Tight lower bound for average number of terms in optimal double-base number system using information-theoretic tools

Abstract

We propose to use information-theoretic tools for analyzing the number of terms in the optimal double-base number system (DBNS). Most previous works analyze the largest number we obtain from the optimal DBNS for 0≤m<2n. They show that the largest number would be in Θ(n/log⁡n). On the other hands, when one analyze the performance of a cryptographic algorithm, it is more common to consider the average number of terms. One believes that we may be able have smaller asymptotic number for the average number. Unfortunately, using tools in information theory, we show in this paper that the average number is also in Θ(n/log⁡n).