Struct EdwardsProjectivePoint 

pub struct EdwardsProjectivePoint<E: IsEllipticCurve>(/* private fields */);

Implementations

impl<E: IsEllipticCurve + IsEdwards> EdwardsProjectivePoint<E>

pub fn new( value: [FieldElement<E::BaseField>; 3], ) -> Result<Self, EllipticCurveError>

Creates an elliptic curve point giving the projective [x: y: z] coordinates.

pub fn x(&self) -> &FieldElement<E::BaseField>

Returns the x coordinate of the point.

pub fn y(&self) -> &FieldElement<E::BaseField>

Returns the y coordinate of the point.

pub fn z(&self) -> &FieldElement<E::BaseField>

Returns the z coordinate of the point.

pub fn coordinates(&self) -> &[FieldElement<E::BaseField>; 3]

Returns a tuple [x, y, z] with the coordinates of the point.

pub fn to_affine(&self) -> Self

Creates the same point in affine coordinates. That is, returns [x / z: y / z: 1] where self is [x: y: z]. Panics if self is the point at infinity.

Trait Implementations

impl<E: Clone + IsEllipticCurve> Clone for EdwardsProjectivePoint<E>

fn clone(&self) -> EdwardsProjectivePoint<E>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<E: Debug + IsEllipticCurve> Debug for EdwardsProjectivePoint<E>

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

Formats the value using the given formatter.

impl<E: IsEdwards> FromAffine<<E as IsEllipticCurve>::BaseField> for EdwardsProjectivePoint<E>

fn from_affine( x: FieldElement<E::BaseField>, y: FieldElement<E::BaseField>, ) -> Result<Self, EllipticCurveError>

impl<E: IsEdwards> IsGroup for EdwardsProjectivePoint<E>

fn neutral_element() -> Self

Returns the point at infinity (neutral element) in projective coordinates.

Safety

• The values [0, 1, 1] are the canonical representation of the neutral element in the Edwards curve, meaning they are guaranteed to be a valid point.
• unwrap() is used because this point is known to be valid, so there is no need for additional runtime checks.

fn operate_with(&self, other: &Self) -> Self

Computes the addition of self and other using the Edwards curve addition formula.

This implementation follows Equation (5.38) from “Moonmath” (page 97).

Safety

• The function assumes both self and other are valid points on the curve.
• The resulting coordinates are computed using a well-defined formula that maintains the elliptic curve invariants.
• unwrap() is safe because the formula guarantees the result is valid.

fn neg(&self) -> Self

Returns the additive inverse of the projective point p

Safety

• Negating the x-coordinate of a valid Edwards point results in another valid point.
• unwrap() is safe because negation does not break the curve equation.

fn is_neutral_element(&self) -> bool

Check if an element the neutral element.

fn operate_with_self<T: IsUnsignedInteger>(&self, exponent: T) -> Self

Applies the group operation times times with itself The operation can be addition or multiplication depending on the notation of the particular group.

impl<E: IsEllipticCurve> PartialEq for EdwardsProjectivePoint<E>

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<E: IsEllipticCurve> Eq for EdwardsProjectivePoint<E>