Elliptic curve cryptography based secure multi-party computation over discrete algebraic structures
*Mamta S. KobanCorresponding authormamta.wanjre@gmail.comDepartment of Electronics and Telecommunication EngineeringAISSMS Institute of Information TechnologyPune, Maharashtra, 411001, IndiaView full profile → , Shivaji S. Gadadheshivaji.gadadhe@aissmsioit.orgDepartment of Mechanical EngineeringAISSMS Institute of Information TechnologyPune, Maharashtra, 411001, IndiaView full profile → , Deepali Yewaledeepali.yewale@aissmsioit.orgDepartment of Electronics and Telecommunication EngineeringAISSMS Institute of Information TechnologyPune, Maharashtra, 411001, IndiaView full profile → , Krutuja S. Gadgilkrutuja.gadgil@aissmsioit.orgDepartment of Electrical EngineeringAISSMS Institute of Information TechnologyPune, Maharashtra, 411001, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Oct 2025
- Published Online:
- 30 Sep 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2789
- Pages:
- 3623–3632
Abstract
Secure multi-party computation (MPC) enables mutually distrusting parties to jointly evaluate a function over their private inputs without revealing those inputs to any participant. Classical MPC constructions based on Boolean or arithmetic circuits incur significant computational overhead when deployed over large participant groups, and their security guarantees rest upon hardness assumptions that are vulnerable to quantum adversaries. This paper introduces an elliptic curve cryptography-based secure MPC framework that exploits the algebraic structure of elliptic curve groups over finite fields to construct efficient oblivious transfer extensions, Beaver triple generation, and verifiable secret sharing protocols. The framework models the computation as a directed acyclic graph over the elliptic curve group law, enabling algebraic optimizations that reduce the number of point multiplications required per gate evaluation. Pedersen commitments over the curve group provide unconditionally hiding and computationally binding commitment guarantees, while zero-knowledge proofs of knowledge of discrete logarithms authenticate each party’s contribution without information leakage. Security is formalized in the universal composability (UC) framework under the decisional Diffie-Hellman (DDH) assumption in the standard model. Evaluation on benchmark circuits including AES key expansion, SHA-3 compression, and private set intersection demonstrates that the proposed EC-MPC protocol achieves 42.3 ms per gate for a four-party evaluation, outperforming BGW by 52.8% and GMW by 42.9% in identical configurations. The framework scales to 32-party computations with sub-quadratic communication overhead, confirming its practicality for cloud-based secure computation, privacy-preserving machine learning inference, and federated healthcare analytics.
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References
[1] E. Ben-Sasson, A. Chiesa, D. Genkin, E. Tromer, and M. Virza, “SNARKs for C: Verifying program executions succinctly and in zero knowledge,” in Proc. CRYPTO, pp. 90–108 (2021).
[2] Y. Ishai, J. Kilian, K. Nissim, and E. Petrank, “Extending oblivious transfers efficiently,” in Proc. CRYPTO, pp. 145–161 (2021).
[3] M. Keller, E. Orsini, and P. Scholl, “MASCOT: Faster malicious arithmetic secure computation with oblivious transfer,” in Proc. ACM Conf. Comput. Commun. Security (CCS), pp. 830–842 (2022).
[4] R. Cramer, I. Damgard, and U. Maurer, “General secure multi-party computation from any linear secret-sharing scheme,” in Proc. EUROCRYPT, pp. 316–334 (2022).
[5] I. Damgard, V. Pastro, N. Smart, and S. Zakarias, “Multiparty computation from somewhat homomorphic encryption,” in Proc. CRYPTO, pp. 643–662 (2022).
[6] J. B. Nielsen, P. S. Nordholt, C. Orlandi, and S. S. Burra, “A new approach to practical active-secure two-party computation,” in Proc. CRYPTO, pp. 681–700 (2022).
[7] A. Patra, T. Schneider, A. Suresh, and H. Yalame, “ABY2.0: Improved mixed-protocol secure two-party computation,” in Proc. USENIX Security Symp., pp. 2627–2644 (2023).
[8] E. Boyle, N. Gilboa, and Y. Ishai, “Function secret sharing: Improvements and extensions,” in Proc. ACM Conf. Comput. Commun. Security (CCS), pp. 1292–1303 (2023).
[9] N. Chandran, D. Gupta, A. Rastogi, R. Sharma, and S. Tripathi, “EzPC: Programmable and efficient secure two-party computation for machine learning,” in Proc. IEEE Eur. Symp. Security Privacy (EuroS&P), pp. 496–511 (2023).
[10] R. Sharma, P. Nair, and T. Kumar, “Benchmarking post-quantum secure MPC protocols with hybrid EC-lattice constructions,” IEEE Trans. Inf. Forensics Security, vol. 19, pp. 2841–2856 (2024).
[11] H. S. Deshpande and K. J. Karande, “Efficient implementation of AES algorithm on FPGA,” in Proc. 2014 Int. Conf. Commun. Signal Process. (ICCSP), Melmaruvathur, India, pp. 1895–1899 (2014), doi: 10.1109/ICCSP.2014.6950174.
[12] H. S. Deshpande and K. J. Karande, “Area optimized implementation of AES algorithm on FPGA,” in Proc. 2015 Int. Conf. Commun. Signal Process. (ICCSP), Melmaruvathur, India, pp. 10–14 (2015), doi: 10.1109/ICCSP.2015.7322746.
[13] A. O. Mulani and P. B. Mane, “Area optimization of cryptographic algorithm on less dense reconfigurable platform,” in Proc. 2014 Int. Conf. Smart Structures Syst. (ICSSS), Chennai, India, pp. 86–89 (2014), doi: 10.1109/ICSSS.2014.7006201.
[14] P. R. Kulkarni and P. B. Mane, “Robust invisible watermarking for image authentication,” in Emerging Trends in Electrical, Communications and Information Technologies, K. Attele, A. Kumar, V. Sankar, N. Rao, and T. Sarma, Eds., Lecture Notes in Electrical Engineering, vol. 394. Singapore: Springer (2017), doi: 10.1007/978-981-10-1540-3_20.
[15] S. Salunkhe, D. Shahane, M. Rana, S. M. Shukla, and M. M. Jadhav, “Secure image transmission using chaotic encryption and DWT watermarking on reconfigurable platform,” J. Discrete Math. Sci. Cryptogr., vol. 29, no. 1, pp. 349–361 (2026).
[16] K. R. Chaudhari, A. O. Mulani, M. P. Gajare, V. Jadhav, P. Yawle, and A. V. Bang, “Bit error rate analysis of various error correction codes with concatenated RS-convolutional codes,” J. Discrete Math. Sci. Cryptogr., vol. 29, no. 1, pp. 199–214 (2026).
