Affine Cipher Encryption Technique Using Residue Number System

Abstract

This paper presents a new encryption technique, which combines affine ciphers and the residue number system. This makes it possible to eliminate the shortcomings and vulnerabilities of affine ciphers, which are sensitive to cryptanalysis, using the advantages of the residue number system, i.e., the parallelization of calculation processes, performing operations on low bit numbers, and the linear combination of encrypted residues. A mathematical apparatus and a graphic scheme of affine encryption using the residue number system is developed, and a corresponding example is given. Special cases of affine ciphers such as shift and linear ciphers are considered. The cryptographic strength of the proposed cryptosystem when the moduli are prime numbers is estimated, and an example of its estimation is given. The number of bits and the number of moduli of the residue number system, which ensure the same cryptographic strength as the longest key of the AES algorithm, are determined.