Welcome to the resource topic for 2013/131
Title:
Two is the fastest prime: lambda coordinates for binary elliptic curves
Authors: Thomaz Oliveira, Julio López, Diego F. Aranha, Francisco Rodríguez-Henríquez
Abstract:In this work, we present new arithmetic formulas for a projective version of the affine point representation (x,x+y/x), for x\ne 0, which leads to an efficient computation of the scalar multiplication operation over binary elliptic curves.A software implementation of our formulas applied to a binary Galbraith-Lin-Scott elliptic curve defined over the field \mathbb{F}_{2^{254}} allows us to achieve speed records for protected/unprotected single/multi-core random-point elliptic curve scalar multiplication at the 127-bit security level. When executed on a Sandy Bridge 3.4GHz Intel Xeon processor, our software is able to compute a single/multi-core unprotected scalar multiplication in 69,500 and 47,900 clock cycles, respectively; and a protected single-core scalar multiplication in 114,800 cycles. These numbers are improved by around 2% and 46% on the newer Ivy Bridge and Haswell platforms, respectively, achieving in the latter a protected random-point scalar multiplication in 60,000 clock cycles.
ePrint: https://eprint.iacr.org/2013/131
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