Struct AffinePoint 

pub struct AffinePoint<F: FieldOps> {
    pub x: F,
    pub y: F,
    pub infinity: bool,
}

An affine point on a Weierstrass elliptic curve over F.

The point at infinity is represented by infinity = true; in that case the x and y fields are meaningless (set to zero by convention).

Fields

x: F

x coordinate

y: F

y coordinate

infinity: bool

true if and only if the ponit at infinity

Implementations

impl<F: FieldOps> AffinePoint<F>

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

Construct a finite affine point (x, y).

No on-curve check is performed; use WeierstrassCurve::contains if you need validation.

pub fn identity() -> Self

The point at infinity O (the group identity).

pub fn is_identity(&self) -> bool

Returns true if this is the point at infinity.

impl<F: FieldOps> AffinePoint<F>

pub fn negate(&self, curve: &WeierstrassCurve<F>) -> Self

Negate a point: -(x, y) = (x, −y − a₁x − a₃).

pub fn double(&self, curve: &WeierstrassCurve<F>) -> Self

Double a point: [2]P.

Uses the tangent-line formula for the general Weierstrass model:

λ = (3x₁² + 2a₂x₁ + a₄ − a₁y₁) / (2y₁ + a₁x₁ + a₃)
x₃ = λ² + a₁λ − a₂ − 2x₁
y₃ = λ(x₁ − x₃) − y₁ − a₁x₃ − a₃

Returns O when the tangent is vertical (i.e. 2y + a₁x + a₃ = 0).

pub fn add(&self, other: &Self, curve: &WeierstrassCurve<F>) -> Self

Add two points: P + Q.

Handles all cases:

• Either operand is O → return the other.
• P = Q → delegate to double.
• P = −Q (same x, opposite y) → return O.
• General chord:

λ  = (y₂ − y₁) / (x₂ − x₁)
x₃ = λ² + a₁λ − a₂ − x₁ − x₂
y₃ = λ(x₁ − x₃) − y₁ − a₁x₃ − a₃

pub fn scalar_mul( &self, k: &[u64], curve: &<AffinePoint<F> as PointOps>::Curve, ) -> Self

Multiply self by k

Arguments

• &self - Point on curve (type: Self)
• k - Integer (type: &[u64])
• curve - The curve we’re on (type: &<AffinePoint<F> as PointOps>::Curve)

Returns

The point k * self (type: Self)

Trait Implementations

impl<F: Clone + FieldOps> Clone for AffinePoint<F>

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<F> ConditionallySelectable for AffinePoint<F>

where F: FieldOps + Copy,

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<F> ConstantTimeEq for AffinePoint<F>

where F: FieldOps + Copy + ConstantTimeEq,

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<F: Debug + FieldOps> Debug for AffinePoint<F>

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

Formats the value using the given formatter.

impl<F> Display for AffinePoint<F>

where F: FieldOps + Display,

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

Formats the value using the given formatter.

impl<F> PartialEq for AffinePoint<F>

where F: FieldOps + ConstantTimeEq,

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<F> PointAdd for AffinePoint<F>

where F: FieldOps,

fn add(&self, other: &Self, curve: &Self::Curve) -> Self

Add a pair of points

impl<F> PointOps for AffinePoint<F>

where F: FieldOps,

type BaseField = F

The base field $\mathbb{F}_{p^M}$

type Curve = WeierstrassCurve<F>

The elliptic curve we’re working on

fn identity(_curve: &Self::Curve) -> Self

Returns the identity

fn is_identity(&self) -> bool

Returns true if and only if self is the identity

fn negate(&self, curve: &Self::Curve) -> Self

Negate a point

fn scalar_mul(&self, k: &[u64], curve: &Self::Curve) -> Self

Scalar multiplication [k]P (variable-time double-and-add).

impl<F: Copy + FieldOps> Copy for AffinePoint<F>

impl<F> Eq for AffinePoint<F>

where F: FieldOps + ConstantTimeEq,