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Improved Common-Multiplicand Multiplication and Fast Exponentiation by Exponent Decomposition
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 1997/06/25
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Information Security
arithmetic algorithm, exponentiation, multiplication, public key cryptography,
Full Text: PDF(284.3KB)>>
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.