Parallelization of Point Operations on Conic Curves over Finite Field GF(2n)

Abstract

It becomes more and more important to design high-speed parallel cryptographic algorithms due to a growing need for information security. Conic curves cryptography is a new developing direction in the field of information security in recent years and there are less works focused on the parallel encryption algorithms for conic curves crypto system. This paper proposes four parallel algorithms for conic curves cryptosystem over finite field GF(2 n ). One parallel algorithm of modular-multiplication is designed by analyzing its data dependency and making some modifications of several steps. In order to figure out the average runtime, we consider the probability distributions of different cases to compute the mathematical expectation. The operations of point-addition, point-double and pointmultiplication, three fundamental point operations in conic curves cryptosystem over finite field GF(2 n ), are paralleled based on this parallel algorithm of modular-multiplication and two parallel algorithms we proposed before. Time complexities and speedup ratios of the parallel algorithms and the sequential algorithms are calculated to make the quantitative comparison. The performance evaluation shows better efficiencies of the proposed parallel algorithms compared to the traditional algorithms.