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10. Polynomial Multiplication over Binary Fields Using Charlier Polynomial Representation with Low Space Complexity

Author

Akleylek, Sedat, Cenk, Murat, Özbudak, Ferruh, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Gong, Guang, editor, and Gupta, Kishan Chand, editor

Published
2010
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13. Polynomial Multiplication over Binary Fields Using Charlier Polynomial Representation with Low Space Complexity

Author

Ferruh Özbudak, Murat Cenk, Sedat Akleylek, and Ondokuz Mayıs Üniversitesi

Subjects
Discrete mathematics, subquadratic space complexity, Polynomial, polynomial multiplication, Charlier polynomials, Alternating polynomial, Irreducible polynomial, binary field representation, Mathematics::Classical Analysis and ODEs, Trinomial, Square-free polynomial, Combinatorics, Finite field, Factorization of polynomials, Mathematics
Abstract

DIT;DRDO;DST;MSRI 11th International Conference on Cryptology in India, INDOCRYPT 2010 -- 12 December 2010 through 15 December 2010 -- Hyderabad -- 83330 In this paper, we give a new way to represent certain finite fields GF(2n ). 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(2283) 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. © 2010 Springer-Verlag Berlin Heidelberg. TBAG-109T672 The second and third authors are partially supported by TÜBİTAK under Grant No.TBAG-107T826 and and TBAG-109T672. The authors thank the anonymous referees for their detailed and very helpful comments.

Published
2010

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