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A Fast Square Root Computation Using the Frobenius Mapping

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2836)

Abstract

The objective of this paper is to give a fast square root computation method. First the Frobenius mapping is adopted. Then a lot of calculations over an extension field are reduced to that over a proper subfield by the norm computation. In addition a inverse square root algorithm and an addition chain are adopted to save the computation cost. All of the above-mentioned steps have been proven to make the proposed algorithm much faster than the conventional algorithm. From the table which compares the computation between the conventional and the proposed algorithm, it is clearly shown that the proposed algorithm accelerates the square root computation 10 times and 20 times faster than the conventional algorithm in F p 11 and F p 12 respectively. At the same time, the proposed algorithm reduces the computation cost 10 times and 20 times less than the conventional algorithm.

Keywords

Elliptic Curve Computation Cost Conventional Algorithm Binary Method Addition Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Dept. of Communication Network EngineeringOkayama UniversityOkayama-shiJapan

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