NAF and Optimal Normal Basis of Type Ⅱ and Efficient Exponentiation in GF(2n) 


Vol. 34,  No. 1, pp. 21-27, Jan.  2009


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  Abstract

We present an efficient exponentiation algorithm for a finite field GF(2n) determined by an optimal normal basis of type Ⅱ using signed digit representation of the exponents. Our signed digit representation uses a non?adjacent form (NAF) for GF(2n). It is generally believed that a signed digit representation is hard to use when a normal basis is given because the inversion of a normal element requires quite a computational delay. However our result shows that a special normal basis, called an optimal normal basis (ONB) of type Ⅱ, has a nice property which admits an effective exponentiation using signed digit representations of the exponents.

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  Cite this article

[IEEE Style]

S. Kwon, B. Go, N. Koo, C. H. Kim, "NAF and Optimal Normal Basis of Type Ⅱ and Efficient Exponentiation in GF(2n)," The Journal of Korean Institute of Communications and Information Sciences, vol. 34, no. 1, pp. 21-27, 2009. DOI: .

[ACM Style]

Soonhak Kwon, Byeonghwan Go, Namhun Koo, and Chang Hoon Kim. 2009. NAF and Optimal Normal Basis of Type Ⅱ and Efficient Exponentiation in GF(2n). The Journal of Korean Institute of Communications and Information Sciences, 34, 1, (2009), 21-27. DOI: .

[KICS Style]

Soonhak Kwon, Byeonghwan Go, Namhun Koo, Chang Hoon Kim, "NAF and Optimal Normal Basis of Type Ⅱ and Efficient Exponentiation in GF(2n)," The Journal of Korean Institute of Communications and Information Sciences, vol. 34, no. 1, pp. 21-27, 1. 2009.

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pISSN : 1226 - 4717
eISSN : 2287 - 3880