**Twisted Hessian curves**

*Daniel J. Bernstein and Chitchanok Chuengsatiansup and 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.

**Category / Keywords: **public-key cryptography / efficiency, elliptic-curve arithmetic, double-base chains, fast arithmetic, Hessian curves, complete addition laws

**Original Publication**** (with minor differences): **LATINCRYPT 2015

**Date: **received 5 Aug 2015, last revised 5 Jul 2016

**Contact author: **authorcontact-hessian at box cr yp to

**Available format(s): **PDF | BibTeX Citation

**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.

**Version: **20160705:153534 (All versions of this report)

**Short URL: **ia.cr/2015/781

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