TY - JOUR
T1 - Affine Cipher Encryption Technique Using Residue Number System
AU - Kasianchuk, Mykhailo
AU - Shevchuk, Ruslan
AU - Adamyk, Bogdan
AU - Benson, Vladlena
AU - Shylinska, Inna
AU - Holembiovskyi, Mykhailo
N1 - Copyright © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
PY - 2025/4/24
Y1 - 2025/4/24
N2 - 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.
AB - 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.
UR - https://www.mdpi.com/2410-387X/9/2/26
U2 - 10.3390/cryptography9020026
DO - 10.3390/cryptography9020026
M3 - Article
VL - 9
JO - Cryptography
JF - Cryptography
IS - 2
M1 - 26
ER -