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New Regular Radix-8 Scheme for Elliptic Curve Scalar Multiplication without Pre-Computation

The recent advances in mobile technologies have increased the demand for high performance parallel computing schemes. In this paper, we present a new algorithm for evaluating elliptic curve scalar multiplication that can be used on any abelian group. We show that the properties of the proposed algorithm enhance parallelism at both the point arithmetic and the field arithmetic levels. Then, we employ this algorithm in proposing a new hardware design for the implementation of an elliptic curve scalar multiplication on a prime extended twisted Edwards curve incorporating eight parallel operations. We further show that in comparison to the other simple side-channel attack protected schemes over prime fields, the proposed design of the extended twisted Edwards curve is the fastest scalar multiplication scheme reported in the literature.