Struct CirclePoint

pub struct CirclePoint<F: IsField> {
    pub x: FieldElement<F>,
    pub y: FieldElement<F>,
}

Given a Field F, we implement here the Group which consists of all the points (x, y) such as x in F, y in F and x^2 + y^2 = 1, i.e. the Circle. The operation of the group will have additive notation and is as follows: (a, b) + (c, d) = (a * c - b * d, a * d + b * c)

Fields

x: FieldElement<F>

y: FieldElement<F>

Implementations

impl<F: IsField + HasCircleParams<F>> CirclePoint<F>

pub const GENERATOR: Self

pub const ORDER: u128 = F::ORDER

pub fn new(x: FieldElement<F>, y: FieldElement<F>) -> Result<Self, CircleError>

pub fn zero() -> Self

Neutral element of the Circle group (with additive notation).

pub fn double(&self) -> Self

Computes 2(x, y) = (2x^2 - 1, 2xy).

pub fn repeated_double(self, n: u32) -> Self

Computes 2^n * (x, y).

pub fn conjugate(self) -> Self

Computes the inverse of the point. We are using -(x, y) = (x, -y), i.e. the inverse of the group opertion is conjugation because the norm of every point in the circle is one.

pub fn antipode(self) -> Self

pub fn get_generator_of_subgroup(log_2_size: u32) -> Self

Returns the generator of the subgroup of order n = 2^log_2_size. We are using that 2^k * g is a generator of the subgroup of order 2^{31 - k}.

Trait Implementations

impl<F: IsField + HasCircleParams<F>> Add<&CirclePoint<F>> for CirclePoint<F>

type Output = CirclePoint<F>

The resulting type after applying the + operator.

fn add(self, rhs: &CirclePoint<F>) -> Self::Output

Performs the + operation.

impl<F: IsField + HasCircleParams<F>> Add<CirclePoint<F>> for &CirclePoint<F>

type Output = CirclePoint<F>

The resulting type after applying the + operator.

fn add(self, rhs: CirclePoint<F>) -> Self::Output

Performs the + operation.

impl<F: IsField + HasCircleParams<F>> Add for &CirclePoint<F>

Addition (i.e. group operation) between two points: (a, b) + (c, d) = (a * c - b * d, a * d + b * c)

type Output = CirclePoint<F>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<F: IsField + HasCircleParams<F>> Add for CirclePoint<F>

type Output = CirclePoint<F>

The resulting type after applying the + operator.

fn add(self, rhs: CirclePoint<F>) -> Self::Output

Performs the + operation.

impl<F: IsField + HasCircleParams<F>> AddAssign<&CirclePoint<F>> for CirclePoint<F>

fn add_assign(&mut self, rhs: &CirclePoint<F>)

Performs the += operation.

impl<F: IsField + HasCircleParams<F>> AddAssign for CirclePoint<F>

fn add_assign(&mut self, rhs: CirclePoint<F>)

Performs the += operation.

impl<F: Clone + IsField> Clone for CirclePoint<F>

fn clone(&self) -> CirclePoint<F>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<F: Debug + IsField> Debug for CirclePoint<F>

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

Formats the value using the given formatter.

impl<F: IsField + HasCircleParams<F>> Mul<u128> for &CirclePoint<F>

Multiplication between a point and a scalar (i.e. group operation repeatedly): (x, y) * n = (x ,y) + … + (x, y) n-times.

type Output = CirclePoint<F>

The resulting type after applying the * operator.

fn mul(self, scalar: u128) -> Self::Output

Performs the * operation.

impl<F: IsField + HasCircleParams<F>> Mul<u128> for CirclePoint<F>

type Output = CirclePoint<F>

The resulting type after applying the * operator.

fn mul(self, scalar: u128) -> Self::Output

Performs the * operation.

impl<F: IsField + HasCircleParams<F>> MulAssign<u128> for CirclePoint<F>

fn mul_assign(&mut self, scalar: u128)

Performs the *= operation.

impl<F: IsField + HasCircleParams<F>> PartialEq for CirclePoint<F>

Equality between two cricle points.

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.