The week's pick
Reseach Article
Normal Elements using Trace Mapping over Finite Fields
by
P. L. Sharma,
Kiran Devi
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 179 - Number 20 |
| Year of Publication: 2018 |
| Authors: P. L. Sharma, Kiran Devi |
10.5120/ijca2018916328
|
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
},
issue_date = { Feb 2018 },
volume = { 179 },
number = { 20 },
month = { Feb },
year = { 2018 },
issn = { 0975-8887 },
pages = {
18-21
},
numpages = {9},
url = {
https://ijcaonline.org/archives/volume179/number20/28984-2018916328/
},
doi = { 10.5120/ijca2018916328 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-07T00:55:57.465933+05:30
%A P. L. Sharma
%A Kiran Devi
%T Normal Elements using Trace Mapping over Finite Fields
%J International Journal of Computer Applications
%@ 0975-8887
%V 179
%N 20
%P 18-21
%D 2018
%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
Keywords