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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Polynomial Multiplication over Binary Fields Using Charlier Polynomial Representation with Low Space Complexity
verfasst von : Sedat Akleylek, Murat Cenk, Ferruh Özbudak
Erschienen in: Progress in Cryptology - INDOCRYPT 2010
Verlag: Springer Berlin Heidelberg
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In this paper, we give a new way to represent certain finite fields
GF
(2
n
). This representation is based on Charlier polynomials. We show that multiplication in Charlier polynomial representation can be performed with subquadratic space complexity. One can obtain binomial or trinomial irreducible polynomials in Charlier polynomial representation which allows us faster modular reduction over binary fields when there is no desirable such low weight irreducible polynomial in other representations. This representation is very interesting for NIST recommended binary field
GF
(2
283
) since there is no ONB for the corresponding extension. We also note that recommended NIST and SEC binary fields can be constructed with low weight Charlier polynomials.