Addition-Subtraction Chain for 160 bit Integers by using 2's Complement

Speeding up the scalar multiplication k.P is the major point in elliptic curve cryptosystem efficiency. The Addition-Subtraction (AS) Chain is efficient tool to do that where integer k is fixed and Point P is variable. Since the optimization problem to find the shortest AS Chain is NP-hard, many algorithms to get sub-optimal AS Chain in polynomial time are proposed. The window method is a class of theses algorithms. In this paper an algorithm for finding a shorter AS Chain is proposed. This algorithm is based on window method with small width by using 2’s Complement for 160 bit integers. It is shown practically that proposed algorithm more efficient than the last result in the subject with 20% improvement.

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