Using incomplete polynomial functions of the odd degree n and their inverses for data encryption and decryption

Abstract

The need and the demand to hide the content of written messages from prying eyes has arisen as long as writing itself has existed. Particularly, recent times the protection of information is considered to be quite crucial due to the increased use and development of streaming applications.Therefore, the urging of having more sophisticated, stronger and hard to break data encryption and decryption systems is increasing. In order to attain these requirements, cryptography plays an important role, where many researchers have come up with different proposals and developed algorithms that have helped out a little in ensuring the confidentiality, integrity and authentication of the given information. However, even the internet security through modern cryptography is quite complex and depends on the difficulty of certain computational problems in mathematics.Modern systems of encryption are based on complex mathematical algorithms and carry out a combination of symmetric and asymmetric key encryption schemes to secure communication. For those a significant background in algebra, number theory and geometry is required. In this paper a new cryptosystem is presented, which is based on compound commutative functions such as exponential and logarithmic functions. After the necessary theoretical deliberation in this paper, we will provide the encryption and decryption approach accompanied with relevant examples.