Twisted Hessian curves

Daniel J.  Bernstein; Chitchanok Chuengsatiansup; David Kohel; Tanja Lange

Paper 2015/781 Original: eprint.iacr.org/2015/781 ↗

Twisted Hessian curves

Daniel J. Bernstein

Chitchanok Chuengsatiansup

David Kohel

Tanja Lange

Abstract

This paper presents new speed records for arithmetic on a large family of elliptic curves with cofactor 3: specifically, 8.77M per bit for 256-bit variable-base single-scalar multiplication when curve parameters are chosen properly. This is faster than the best results known for cofactor 1, showing for the first time that points of order 3 are useful for performance and narrowing the gap to the speeds of curves with cofactor 4.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2016-07-05: last updated; 2015-08-06: published
Short URL: https://ia.cr/2015/781
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2015/781,
      author = {Daniel J.  Bernstein and Chitchanok Chuengsatiansup and David Kohel and Tanja Lange},
      title = {Twisted Hessian curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2015/781},
      year = {2015},
      url = {https://eprint.iacr.org/2015/781}
}