A design of public key Cryptosystem in an algebraic extension field over a finite field using the difficulty of solving DLP

Abstract

Through this research paper, authors construct a public key cryptosystem which works in the finite algebraic extension field $\mathbb{F}_{p^n}$ of the finite field $\mathbb{F}_p$. The security of this system is based on difficulty of solving DLP in $\mathbb{F}_{p^n}$. The primitive polynomials are used in the construction of algebraic extension fields. In this system all users select commonly a primitive polynomial $f(x)$ of degree $n$ over the finite field $\mathbb{F}_p$. The prime number $p$, the primitive polynomial $f(x)$, encryption rule and decryption rule are given to the public, and all other features kept secret. In this system each character is treated as a polynomial of degree less than $n$ over $\mathbb{F}_p$. After the encryption the character divided into two parts. The first part is sent to the other and the second part is used for the decryption. In this system we use similar procedure of EIGamal Exchange Cryptosystem. But our system has used more parameters than the EIGamal Exchange Cryptosystem. Hence our proposed system is more secure than EIGamal Exchange PKC.