A Novel Asymmetric Encryption Technique Using Onto Functions

Abstract

The concept of onto functions plays a very important role in the theory of Analysis and has got rich applications in many engineering and scientific techniques. In this paper, we are proposing a new application in the field of cryptography by using onto functions on the algebraic structures like rings like \((\mathbb{Z}_m,+_m,X_m)\) and fields like \((\mathbb{Z}_p,+_p,X_p)\) to get a strong encryption technique. A new asymmetric cryptographic system based on Hill ciphers is developed using onto functions with two keys- Primary and Secondary, to enhance the security. This is the first algorithm in cryptography developed using onto functions which ensures a strong security for the system while maintaining the simplicity of the existing Hill cipher. The concept of using two keys is also novel in the symmetric key cryptography. The usage of onto functions in the encryption technique eventually gives the highest security to the algorithm which has been discussed through different examples. The original Hill cipher is obsolete in the present-day technology and serves as pedagogical purpose but whereas this newly proposed algorithm can be safely used in the present-day technology.\ Vulnerability from different types of attacks of the algorithm and the cardinality of key spaces have also been discussed.