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http://dx.doi.org/10.13067/JKIECS.2017.12.4.621

On Implementations of Algorithms for Fast Generation of Normal Bases and Low Cost Arithmetics over Finite Fields  

Kim, Yong-Tae (Dept. of Mathematics Education, Gwangju National University of Education)
Publication Information
The Journal of the Korea institute of electronic communication sciences / v.12, no.4, 2017 , pp. 621-628 More about this Journal
Abstract
The efficiency of implementation of the arithmetic operations in finite fields depends on the choice representation of elements of the field. It seems that from this point of view normal bases are the most appropriate, since raising to the power 2 in $GF(2^n)$ of characteristic 2 is reduced in these bases to a cyclic shift of the coordinates. We, in this paper, introduce our algorithm to transform fastly the conventional bases to normal bases and present the result of H/W implementation using the algorithm. We also propose our algorithm to calculate the multiplication and inverse of elements with respect to normal bases in $GF(2^n)$ and present the programs and the results of H/W implementations using the algorithm.
Keywords
Finite Field; Normal Basis; Multiplication Function; Boolean Matrix; Multiplication; Inverse;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
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