{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:12:02Z","timestamp":1760058722355,"version":"build-2065373602"},"reference-count":50,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,4,24]],"date-time":"2025-04-24T00:00:00Z","timestamp":1745452800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cryptography"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/cryptography9020026","type":"journal-article","created":{"date-parts":[[2025,4,24]],"date-time":"2025-04-24T06:18:02Z","timestamp":1745475482000},"page":"26","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Affine Cipher Encryption Technique Using Residue Number System"],"prefix":"10.3390","volume":"9","author":[{"given":"Mykhailo","family":"Kasianchuk","sequence":"first","affiliation":[{"name":"Department of Cyber Security, West Ukrainian National University, 46009 Ternopil, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5381-9528","authenticated-orcid":false,"given":"Ruslan","family":"Shevchuk","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Automatics, University of Bielsko-Biala, 43-309 Bielsko-Biala, Poland"},{"name":"Department of Computer Science, West Ukrainian National University, 46009 Ternopil, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5136-3854","authenticated-orcid":false,"given":"Bogdan","family":"Adamyk","sequence":"additional","affiliation":[{"name":"Aston Business School, Aston University, Birmingham B4 7ET, UK"}]},{"given":"Vladlena","family":"Benson","sequence":"additional","affiliation":[{"name":"Aston Business School, Aston University, Birmingham B4 7ET, UK"}]},{"given":"Inna","family":"Shylinska","sequence":"additional","affiliation":[{"name":"Department of Foreign Languages, Information and Communication Technologies, West Ukrainian National University, 46009 Ternopil, Ukraine"}]},{"given":"Mykhailo","family":"Holembiovskyi","sequence":"additional","affiliation":[{"name":"Department of Cyber Security, West Ukrainian National University, 46009 Ternopil, Ukraine"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Nieles, M., Dempsey, K., and Pillitteri, V.Y. (2017). An Introduction to Information Security, National Institute of Standards and Technology.","DOI":"10.6028\/NIST.SP.800-12r1"},{"key":"ref_2","unstructured":"Shirazi, S.-R., Shah, S.A., and Anwar, A. (2024, January 23\u201325). Information Security. Proceedings of the 27th International Conference, Arlington, VA, USA."},{"key":"ref_3","first-page":"1","article-title":"Security Information Management Systems","volume":"24","author":"Andrzejewski","year":"2020","journal-title":"Nauki Zarz."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Andrijchuk, V.A., Kuritnyk, I.P., Kasyanchuk, M.M., and Karpinski, M.P. (2005, January 5\u20137). Modern Algorithms and Methods of the Person Biometric Identification. Proceedings of the 2005 IEEE Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications, Sofia, Bulgaria.","DOI":"10.1109\/IDAACS.2005.283012"},{"key":"ref_5","first-page":"76","article-title":"Information Security","volume":"33","author":"Laybats","year":"2016","journal-title":"Bus. Inf. Rev."},{"key":"ref_6","unstructured":"Hoffstein, J., Pipher, J., and Silverman, J. (2008). An Introduction to Mathematical Cryptography, Springer New York."},{"key":"ref_7","unstructured":"Jeffrey, H., Jill, P., and Joseph, H. (2008). An Introduction to Cryptography, Springer."},{"key":"ref_8","first-page":"469","article-title":"A Survey on Cryptography Techniques","volume":"6","author":"Adki","year":"2015","journal-title":"Int. J. Adv. Res. Comput. Sci. Softw. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Washington, L.C. (2008). Elliptic Curves, Chapman and Hall\/CRC.","DOI":"10.1201\/9781420071474"},{"key":"ref_10","first-page":"1","article-title":"Evolution of the Cyber Security Threat: An Overview of the Scale of Cyber Threat","volume":"3","author":"Fadziso","year":"2023","journal-title":"Digit. Sustain. Rev."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"227","DOI":"10.52098\/acj.202260","article-title":"A Cyber Security Threats, Vulnerability, Challenges and Proposed Solution","volume":"2","author":"Asaad","year":"2022","journal-title":"Appl. Comput. J."