A Mathematical Model of Asymmetric Encryption Based on Linear Diophantine Equations

in this paper, an information cryptography system is presented as asymmetric encryption based on the linear Diophantine equation ax + by=c. This system consists of two parts for encrypting plain text. In the first, the plain text is encrypted using a linear equation repeatedly with two public keys that were previously generated. As for the second, encrypted cipher texts are derived from the first part and encrypted again through the use of a proposed equation by another two public keys, which led to overcoming complexity in the related works by setting precedent for complexity generating keys and increasing the number of keys with the increase in the number of plain texts to be encrypted. Thus, this system provides a simple and, at the same time, more secure system, as analyzed in this paper.