

where P::BaseField: Copy,

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<P: TECurveConfig> Debug for Affine<P>

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

Formats the value using the given formatter.

impl<P: TECurveConfig> Default for Affine<P>

fn default() -> Self

Returns the “default value” for a type.

impl<P: TECurveConfig> Display for Affine<P>

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

Formats the value using the given formatter.

impl From<Affine<Curve25519Config>> for CompressedPointY

fn from(point: AffinePoint) -> Self

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

impl<P: TECurveConfig> Hash for Affine<P>

where P::BaseField: Hash,

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: TECurveConfig, T: Borrow<P::ScalarField>> Mul<T> for Affine<P>

type Output = Projective<P>

The resulting type after applying the * operator.

fn mul(self, other: T) -> Self::Output

Performs the * operation.

impl<P: TECurveConfig> Neg for Affine<P>

type Output = Affine<P>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<P: TECurveConfig> 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: TECurveConfig> 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: TECurveConfig> PartialEq for Affine<P>

where P::BaseField: PartialEq,

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<'a, P: TECurveConfig> 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<P: TECurveConfig> 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: TECurveConfig, T: Borrow<Self>> Sub<T> for Affine<P>

type Output = Projective<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<P: TECurveConfig> Zeroize for Affine<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: TECurveConfig> Copy for Affine<P>

where P::BaseField: Copy,

impl<P: TECurveConfig> Eq for Affine<P>

where P::BaseField: PartialEq,