},{"key":"ref_12","first-page":"32","article-title":"Summary of Cyber Threat Intelligence","volume":"8","author":"Wang","year":"2022","journal-title":"Int. J. Innov. Res. Multidiscip. Field"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3171","DOI":"10.1007\/s13369-019-04319-2","article-title":"Cyber Security Threats and Vulnerabilities: A Systematic Mapping Study","volume":"45","author":"Humayun","year":"2020","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Tarawneh, M. (2024). Perspective Chapter: Cryptography\u2014Recent Advances and Research Perspectives. Biometrics and Cryptography, IntechOpen.","DOI":"10.5772\/intechopen.111847"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"29","DOI":"10.24297\/ijct.v4i1a.3030","article-title":"CRYPTOGRAPHY","volume":"4","author":"Kumar","year":"2013","journal-title":"Int. J. Comput. Technol."},{"key":"ref_16","first-page":"1","article-title":"Overview of Cryptography","volume":"1","author":"Onwutalobi","year":"2011","journal-title":"SSRN Electron. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1080\/09720529.2008.10698166","article-title":"Affine Transformation in Cryptography","volume":"11","author":"Om","year":"2008","journal-title":"J. Discret. Math. Sci. Cryptogr."},{"key":"ref_18","first-page":"25","article-title":"Encryption of Data Based on Triple Encryption and Affine Algorithm","volume":"7","author":"Dhaief","year":"2021","journal-title":"Int. J. Adv. Sci. Res. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Rachmawati, D., and Budiman, M.A. (2017, January 8\u201310). New Approach toward Data Hiding by Using Affine Cipher and Least Significant Bit Algorithm. Proceedings of the 2017 4th International Conference on Computer Applications and Information Processing Technology (CAIPT), Kuta Bali, Indonesia.","DOI":"10.1109\/CAIPT.2017.8320737"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Omondi, A.R., and Benjamin Premkumar, A. (2007). Residue Number Systems: Theory and Implementation, World Scientific.","DOI":"10.1142\/9781860948671"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Mohan, P.-A. (2016). Residue Number Systems, Springer International Publishing.","DOI":"10.1007\/978-3-319-41385-3"},{"key":"ref_22","first-page":"785","article-title":"Affine Cipher Cryptanalysis Using Genetic Algorithms","volume":"39","author":"Mezaal","year":"2017","journal-title":"JP J. Algebra Number Theory Appl."},{"key":"ref_23","first-page":"507","article-title":"Quantum Cryptanalysis of Affine Cipher","volume":"14","author":"Mathews","year":"2022","journal-title":"Res. Sq."},{"key":"ref_24","first-page":"1323","article-title":"High Performance Adder Using Residue Number System","volume":"5","author":"Lalitha","year":"2014","journal-title":"J. Mater. Chem. A Mater. Energy Sustain."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1007\/s10559-014-9654-0","article-title":"Theoretical Foundations for the Analytical Computation of Coefficients of Basic Numbers of Krestenson\u2019s Transformation","volume":"50","author":"Nykolaychuk","year":"2014","journal-title":"Cybern. Syst. Anal."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/s10559-021-00358-6","article-title":"Symmetric Cryptoalgorithms in the Residue Number System","volume":"57","author":"Kasianchuk","year":"2021","journal-title":"Cybern. Syst. Anal."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Kazemi, M., Naraghi, H., and Golshan, H.M. (2011). On the Affine Ciphers in Cryptography. Communications in Computer and Information Science, Springer Berlin Heidelberg.","DOI":"10.1007\/978-3-642-25327-0_17"},{"key":"ref_28","first-page":"264","article-title":"Implementation and Enhancement Affine Cipher of Database","volume":"20","author":"Hammood","year":"2016","journal-title":"J. Eng. Sustain. Dev."},{"key":"ref_29","first-page":"346","article-title":"Modification Affine Ciphers Algorithm for Cryptography Password","volume":"3","author":"Babu","year":"2017","journal-title":"Int. J. Res. Sci. Eng."},{"key":"ref_30","first-page":"1","article-title":"Internal Affine Stream Cipher","volume":"1","year":"2014","journal-title":"J. Appl. Eng. Technol. Sci. (JAETS)"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2919","DOI":"10.30534\/ijeter\/2020\/06872020","article-title":"A Keystream-Based Affine Cipher for Dynamic Encryption","volume":"8","author":"Carlo","year":"2020","journal-title":"Int. J. Emerg. Trends Eng. Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"849","DOI":"10.52436\/1.jutif.2023.4.4.1129","article-title":"Secure Text Encryption for IoT Communication Using Affine Cipher and Diffie-Hellman Key Distribution on Arduino Atmega2560 IoT Devices","volume":"4","author":"Putra","year":"2023","journal-title":"J. Tek. Inform. (JUTIF)"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"5919","DOI":"10.1007\/s11071-022-07995-2","article-title":"Encryption Scheme for RGB Images Using Chaos and Affine Hill Cipher Technique","volume":"111","author":"Lone","year":"2023","journal-title":"Nonlinear Dyn."