A note on asynchronous multi-exponentiation algorithm using binary representation

Authors:
Da-Zhi Sun;Jin-Peng Huai;Jian-Xin Li
Affiliations:
School of Computer Science and Technology, Tianjin University, No. 92 Weijin Road, Nankai District, Tianjin 300072, PR China and School of Computer Science, Beihang University, Beijing 100083, PR ...;School of Computer Science, Beihang University, Beijing 100083, PR China;School of Computer Science, Beihang University, Beijing 100083, PR China
Venue:
Information Processing Letters
Year:
2012

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Abstract

A basic but expensive operation in implementations of several famous public-key cryptosystems is the computation of the multi-exponentiation in a certain finite multiplication group. In 2007, Yang et al. presented an interesting asynchronous multi-exponentiation algorithm called the SU"t method, which uses the binary representations for the exponents. In this note, we analyze the computational efficiency of the SU"t method by modeling the scanning process as a Markov chain. It shows that their computational efficiency result is incorrect. Moreover, we make a performance comparison among the published techniques and show that the performance of a modified sliding window method is better than that of the SU"t method, when there are 4 or more additional registers. We hope that our research will be convenient to the development of the cryptographic devices.