A comment on "An efficient common-multiplicand-multiplication method to the Montgomery algorithm for speeding up exponentiation"

Authors:
Da-Zhi Sun;Jin-Peng Huai;Zhen-Fu Cao
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;Department of Computer Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, PR China
Venue:
Information Sciences: an International Journal
Year:
2013

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An efficient common-multiplicand-multiplication method to the Montgomery algorithm for speeding up exponentiation

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Abstract

In 2009, Wu proposed a fast modular exponentiation algorithm and claimed that the proposed algorithm on average saved about 38.9% and 26.68% of single-precision multiplications as compared to Dusse-Kaliski's Montgomery algorithm and Ha-Moon's Montgomery algorithm, respectively. However, in this comment, we demonstrate that Wu's algorithm on average reduces the number of single-precision multiplications by at most 22.43% and 6.91%, when respectively compared with Dusse-Kaliski's version and Ha-Moon's version. That is, the computational efficiency of Wu's algorithm is obviously overestimated.