On multiplication in finite fields

Date

2010-04-01

Author

Cenk, Murat
Özbudak, Ferruh

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We present a method for multiplication in finite fields which gives multiplication algorithms with improved or best known bilinear complexities for certain finite fields. Our method generalizes some earlier methods and combines them with the recently introduced complexity notion (M) over cap (q)(l), which denotes the minimum number of multiplications needed in F-q in order to obtain the coefficients of the product of two arbitrary l-term polynomials modulo x(l) in F-q[x]. We study our method for the finite fields F(q)n, where 2 <= n <= 18 and q = 2, 3,4 and we improve or reach the currently best known bilinear complexities. We also give some applications in cryptography. (C) 2010 Published by Elsevier Inc.

Subject Keywords

Finite fields, Algebraic function fields, Bilinear complexity

URI

https://hdl.handle.net/11511/32570

Journal

JOURNAL OF COMPLEXITY

DOI

https://doi.org/10.1016/j.jco.2009.11.002

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

M. Cenk and F. Özbudak, “On multiplication in finite fields,” JOURNAL OF COMPLEXITY, pp. 172–186, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32570.