3 years ago

# A fast optimal parallel algorithm for a short addition chain

Hazem M. Bahig

### Abstract

Given a natural number e, an addition chain for e is a finite sequence of numbers having the following properties: (1) the first number is one, (2) every element is the sum of two earlier elements, and (3) the given number occurs at the end of the sequence. We introduce a fast optimal algorithm to generate a chain of short length for the number e of n-bits. The algorithm is based on the right–left binary strategy and barrel shifter circuit. The algorithm uses $$O((\frac{n}{\log {n}})^2)$$ processors and runs in $$O((\log {n})^2)$$ time under exclusive read exclusive write parallel random access machine.

DOI: 10.1007/s11227-017-2129-0

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