Secure multi-party computation protocols based on discrete algebraic structures and finite group representations
*Amardeep KaurCorresponding authoramardeeptiet@gmail.comDepartment of Computer SciencePunjabi University Centre for Emerging and Innovative TechnologyPunjabi UniversityMohali, Punjab, 160062, IndiaView full profile → , Kamaljeet Kaur Mangatkamalmangat@yahoo.co.inDepartment of Computer SciencePunjabi University Centre for Emerging and Innovative TechnologyPunjabi UniversityMohali, Punjab, 160062, 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-3087
- Pages:
- 4731–4739
Abstract
Secure Multi-Party Computation (SMPC) enables the various parties to collectively compute functions on sensitive inputs without the sensitive information being revealed, yet the problem of scalability, efficiency and security remains a significant issue. To increase the computational security and efficiency of the postulated framework in this paper a framework on algebraic SMPC is defined that is based on discrete algebraic structures and finite group representations. This approach is founded on the group-theoretic encoding, homomorphic mappings and structured secret sharing between algebraic space to provide confidentiality and integrity against semi-honest and malicious adversarial structures. The suggested plan entails use of representation theory to not only compress data, but also easily combine the data to minimize on communication overhead and increase processing speed.
Keywords
Subject Classifications
References
[1] Y. Zhao and H. Sun, “Expand-and-randomize: An algebraic approach to secure computation,” Entropy, vol. 23, no. 11, Art. no. 1461 (2021), doi: 10.3390/e23111461.
[2] B. Schoenmakers and T. Segers, “Secure groups for threshold cryptography and number-theoretic multiparty computation,” Cryptography, vol. 7, no. 4, Art. no. 56 (2023), doi: 10.3390/cryptography7040056.
[3] R. K. Rongon and K. Das, “An energy-efficient cloud data center architectural model for the national data center of Bangladesh,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 27, no. 6, pp. 1905–1917 (2024), doi: 10.47974/JDMSC-1916.
[4] T. Wang, Z. Liu, Z. Han, and L. Zhou, “Efficient decision-making scheme using secure multiparty computation with correctness validation,” Electronics, vol. 12, no. 23, Art. no. 4840 (2023), doi: 10.3390/electronics12234840.
[5] Y. Jiang, Y. Zhou, and T. Feng, “A blockchain-based secure multi-party computation scheme with multi-key fully homomorphic proxy re-encryption,” Information, vol. 13, no. 10, Art. no. 481 (2022), doi: 10.3390/info13100481.
[6] A. Kichna and A. Farchane, “Secure and efficient code-based cryptography for multi-party computation and digital signatures,” Computer Sciences & Mathematics Forum, vol. 6, no. 1, Art. no. 1 (2023), doi: 10.3390/cmsf2023006001.
[7] H. Mao, T. Nie, M. Yu, X. Dong, X. Li, and G. Yu, “SMPTC3: Secure multi-party protocol based trusted cross-chain contracts,” Mathematics, vol. 12, no. 16, Art. no. 2562 (2024), doi: 10.3390/math12162562.
[8] I. Suleimenov and A. Bakirov, “Prospects for using finite algebraic rings for constructing discrete coordinate systems,” Symmetry, vol. 17, no. 3, Art. no. 410 (2025), doi: 10.3390/sym17030410.
[9] S. J. Modi, A. R. Panhalkar, N. Martin, P. V. Baviskar, T. A. Wani, and E. Kholiyarov, “Exploring advanced mathematical concepts in quantum computing for algorithm enhancement,” Journal of Interdisciplinary Mathematics, vol. 29, no. 3, pp. 527–535 (2026), doi: 10.47974/JIM-2487.
[10] H. Ballhausen and L. C. Hinske, “Federated secure computing,” Informatics, vol. 10, no. 4, Art. no. 83 (2023), doi: 10.3390/informatics10040083.
[11] L. Yin, J. Xu, Z. Wang, and C. Wang, “A provable secure session key distribution protocol based on NSSK for in-vehicle CAN network,” Mathematics, vol. 10, no. 16, Art. no. 2903 (2022), doi: 10.3390/math10162903.
[12] P. Balbudhe, O. Lomate, M. Tonde, G. Parwate, and P. Bhute, “QR code based emergency information sharing and real-time communication,” International Journal on Advanced Computer Engineering and Communication Technology, vol. 14, no. 1, pp. 195–199 (2025), doi: 10.65521/ijacect.v14i1.371.
