Construction of Normal Bases over Finite Fields

By : Arun Kumar, P. L. Sharma, Kiran Devi

Page No: 1-11

Abstract
Normal bases in finite fields are of much importance in many applications of cryptography and coding theory. The arithmetic computations of normal bases in finite fields are fast. In the extensions of finite fields there exist normal elements. A normal element generates the normal basis. In the present paper, we use a root of an irreducible polynomial and the trace function associated with it to obtain the normal element of the normal polynomial. Further, we find the normal basis whose elements are exactly the roots of the normal polynomial.

Authors :
P. L. Sharma : Department of Mathematics & Statistics Himachal Pradesh University, Shimla 171 005, India
Kiran Devi : Assistant Professor Mahatma Gandhi Govt Engineering College Jeori Camp at Sundernagar, Mandi 175018, (H.P)
Arun Kumar : Assistant Professor Mathematics Swami Vivekanand Govt. College Ghumarwin (H.P.)
 

DOI: https://doi.org/10.32381/JCISS.2018.43.1-4.1