Complements and signed digit representations: Analysis of a multi-exponentiation-algorithm of Wu, Lou, Lai and Chang

TL;DR

This paper critically re-evaluates a multi-exponentiation algorithm using signed digit representations, revealing that the original analysis was incorrect and that the complement operation is unnecessary for its performance.

Contribution

The paper corrects the analysis of Wu, Lou, Lai, and Chang's algorithm and shows that the complement step can be omitted without affecting efficiency.

Findings

Original analysis was incorrect

Complement operation has negligible impact on performance

Omitting the complement simplifies the algorithm

Abstract

Wu, Lou, Lai and Chang proposed a multi-exponentiation algorithm using binary complements and the non-adjacent form. The purpose of this paper is to show that neither the analysis of the algorithm given by its original proposers nor that by other authors are correct. In fact it turns out that the complement operation does not have significant influence on the performance of the algorithm and can therefore be omitted.