Vol.10 (2020) No. 3 ISSN: 2088-5334 A New Method of Data Encryption based on One to One Functions Osama R. Shahin a,b,1 , Anis Ben Aissa a,2 , Yasser Fouad c , Hassan Al-Mahdi d , Mansi Alsmarah a a Department of Computer Science & Information, Jouf University, Gurayat, Saudi Arabia E-mail: 1 orshahin@ju.edu.sa; 2 aabenaissi @ju.edu.sa b Physics and Mathematics Department, Faculty of Engineering, Helwan University, Egypt c Department of Computer Science, Faculty of Computers & Information, Suez University, Suez, Egypt d Department of Computer Science, Faculty of Computers & Informatics, Suez Canal University, Ismailia 41522, Egypt Abstract— Due to the rapid growth of computer networks, critical highly confidential information shared across these networks. Accordingly, securing such information from unauthorized intruders has become a vital issue in the field of information technology. In this paper, we present a new algorithm for encrypting and decrypting English plain text based on the well-known Caesar's algorithm and a special type of functions called One to One function. The proposed algorithm is referred to as the One to One function algorithm (OtO). The OtO belongs to a symmetric key concept where the same key is used in both encryption and decryption processes. In the OtO algorithm, the triplet (K, a, b) represent the private keys. To speed up the proposed OtO computation, the value of K is calculated based on Fibonacci sequence, on eigenvalues, Leslie matrices and Markov chain. This private key K only knew to the transmitter and receiver and considered one of the private keys used in the encryption process. When the message arrives at the receiver, it uses the inverse function of the proposed one to one function that used at the transmitter. The proposed OtO algorithm is conducted using MATLAB and its efficiency is checked in terms of encrypted time, decrypted time, and Avalanche Effect. We think that the obtained results are acceptable compared to famous algorithms DES, 3DES, AES and RSA. Keywords— cryptography; symmetric encryption; fibonacci sequence; eigenvalues; one to one function. I. INTRODUCTION Information is currently a treasure and wealth of peoples and countries, especially with the expansion of communication between the various parts of the globe. The extensive use of technology is due to the development of new technologies such as the Internet, mobile phones, and computers. Therefore the subject of information security has gained particular importance in different areas of daily life. Information security can be defined as a set of techniques, standards, and practices that are applied to information to maintain its integrity [1, 2]. Encryption is a method of converting plain text data into something that looks random and meaningless (ciphertext) to protect information from being accessed by unauthorized people. It was developed by mathematicians such as Francois Vite 1540-1603, John Willias 1616-1703, William F. Friedman 1920, and Lester S. Hill 1929. Ronald Reeves (1977), also known as a science that uses mathematical methods to encrypt and decrypt data. [3]. The exchange of hidden information and encryption is an important area of information security that involves different methods. [4] Encryption provides an essential tool for securing and moving messages from one location to another. There are many encryption algorithms, such as public and private keys and digital signature. Encryption has four objectives: Confidentiality, Integrity, Authentication, and Non-repudiation. Encryption algorithms are divided into two main types: symmetric (or private key) encryption and asymmetric (or public key) encryption [5]. Fig. 1 General Construction of Symmetric Encryption Algorithms. 1169