Travis's profile - activity

Did you mean Curve25519? It looks like the standard way to write Curve 25519 is already in long Weirstrass form (see the wiki site: wikipedia.org/wiki/Curve25519). In Sage we can build this as:

E = EllipticCurve(GF(2^255-19),[0,486662,0,1,0])

I verified that the trace matched that listed on the safecurves site. Namely,

E.trace_of_frobenius() == -221938542218978828286815502327069187962

The curve used in the signature scheme Ed25519 (as explained on wikipedia.org/wiki/EdDSA#Ed25519 ), is birationaly equivalent to Curve25519, which is what we constructed above. A change of variables is given in the wikipedia entry.

I hope this helps,

Travis