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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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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.