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2018-02-20 12:56:14 +0200 commented answer ed25519 elliptic curve

Did you mean Curve25519?

No. I mean the curve used by ed25519 signature scheme. It is birationally equivalent to E = EllipticCurve(GF(2^255-19),[0,486662,0,1,0]), but I wish to define a Sage EllipticCurve for the ed25519 curve:

  -x^2 + y^2 = 1 - (121665/121666) x^2 y^2

I wish I could express, for example, Diffie-Hellman, with simple Sage code like:

  E = EllipticCurve(???)
  P = ... base point...
  a, b = random field elements
  A = a*P
  B = b*P
  a*B == b*A  # Returns True

I would like to experiment with ed25519 signatures, including distributed signing. I need Sage to generate the correct test data.

I suppose I could convert coordinates in x15519 to ed25519 coordinates as Travis says. However, I don't want to loose nice Sage syntax.

2018-02-20 03:30:37 +0200 received badge  Student (source)
2018-02-20 00:49:29 +0200 asked a question ed25519 elliptic curve

Is is possible to represent the elliptic curve used by the ed25519 signature scheme in Sage? How?

EllipticCurve takes parameters for the long Weierstrass form of an Elliptic curve. But I don't know how to convert the ed25519 curve to that form, if it even is possible.