Twisted Hessian curves

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

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Paper 2015/781

Twisted Hessian curves

Daniel J. Bernstein, Chitchanok Chuengsatiansup, David Kohel, and 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.

Note: Erratum: At the end of the proof of Theorem 4.4, 27a^3X_1^9 = dX_1^3Y_1^3Z_1^3 = da^2X_1^3 should say 27a^3X_1^9 = d^3X_1^3Y_1^3Z_1^3 = d^3a^2X_1^3.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Minor revision. LATINCRYPT 2015
Keywords: efficiency elliptic-curve arithmetic double-base chains fast arithmetic Hessian curves complete addition laws
Contact author(s): authorcontact-hessian @ box cr yp to
History: 2016-07-05: revised; 2015-08-06: received; See all versions
Short URL: https://ia.cr/2015/781
License: CC BY

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},
      note = {\url{https://eprint.iacr.org/2015/781}},
      url = {https://eprint.iacr.org/2015/781}
}