I'm interested exploring key derivation and threshold signature protocol that require point arithmetic (addition) on the private scalar values and $S$ values of the signatures in ed25519. ...
I currently try to implement Ed25519 following this draft. I have implemented every field operation except the reduction by the group order $q$ (in chapter 5). I looked for a reduction algorithm and ...
I would like to map integer values to points on Ed25519, and then back again. Is there a technique that takes advantage of the specific structure of Ed25519?