Square Root Algorithm in Fq for Special Class of Finite Fields 


Vol. 38,  No. 9, pp. 759-764, Sep.  2013


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  Abstract

We present a square root algorithm in F<SUB>q</SUB> which generalizes Atkin"s square root algorithm [9] for finite field F<SUB>q</SUB> of q elements where q=5(mod 8) and Kong et al."s algorithm [11] for the case q≡9 (mod 16) . Our algorithm precomputes ζ a primitive 2<SUP>s</SUP> -th root of unity where s is the largest positive integer satisfying 2<SUP>s</SUP> lq-1, and is applicable for the cases when s is small. The proposed algorithm requires one exponentiation for square root computation and is favorably compared with the algorithms of Atkin, Muller and Kong et al.

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  Cite this article

[IEEE Style]

N. Koo, G. H. Jo, S. Kwon, "Square Root Algorithm in Fq for Special Class of Finite Fields," The Journal of Korean Institute of Communications and Information Sciences, vol. 38, no. 9, pp. 759-764, 2013. DOI: .

[ACM Style]

Namhun Koo, Gooc Hwa Jo, and Soonhak Kwon. 2013. Square Root Algorithm in Fq for Special Class of Finite Fields. The Journal of Korean Institute of Communications and Information Sciences, 38, 9, (2013), 759-764. DOI: .

[KICS Style]

Namhun Koo, Gooc Hwa Jo, Soonhak Kwon, "Square Root Algorithm in Fq for Special Class of Finite Fields," The Journal of Korean Institute of Communications and Information Sciences, vol. 38, no. 9, pp. 759-764, 9. 2013.

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pISSN : 1226 - 4717
eISSN : 2287 - 3880