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Ke, Q., Liao, Q.-N., Li, A.-Q., and Gao, R. (2019). Digital Image Encryption Algorithm Based on Affine Cipher. Advances in Intelligent Systems and Computing, Springer International Publishing.","DOI":"10.1007\/978-3-319-98776-7_63"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"137","DOI":"10.12928\/mf.v4i2.5992","article-title":"Implementation of Affine Group Algebra on Digital Image Security","volume":"4","author":"Soekarta","year":"2023","journal-title":"Mob. Forensics"},{"key":"ref_36","first-page":"8","article-title":"A Combine Technique of an Affine Cipher and Transposition Cipher","volume":"7","author":"Alhassan","year":"2021","journal-title":"J. Res. Appl. Math."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"012042","DOI":"10.1088\/1742-6596\/1898\/1\/012042","article-title":"An Implementation of Rabin-p Cryptosystem and Affine Cipher in a Hybrid Scheme to Secure Text","volume":"1898","author":"Budiman","year":"2021","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"181","DOI":"10.18860\/ca.v5i4.4408","article-title":"Application of Rectangular Matrices: Affine Cipher Using Asymmetric Keys","volume":"5","author":"Maxrizal","year":"2019","journal-title":"CAUCHY"},{"key":"ref_39","first-page":"919","article-title":"A Public Key Cryptosystem Using Affine Hill Cipher under Modulation of Prime Number","volume":"40","author":"Sundarayya","year":"2019","journal-title":"J. Inf. Optim. Sci."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"3295","DOI":"10.30534\/ijatcse\/2020\/126932020","article-title":"An Improved Affine Cipher Using Blum Blum Shub Algorithm","volume":"9","author":"Arroyo","year":"2020","journal-title":"Int. J. Adv. Trends Comput. Sci. Eng."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Shoup, V. (2009). A Computational Introduction to Number Theory and Algebra, Cambridge University Press.","DOI":"10.1017\/CBO9780511814549"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"012001","DOI":"10.1088\/1742-6596\/1361\/1\/012001","article-title":"Application of Linear Congruent Generator in Affine Cipher Algorithm to Produce Dynamic Encryption","volume":"1361","author":"Laia","year":"2019","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Stillwell, J. (2003). Elements of Number Theory, Springer New York.","DOI":"10.1007\/978-0-387-21735-2"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Hardy, G.H., Wright, E.M., and Silverman, J. (2008). An Introduction to the Theory of Numbers, Oxford University Press. [6th ed.].","DOI":"10.1093\/oso\/9780199219858.001.0001"},{"key":"ref_45","first-page":"1","article-title":"The Rabin Cryptosystem & Analysis in Measure of Chinese Reminder Theorem","volume":"3","author":"Srivastava","year":"2013","journal-title":"Int. J. Sci. Res. Publ."},{"key":"ref_46","unstructured":"Venturi, D. (2009). Lecture Notes on Algorithmic Number Theory, Springer."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Karpinski, M., Rajba, S., Zawislak, S., Warwas, K., Kasianchuk, M., Ivasiev, S., and Yakymenko, I. (2019, January 18\u201321). A Method for Decimal Number Recovery from Its Residues Based on the Addition of the Product Modules. Proceedings of the 2019 10th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS), Metz, France.","DOI":"10.1109\/IDAACS.2019.8924395"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s10559-016-9817-2","article-title":"Theoretical Foundations of the Modified Perfect Form of Residue Number System","volume":"52","author":"Nykolaychuk","year":"2016","journal-title":"Cybern. Syst. Anal."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Bogdanov, A., Khovratovich, D., and Rechberger, C. (2011). Biclique Cryptanalysis of the Full AES. Lecture Notes in Computer Science, Springer Berlin Heidelberg.","DOI":"10.1007\/978-3-642-25385-0_19"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Tiessen, T. (2016). Polytopic Cryptanalysis. Lecture Notes in Computer Science, Springer Berlin Heidelberg.","DOI":"10.1007\/978-3-662-49890-3_9"}],"container-title":["Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2410-387X\/9\/2\/26\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:20:36Z","timestamp":1760030436000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2410-387X\/9\/2\/26"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,24]]},"references-count":50,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["cryptography9020026"],"URL":"https:\/\/doi.org\/10.3390\/cryptography9020026","relation":{},"ISSN":["2410-387X"],"issn-type":[{"type":"electronic","value":"2410-387X"}],"subject":[],"published":{"date-parts":[[2025,4,24]]}}}