module Ed25519::Curve

Overview

ed25519 is Twisted Edwards curve with equation of

−x² + y² = 1 − (121665/121666) * x² * y²

Defined in:

ed25519/curve.cr

Constant Summary

A = BigInt.new(-1)

Param: a

D = BigInt.new("37095705934669439343138083508754565189542113879843219016388785533085940283555")

Equal to -121665/121666 over finite field. Negative number is P - number, and division is invert(number, P)

Gx = BigInt.new("15112221349535400772501151409588531511454012693041857206046113283949847762202")

Base point (x, y) aka generator point

Gy = BigInt.new("46316835694926478169428394003475163141307993866256225615783033603165251855960")

H = BigInt.new(8)

Cofactor

L = CURVE_ORDER

Subgroup order: how many points ed25519 has

N = CURVE_ORDER

P = (Ed25519::Two ** BigInt255) - (BigInt.new(19))

Finite field 𝔽p over which we'll do calculations