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Faster Group Operations on Elliptic Curves

Hisil, H., Wong, K.K.-H., Carter, G. and Dawson, E.

    This paper improves implementation techniques of Elliptic Curve Cryptography. We introduce new formulae and algorithms for the group law on Jacobi quartic, Jacobi intersection, Edwards, and Hessian curves. The proposed formulae and algorithms can save time in suitable point representations. To support our claims, a cost comparison is made with classic scalar multiplication algorithms using previous and current operation counts. Most notably, the best speeds are obtained from Jacobi quartic curves which provide the fastest timings for most scalar multiplication strategies benefiting from the proposed 2M + 5S + 1D point doubling and 7M + 3S + 1D point addition algorithms. Furthermore, the new addition algorithm provides an efficient way to protect against side channel attacks which are based on simple power analysis (SPA).
Cite as: Hisil, H., Wong, K.K.-H., Carter, G. and Dawson, E. (2009). Faster Group Operations on Elliptic Curves. In Proc. Seventh Australasian Information Security Conference (AISC 2009), Wellington, New Zealand. CRPIT, 98. Brankovic, L. and Susilo, W., Eds. ACS. 7-19.
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