Efficient τ-Adic Sliding Window Method on Elliptic Curve Cryptosystems

摘要

Wo introduce efficient algorithms for the τ-adic sliding window method, which is a scalar multiplication algorithm on Koblitz curves over F_2~m. The τ-adic sliding window method is divided into two parts: the precornputation part and the main computation part. Until now, there has been no efficient way to deal with the precornputation part; the required points of the elliptic curves were calculated one by one. We propose two fast algorithms for the precomputation part. One of the proposed methods decreases the cost of the precornputation part by approximately 80%. Since more points are calculated, the total cost of scalar multiplication is decreased by approximately 7.5%.