**Borislav Stoyanov \* and Gyurhan Nedzhibov**

Department of Computer Informatics, Faculty of Mathematics and Informatics, Konstantin Preslavski University of Shumen, 9712 Shumen, Bulgaria; g.nedzhibov@shu.bg

**\*** Correspondence: borislav.stoyanov@shu.bg

Received: 12 November 2019; Accepted: 25 December 2019; Published: 2 January 2020

**Abstract:** In this paper, an improved encryption algorithm based on numerical methods and rotation–translation equation is proposed. We develop the new encryption-decryption algorithm by using the concept of symmetric key instead of public key. Symmetric key algorithms use the same key for both encryption and decryption. Most symmetric key encryption algorithms use either block ciphers or stream ciphers. Our goal in this work is to improve an existing encryption algorithm by using a faster convergent iterative method, providing secure convergence of the corresponding numerical scheme, and improved security by a using rotation–translation formula.

**Keywords:** nonlinear equations; iterative methods; rotation–translation formula; symmetric encryption
