Improved Common-Multiplicand Multiplication and Fast Exponentiation by Exponent Decomposition

Sung-Ming YEN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E80-A   No.6   pp.1160-1163
Publication Date: 1997/06/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Information Security
arithmetic algorithm,  exponentiation,  multiplication,  public key cryptography,  

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The technique of common-multiplicand multiplication, CMM, is modified and the similar approach is utilized to enhance the performance of a recently proposed fast exponentiation algorithm by exponent decomposition. On average, the improved exponentiation, its original version, and the traditional right to left binary exponentiation algorithm take 1.292m+11,1.375m+3, and 1.5m multiplications, respectively where m is the bit length of the exponent. Finally, it is shown how to improve the overall performance of an exponentiation by employing the improved exponentiation algorithm, the improved CMM algorithm , and any general purpose fast multiplication algorithm.