Twisted Hessian Isogenies

Thinh Dang; Dustin Moody

Paper 2019/1003

Twisted Hessian Isogenies

Thinh Dang and Dustin Moody

Abstract

Elliptic curves are typically defined by Weierstrass equations. Given a kernel, the well-known Velu’s formula shows how to explicitly write down an isogeny between Weierstrass curves. However, it is not clear how to do the same on other forms of elliptic curves without isomorphisms mapping to and from the Weierstrass form. Previous papers have shown some isogeny formulas for (twisted) Edwards, Huff, and Montgomery forms of elliptic curves. Continuing this line of work, this paper derives an explicit formula for isogenies between elliptic curves in (twisted) Hessian form.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Preprint. MINOR revision.
Keywords: Isogeny Elliptic Curves Hessian curves
Contact author(s): dustin moody @ nist gov
History: 2019-09-05: received
Short URL: https://ia.cr/2019/1003
License: CC BY

BibTeX

@misc{cryptoeprint:2019/1003,
      author = {Thinh Dang and Dustin Moody},
      title = {Twisted Hessian Isogenies},
      howpublished = {Cryptology ePrint Archive, Paper 2019/1003},
      year = {2019},
      note = {\url{https://eprint.iacr.org/2019/1003}},
      url = {https://eprint.iacr.org/2019/1003}
}