Eddy255 is a prime-order elliptic curve that embeds the Edwards curve ed25519, i.e. the order of Eddy255 is equal to the base field size of ed25519(2^255 - 19).
This repository contains the parameters for the curve, as well as a reference implementation of the curve using arkworks. Additionally, it includes a script to check the SafeCurves criteria for the curve (and some other generation utilities).
The primary use case for Eddy255 is to provide a curve where we can perform native-computation for ed25519 EC operations. This right-field arithmetic is particularly useful for constructing zero-knowledge proofs verifying knowledge of EDDSA signatures, for instance with the Spartan proving system, which uses the IPA commitment scheme.
This was found using eccons thanks to kwantam and Srinath Setty.
A related curve is Yafa-108/146, which also embeds ed25519, but with a pairing-friendly curve. Eddy255 is much smaller (~2x bits) but it is not pairing-friendly.
