Finite Field Extension and Public Key Cryptosystem

Abstract

We propose DLP over Gauss’s finite cylcotomic extension fields (GFCEF) subsequently design a PKC. In this paper, we consider the concept known as of Gauss’s Finite Cyclotomic Extension Field (GFCEF) to propose seven DLPs. Our basic idea is to study the splitting fields of polynomial with special attention to the case K = Q. Then splitting fields turn out to be an Abelian extensions whose Galois Groups are well known. There are in general, referred as Finite Cyclotomic Extension Field (FCEF).

2010 AMS Mathematics Subject Classification Number: 94A60.

Keywords: DLP, GFCEF, PKC, Galois Groups, Abelian Extension.

Cite this Article: Sunil Kumar Kashyap, Birendra Kumar Sharma, Amitabh Banerjee. Finite Field Extension and Public Key Cryptosystem. Journal of Open Source Developments. 2020; 7(2): 22–24p.