Binary addition chain on EREW PRAM

Abstract

An addition chain for a natural number x of n bits is a sequence of numbers a 0, a 1, ... , a l , such that a 0 = 1, a l = x, and a k = a i + a j with 0 ≤ i,j < k ≤ l. The addition chain problem is what is the minimal number of additions needed to compute x starting from 1? In this paper, we present a new parallel algorithm to generate a short addition chain for x. The algorithm has running time O(log2 n) using polynomial number processors under EREW PRAM (exclusive read exclusive write parallel random access machine). The algorithm is faster than previous algorithms and is based on binary method. © 2011 Springer-Verlag.