Struct JacobiIntersectionPoint 

pub struct JacobiIntersectionPoint<F: FieldOps> {
    pub s: F,
    pub c: F,
    pub d: F,
}

An affine point $(s, c, d)$ on a Jacobi intersection.

Fields

s: F

The coordinate s of the point

c: F

The coordinate c of the point

d: F

The coordinate d of the point

Implementations

impl<F: FieldOps> JacobiIntersectionPoint<F>

pub fn new(s: F, c: F, d: F) -> Self

Creates a new point on a Jacobi intersection

The point should satisfy $$ s^2 + c^2 = 1 \quad a s^2 + d^2 = 1. $$

Arguments

• s - Element of F (type: F)
• c - Element of F (type: F)
• d - Element of F (type: F)

Returns

Returns the point on the Jacobi intersection (type: Self)

pub fn identity() -> Self

The neutral element $(0, 1, 1)$.

pub fn is_identity(&self) -> bool

Checks if the point is the indentity point

Arguments

• &self - A point on the curve (type: self)

Returns

True if and only if it is $(0,1,1)$ (type: bool)

impl<F: FieldOps> JacobiIntersectionPoint<F>

pub fn negate(&self, _curve: &JacobiIntersectionCurve<F>) -> Self

Negation: -(s, c, d) = (-s, c, d).

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

Affine addition formulas from the EFD:

s₃ = (c₂ s₁ d₂ + d₁ s₂ c₁)/(c₂² + (d₁ s₂)²)
c₃ = (c₂ c₁ - d₁ s₂ s₁ d₂)/(c₂² + (d₁ s₂)²)
d₃ = (d₁ d₂ - a s₁ c₁ s₂ c₂)/(c₂² + (d₁ s₂)²).

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

Affine doubling formulas from the EFD:

s₃ = 2c s d / (c² + (d s)²)
c₃ = (c² - d² s²) / (c² + (d s)²)
d₃ = (d² - a s² c²) / (c² + (d s)²).

pub fn scalar_mul(&self, k: &[u64], curve: &JacobiIntersectionCurve<F>) -> Self

Scalar multiplication on the curve

Multiplies a point by an integers

Arguments

• &self - Point on the curve (type: Self)
• k - An integer represented as a vec of u64 (type: &[u64])
• curve - The curve on which self lies (type: &JacobiIntersectionCurve<F>)

Returns

The point k * self (type: Self)

Trait Implementations

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

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<F> ConditionallySelectable for JacobiIntersectionPoint<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 JacobiIntersectionPoint<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 JacobiIntersectionPoint<F>

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

Formats the value using the given formatter.

impl<F> Display for JacobiIntersectionPoint<F>

where F: FieldOps + Display,

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

Formats the value using the given formatter.

impl<F: FieldOps> PartialEq for JacobiIntersectionPoint<F>

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: FieldOps> PointAdd for JacobiIntersectionPoint<F>

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

Add a pair of points

impl<F: FieldOps> PointOps for JacobiIntersectionPoint<F>

type BaseField = F

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

type Curve = JacobiIntersectionCurve<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 JacobiIntersectionPoint<F>

impl<F: FieldOps> Eq for JacobiIntersectionPoint<F>