Struct eccoxide::curve::projective::Point

pub struct Point<FE> {
    pub x: FE,
    pub y: FE,
    pub z: FE,
}

Projective point with field element FE

Affine point associated with (X,Y,Z) : (X/Z, Y/Z)

Note that 2 points are equal if they are in the same equivalence class, which is determined with 4 FieldElement multiplications.

Example: (1,2,1) and (2,4,2) are equal

Fields

x: FE

y: FE

z: FE

Implementations

impl<FE> Point<FE> where
    FE: Field + CtEqual,
    for<'a, 'b> &'a FE: Mul<&'b FE, Output = FE>, 

pub fn is_infinity(&self) -> Choice

Check if a point is at infinity

impl<FE> Point<FE> where
    FE: Field, 

pub fn infinity() -> Self

Returns the point at infinity

pub fn from_affine(p: &Point<FE>) -> Self

impl<FE> Point<FE> where
    FE: Field,
    for<'a, 'b> &'a FE: Add<&'b FE, Output = FE>,
    for<'a, 'b> &'a FE: Mul<&'b FE, Output = FE>,
    for<'a, 'b> &'a FE: Sub<&'b FE, Output = FE>, 

pub fn normalize(&mut self)

impl<FE: Field> Point<FE>

pub fn add_different<'x, 'y, C: WeierstrassCurve<FieldElement = FE>>(
    &'x self,
    other: &'y Point<FE>,
    curve: C
) -> Point<FE> where
    for<'a> &'a FE: Add<FE, Output = FE>,
    for<'a> &'a FE: Mul<FE, Output = FE>,
    for<'a> &'a FE: Sub<FE, Output = FE>,
    for<'a, 'b> &'a FE: Add<&'b FE, Output = FE>,
    for<'a, 'b> &'a FE: Mul<&'b FE, Output = FE>,
    for<'a, 'b> &'a FE: Sub<&'b FE, Output = FE>, 

pub fn add_different_a0<'x, 'y, C: WeierstrassCurve<FieldElement = FE> + WeierstrassCurveA0>(
    &'x self,
    other: &'y Point<FE>,
    curve: C
) -> Point<FE> where
    for<'a> &'a FE: Add<FE, Output = FE>,
    for<'a> &'a FE: Mul<FE, Output = FE>,
    for<'a> &'a FE: Sub<FE, Output = FE>,
    for<'a, 'b> &'a FE: Add<&'b FE, Output = FE>,
    for<'a, 'b> &'a FE: Mul<&'b FE, Output = FE>,
    for<'a, 'b> &'a FE: Sub<&'b FE, Output = FE>, 

impl<FE> Point<FE> where
    FE: Field,
    for<'a> &'a FE: Add<FE, Output = FE>,
    for<'a> &'a FE: Mul<FE, Output = FE>,
    for<'a> &'a FE: Sub<FE, Output = FE>,
    for<'a, 'b> &'a FE: Add<&'b FE, Output = FE>,
    for<'a, 'b> &'a FE: Mul<&'b FE, Output = FE>,
    for<'a, 'b> &'a FE: Sub<&'b FE, Output = FE>, 

pub fn double<C: WeierstrassCurve<FieldElement = FE>>(&self, curve: C) -> Self

pub fn double_a0<C: WeierstrassCurve<FieldElement = FE> + WeierstrassCurveA0>(
    &self,
    curve: C
) -> Self

pub fn to_affine(&self) -> Option<Point<FE>>

pub fn scale<C: WeierstrassCurve<FieldElement = FE>>(
    &self,
    n: &[u8],
    curve: C
) -> Self

pub fn scale_a0<C: WeierstrassCurve<FieldElement = FE> + WeierstrassCurveA0>(
    &self,
    n: &[u8],
    curve: C
) -> Self

pub fn add_or_double<'b, C: WeierstrassCurve<FieldElement = FE>>(
    &self,
    other: &'b Point<FE>,
    curve: C
) -> Point<FE>

pub fn add_or_double_a0<'b, C: WeierstrassCurve<FieldElement = FE> + WeierstrassCurveA0>(
    &self,
    other: &'b Point<FE>,
    curve: C
) -> Point<FE>

Trait Implementations

impl<FE: Clone> Clone for Point<FE>

fn clone(&self) -> Point<FE>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<FE: Debug> Debug for Point<FE>

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

Formats the value using the given formatter.

impl<FE> Neg for Point<FE> where
    FE: Neg<Output = FE>, 

type Output = Point<FE>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<'a, FE> Neg for &'a Point<FE> where
    FE: Clone + Neg<Output = FE>,
    &'a FE: Neg<Output = FE>, 

type Output = Point<FE>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<FE: Field + CtEqual> PartialEq<Point<FE>> for Point<FE> where
    for<'a, 'b> &'a FE: Mul<&'b FE, Output = FE>, 

fn eq(&self, other: &Point<FE>) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<FE: Field> TryFrom<Point<FE>> for Point<FE> where
    for<'a> &'a FE: Add<FE, Output = FE>,
    for<'a> &'a FE: Mul<FE, Output = FE>,
    for<'a> &'a FE: Sub<FE, Output = FE>,
    for<'a, 'b> &'a FE: Add<&'b FE, Output = FE>,
    for<'a, 'b> &'a FE: Mul<&'b FE, Output = FE>,
    for<'a, 'b> &'a FE: Sub<&'b FE, Output = FE>, 

type Error = AffineAtInfinity

The type returned in the event of a conversion error.

fn try_from(p: Point<FE>) -> Result<Point<FE>, Self::Error>

Performs the conversion.

impl<FE: Field + CtEqual> Eq for Point<FE> where
    for<'a, 'b> &'a FE: Mul<&'b FE, Output = FE>,