Module coords 

Elliptic points coordinates

Elliptic points are defined differently for different types of curves:

• Curves in non-complete form (Weierstrass or Montgomery curves):
  Points have $(x, y)$ coordinates that must satisfy curve equation unless it’s point at infinity that has no coordinates (see points at infinity)
• Curves in complete form (Edwards curves):
  Points always have $(x, y)$ coordinates that must satisfy curve equation

Usage

This module provides various traits that can be used to retrieve coordinates. Refer to curve documentation to see what coordinates it exposes.

use generic_ec::{Point, coords::HasAffineX, curves::Secp256k1};

let point = Point::<Secp256k1>::generator().to_point();
let x = point.x();

In generic code

Generic code needs to explicitly state that it needs access to coordinates by specifying it in bounds:

use generic_ec::{Point, Curve, coords::HasAffineX};

fn func_that_accesses_x_coord<E: Curve>(point: &Point<E>)
where
    Point<E>: HasAffineX<E>
{
    let x = point.x();
    // ...
}

Note: it’s not recommended to access points coordinates in generic code unless it’s really necessary. Practically it lessens variety of curves that can work with your code. If you need unique representation of a point, use its byte representation.

Curves support

Some curve implementations intentionally chosen not to expose coordinates, so they, for instance, can expose $y$ coordinate but hide $x$.

Structs

Coordinate

Affine coordinate of a point on elliptic curve

Coordinates

Affine $x, y$ coordinates of a point on elliptic curve

Enums

Parity

Parity of coordinate

Sign

Sign of coordinate

Traits

AlwaysHasAffineX

Point always has affine $x$ coordinate (for Edwards curves and non-zero points)

AlwaysHasAffineXY

Point is uniquely represented by affine $x$ and $y$ coordinates (for Edward curves and non-zero points)

AlwaysHasAffineY

Point always has affine $y$ coordinate (for Edwards curves and non-zero points)

AlwaysHasAffineYAndSign

Point is uniquely represented by affine $y$ coordinate and sign of $x$ coordinate (for Edwards curves)

HasAffineX

Point has affine $x$ coordinate

HasAffineXAndParity

Point is uniquely represented by $x$ coordinate and parity of $y$ coordinate

HasAffineXY

Point is uniquely represented by affine $x, y$ coordinates

HasAffineY

Point has affine $y$ coordinate