Cryptology ePrint Archive: Report 2008/522

Twisted Edwards Curves Revisited

Huseyin Hisil and Kenneth Koon-Ho Wong and Gary Carter and Ed Dawson

Abstract: This paper introduces fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a wide range of applications. Notably, the new addition algorithm uses 8M for suitably selected curve constants. In comparison, the fastest point addition algorithms for (twisted) Edwards curves stated in the literature use 9M+1S. It is also shown that the new addition algorithm can be implemented with four processors dropping the effective cost to 2M. This implies an effective speed increase by the full factor of 4 over the sequential case. Our results allow faster implementation of elliptic curve scalar multiplication. In addition, the new point addition algorithm can be used to provide a natural protection from side channel attacks based on simple power analysis (SPA).

(M: Multiplication, S: Squaring)

Category / Keywords: public-key cryptography / Effcient elliptic curve arithmetic, unifi ed addition, side channel attack, SPA.

Date: received 14 Dec 2008

Contact author: h hisil at isi qut edu au

Available format(s): PDF | BibTeX Citation

Version: 20081216:124446 (All versions of this report)

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