Cryptology ePrint Archive: Report 2007/441

Faster Group Operations on Elliptic Curves

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

Abstract: This paper is on improving implementation techniques of Elliptic Curve Cryptography. We introduce new addition formulae for Jacobi-quartic, Edwards, Hessian forms and new doubling formulae for Jacobi-quartic and Jacobi-intersection forms of elliptic curves. The new formulae speed up the group operations for each of these forms on suitable coordinate systems. To show this, a comparison is made in respect to their performance evaluations with classic point multiplication algorithms using the previous and current operation counts. The most significant outcomes are obtained from the modified Jacobi-quartic coordinates which provide the fastest timings for most point multiplication strategies and the fastest unified addition which costs 7M+3S+1D. The new unified addition formulae can be used to provide a natural way to protect against side channel attacks which are based on simple power analysis (SPA).

(M: The cost of field multiplication, S: The cost of field squaring, D: The cost of multiplication by a curve constant.)

Category / Keywords: Efficient elliptic curve arithmetic, unified addition, side channel attack.

Date: received 26 Nov 2007, last revised 29 Apr 2008

Contact author: h hisil at qut edu au

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Version: 20080429:164124 (All versions of this report)

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