Analysis of the Dimitrov-Jullien-Miller Recoding Algorithm

Wu-Chuan YANG  Ching-Po HUNG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E99-A   No.1   pp.139-144
Publication Date: 2016/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E99.A.139
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
average joint Hamming ratio (AJHR),  binary signed-digit representation recoding,  double-exponentiation,  

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In 2000, Dimitrov, Jullien, and Miller proposed an efficient and simple double-exponentiation algorithm based on a signed-digit recoding algorithm. The average joint Hamming ratio (AJHR) was reduced from 0.556 to 0.534 by using the recoding algorithm. In this paper, the DJM recoding algorithm was extended to three types: the 3-digit sliding window, the 1-digit right-to-left sliding window, and the 1-digit left-to-right sliding window. The average joint Hamming ratios of the three cases were 0.521, 0.515, and 0.511, respectively.