🎯

# Representing a point

We call a

`Point`

an element of the elliptic curve group, which we can represent with its coordinates. Let's define a `Point`

class to encapsulate the $x$ and $y$ coordinates in the generalised curve equation of $y^2 = x^3 + ax + b$**.**from typing import Optional

@dataclass

class Point:

x: Optional[int]

y: Optional[int]

curve: EllipticCurve

def __post_init__(self):

# Ignore validation for I

if self.x is None and self.y is None:

return

# Encapsulate int coordinates in FieldElement

self.x = FieldElement(self.x, self.curve.field)

self.y = FieldElement(self.y, self.curve.field)

# Verify if the point satisfies the curve equation

if self not in self.curve:

raise ValueError

**Point-compression:**To reduce the storage size for a curve point, one can also store a sign and the

`x `

coordinate. It is then possible to reconstruct the `y`

by calculating `sign * sqrt(x^3+a*x+b).`

Last modified 2mo ago