Applications of group actions in symmetric cryptosystems
*Nikhil GovilCorresponding authornikhil.govil@gla.ac.inDepartment of Computer Engineering & ApplicationsGLA UniversityMathura, Uttar Pradesh, 281406, IndiaView full profile → , K. Keerthikakeerthikak@maher.ac.inDepartment of Computer ScienceMeenakshi College of Arts and ScienceMeenakshi Academy of Higher Education & Research (Deemed to be University)Chennai, Tamil Nadu, 600078, IndiaView full profile → , Sakshi Sobtisakshi.sobti.orp@chitkara.edu.inCentre for Research Impact and OutcomeChitkara UniversityRajpura, Punjab, 140417, IndiaView full profile → , Manni SruthimanniSruthi2024@protonmail.comCentre for Multidisciplinary ResearchAnurag UniversityHyderabad, Telangana, 500088, India0009-0007-1580-465XView full profile → , Dilshod Raupovdilshod@astrin.uzDepartment of Physics and ChemistryTashkent Institute of Irrigation and Agricultural Mechanization EngineersNational Research UniversityKori Niyoziy 39, Tashkent, 100000, UzbekistanView full profile → , A. K. Bhuvaneswaribhuvaneswari@avit.ac.inDepartment of Humanities and Sciences (Mathematics Division)Aarupadai Veedu Institute of TechnologyVinayaka Mission’s Research Foundation (Deemed to be University)Paiyanoor, Chennai, Tamil Nadu, 603104, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2026
- Published Online:
- 31 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-3029
- Pages:
- 4033–4044
Abstract
A strict algebraic structure of group actions models the symmetry, permutation and transformation properties in symmetric cryptosystems. In this paper, the reasons why permutation groups are critical and the way they are used to attack the design of block and stream ciphers towards diffusion and confusion are discussed. Group-theoretic properties are pertinent to enhance the strength of cryptography by studying structures like Feistel networks and substitution-permutation networks (SPNs), a fact that the work highlights. Algebraic properties, such as orbit structures and stabilizers are dealt with in respect to their effects on resistance to linear and differential cryptanalysis. Comparison analysis has been determined to introduce well-defined group action that has enhanced resistance to 18-25% against algebraic attacks without a loss in the computational efficiency. These results highlight the importance of the symmetry-breaking towards the creation of secure ciphers. Among the contributions of the study is presenting a single algebraic design of strong symmetric encryption schemes with a better security guarantee.
Keywords
Subject Classifications
References
References
[1] S. A. Baowidan, A. Alamer, M. Hassan, and A. Yousaf, “Group-action-based S-box generation technique for enhanced block cipher security and robust image encryption scheme,” Symmetry, vol. 16, no. 8, Art. no. 954 (2024), doi: 10.3390/sym16080954.
[2] S. Kalaiselvan and S. Vijayabalaji, “Soft expert symmetric group and its application in MCDM problem,” Symmetry, vol. 14, no. 12, Art. no. 2685 (2022), doi: 10.3390/sym14122685.
[3] M. M. Hazzazi, S. A. Baowidan, A. Yousaf, and M. Adeel, “An innovative algorithm based on chaotic maps amalgamated with bit-level permutations for robust S-box construction and its application in medical image privacy,” Symmetry, vol. 16, no. 8, Art. no. 1070 (2024), doi: 10.3390/sym16081070.
[4] E. Corona-Bermúdez, J. C. Chimal-Eguía, U. Corona-Bermúdez, and M. E. Rivero-Ángeles, “Chaos meets cryptography: Developing an S-box design with the Rössler attractor,” Mathematics, vol. 11, no. 22, Art. no. 4575 (2023), doi: 10.3390/math11224575.
[5] G. Nişancı, P. G. Flikkema, and T. Yalçın, “Symmetric cryptography on RISC-V: Performance evaluation of standardized algorithms,” Cryptography, vol. 6, no. 3, Art. no. 41 (2022), doi: 10.3390/cryptography6030041.
[6] A. Shafique, K. H. Khan, M. M. Hazzazi, I. Bahkali, Z. Bassfar, and M. U. Rehman, “Chaos and cellular automata-based substitution box and its application in cryptography,” Mathematics, vol. 11, no. 10, Art. no. 2322 (2023), doi: 10.3390/math11102322.
[7] R. S. Kale, J. Hase, S. Deshmukh, S. N. Ajani, P. K. Agrawal, and C. S. Khandelwal, “Ensuring data confidentiality and integrity in edge computing environments: A security and privacy perspective,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 27, no. 2-A, pp. 421–430 (2024).
[8] T. Vandervelden, R. De Smet, K. Steenhaut, and A. Braeken, “Symmetric-key-based authentication among the nodes in a wireless sensor and actuator network,” Sensors, vol. 22, no. 4, Art. no. 1403 (2022), doi: 10.3390/s22041403.
[9] M. Gabr, H. Younis, M. Ibrahim, S. Alajmy, I. Khalid, E. Azab, R. Elias, and W. Alexan, “Application of DNA coding, the Lorenz differential equations and a variation of the logistic map in a multi-stage cryptosystem,” Symmetry, vol. 14, no. 12, Art. no. 2559 (2022), doi: 10.3390/sym14122559.
[10] R. C. Poonia, T. Singh, C. K. Rajashri, D. Mondal, and S. M. Patil, “Optimizing communication system security through comprehensive testing and intelligent network configurations,” Journal of Information and Optimization Sciences, vol. 47, no. 5-A, pp. 1709–1717 (2026), doi: 10.47974/JIOS-2261.
[11] M. N. S. Perera, T. Nakamura, M. Hashimoto, H. Yokoyama, C.-M. Cheng, and K. Sakurai, “A survey on group signatures and ring signatures: Traceability vs. anonymity,” Cryptography, vol. 6, no. 1, Art. no. 3 (2022), doi: 10.3390/cryptography6010003.
[12] M. J. Mihaljević, M. Knežević, D. Urošević, L. Wang, and S. Xu, “An approach for blockchain and symmetric keys broadcast encryption based access control in IoT,” Symmetry, vol. 15, no. 2, Art. no. 299 (2023), doi: 10.3390/sym15020299.
[13] M. T. Anderson, F. Müller, and L. Kovács, “A comprehensive review of attribute-based encryption schemes: Models, methods, and emerging applications,” International Journal of Recent Advances in Engineering and Technology, vol. 14, no. 2, pp. 160–166 (2025), doi: 10.65521/intjournalrecadvengtech.v14i2.2027.
[14] A. A. A. El-Latif, J. Ramadoss, B. Abd-El-Atty, H. S. Khalifa, and F. Nazarimehr, “A novel chaos-based cryptography algorithm and its performance analysis,” Mathematics, vol. 10, no. 14, Art. no. 2434 (2022), doi: 10.3390/math10142434.
[15] M. Mehdi, M. T. Ajani, H. Tahir, S. Tahir, Z. Alizai, F. Khan, Q. Riaz, and M. Hussain, “PUF-based key generation scheme for secure group communication using MEMS,” Electronics, vol. 10, no. 14, Art. no. 1691 (2021), doi: 10.3390/electronics10141691.
