Research Article

Normal Elements using Trace Mapping over Finite Fields

by  P. L. Sharma, Kiran Devi
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 179 - Issue 20
Published: Feb 2018
Authors: P. L. Sharma, Kiran Devi
10.5120/ijca2018916328
PDF

P. L. Sharma, Kiran Devi . Normal Elements using Trace Mapping over Finite Fields. International Journal of Computer Applications. 179, 20 (Feb 2018), 18-21. DOI=10.5120/ijca2018916328

                        @article{ 10.5120/ijca2018916328,
                        author  = { P. L. Sharma,Kiran Devi },
                        title   = { Normal Elements using Trace Mapping over Finite Fields },
                        journal = { International Journal of Computer Applications },
                        year    = { 2018 },
                        volume  = { 179 },
                        number  = { 20 },
                        pages   = { 18-21 },
                        doi     = { 10.5120/ijca2018916328 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2018
                        %A P. L. Sharma
                        %A Kiran Devi
                        %T Normal Elements using Trace Mapping over Finite Fields%T 
                        %J International Journal of Computer Applications
                        %V 179
                        %N 20
                        %P 18-21
                        %R 10.5120/ijca2018916328
                        %I Foundation of Computer Science (FCS), NY, USA
Abstract

Normal bases over finite fields have been widely used in many applications of cryptography and coding theory. They are also important for Frobenius mapping and efficient for the implementation of the arithmetic of finite fields. Let

References
  • Gao, S. 1993. Normal bases over finite fields, Ph.D. thesis, University of Waterloo, Canada.
  • Gao, S., Gathen, Vonzur J., Panario, D. and Shoup, V., 2000. Algorithms for exponentiation in finite fields, J. Symb. Comput., 29(6), 879-889.
  • Hasan, M. A., Wang, M. Z. and Bhargava, V. K., 1993. A modified Massey-Omura parallel multiplier for a class of finite fields, IEEE Trans. Comput., 42, 1278-1280.
  • Huczynska, S., Mullen, G. l., Panario, D. and Thomson, D. 2013. Existence and properties of k- normal elements over finite fields, Finite Field and their Applications, 24, 170-183.
  • Kavut, S., Maitra, S. and Yucel, M. D. 2007. Search for Boolean functions with excellent profiles in the rotation symmetric class, IEEE Trans. Inf. Theory, 53(5), 1743--1751.
  • Lempel, A. and Weinberger, M. J. 1988, Self-complementary normal bases in finite fields, SIAM J. Discrete Math., 1(2), 193-198.
  • Liao, Q. Y., 2013. A survey on normal bases over finite fields, Advances in Mathematics China, 42(5), 577-586.
  • Lidl R. and Niederreiter, H. 1997. Finite Fields, Cambridge University Press, second edition.
  • Massey J. L. and Omura, J. K. 1986. Computation method and apparatus for finite field arithmetic, US Patent No. 4587627.
  • Menezes, A. J., Blake, F. I. Gao, X., Vanstone, A. S. and Yaghoobian, T. 1993. Applications of finite fields, Kluwer Academic Publishers.
  • Mullen G. L. and Panario, D., 2013. Handbook of Finite Fields, CRC Press.
  • Perlis, S. 1942. Normal bases of cyclic fields of prime-power degree, Duke Math. J., 9, 507-517.
  • Sharma, P. L., Rehan, M. and Sharma, S. 2015. Counting irreducible polynomials over  with first and third coefficients given, Asian-European Journal of Mathematics, 8(1), 1550015 (27 Pages).
  • Sharma, P. L., Sharma S. and Rehan, M. 2015. On construction of irreducible polynomials over  Journal of discrete Mathematical Sciences and Cryptography, 8(4), 335-347.
  • Silva D. and Kschischang, F. R. 2009. Fast encoding and decoding of Gabidulin codes, In: Proceedings of the IEEE International Symposium of Information Theory, Seoul: Korea, 2858-2862.
  • Vonzur Gathen, J. and Nöcker, M. 2004. Fast arithmetic with general Gauss periods, Theor. Comput. Sci., 315, 419-452.
  • Wan, Z. X. 2003. Lectures on finite fields and Galois rings, Singapore: World Scientific.
  • Wang, C. C. 1989. An algorithm to design finite field multipliers using a self dual normal basis, IEEE Trans. Comput., 38(10), 1457-1460.
  • Zhang, X., Feng, R., Liao, Q. and Gao, X. 2014. Finding normal bases over finite fields with prescribed trace self orthogonal relations, Finite Field and their Applications, 28, 1-21.
Index Terms
Computer Science
Information Sciences
No index terms available.
Keywords

Normal basis Trace function Hamming weight Symmetric vector.

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