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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