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Trends in Applied Sciences Research
  Year: 2012 | Volume: 7 | Issue: 3 | Page No.: 240-247
DOI: 10.3923/tasr.2012.240.247
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A New CMM-NAF Modular Exponentiation Algorithm by using a New Modular Multiplication Algorithm

Abdalhossein Rezai and Parviz Keshavarzi

This study presents a novel modular multiplication algorithm based on a new multiplier Non-Adjacent Form (NAF). In this new multiplier representation, the sliding window method is applied on the canonical recoded multiplier to reduce the average number of multiplier digits and thereby the average number of the required clock cycle for the modular multiplication algorithm. Moreover, a new and efficient modular exponentiation algorithm is presented based on this new modular multiplication algorithm, Common-Multiplicand-Multiplication (CMM) method and parallel structure. In this new CMM-NAF modular exponentiation algorithm, not only the common part of the modular multiplication is computed once rather than several times but also the modular multiplication and modular squaring operations are performed in parallel. Our analysis shows that the average number of required clock cycle in the proposed CMM-NAF modular exponentiation algorithm is reduced in comparison with other modular exponentiation algorithms considerably.
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How to cite this article:

Abdalhossein Rezai and Parviz Keshavarzi, 2012. A New CMM-NAF Modular Exponentiation Algorithm by using a New Modular Multiplication Algorithm. Trends in Applied Sciences Research, 7: 240-247.

DOI: 10.3923/tasr.2012.240.247






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