Research on Proactive Generation Protocol of Beaver Triples

doi:10.3969/j.issn.1671-1122.2022.12.003

Abstract

Abstract:

In secure multi-party computation, Beaver triples have been one of basic technique to realize the secure computation of addition and multiplication under secret sharing, which can make the number of protocol rounds reach the polynomial of the number of participating parties. This paper studied secure generation protocol of Beaver triples in the mobile adversary model. First, a computational security, effective two-party active Beaver triple generation protocol was designed based on Paillier public key cryptosystem, whose number of rounds was twice the number of renew operations and sent three ciphertexts of Paillier cryptosystem in each round. Then the effective n-party Beaver triplet initiative generation protocol for information theory security was designed using primary cryptographic tools such as Shamir secret sharing, where n ≥ 3, the total number of elements sent by the protocol was at most 6nκ+6n, and the number of execution rounds is not more than 2κ+2, where к was the number of sharing fragment updates and the number of adversary control participants does not exceed n-2. Finally, protocol design ideas were given for malicious adversary articles.

Key words: secure multi-party computation, Beaver triples, Shamir secret sharing, mobile adversary, proactive secret sharing

CLC Number:

TP309

LYU Kewei, CHEN Chi. Research on Proactive Generation Protocol of Beaver Triples[J]. Netinfo Security, 2022, 22(12): 16-24.

References 16

[1]	GOLDREICH O. Foundations of Cryptography Volume II: Basic Applications[M]. London: Cambridge University Press, 2004.
[2]	DEMMLER D, SCHNEIDER T, ZOHNER M. ABY-A Framework for Efficient Mixed-Protocol Secure Two-Party Computation[C]// ISOC.Network and Distributed System Security Symposium. San Diego: ISOC, 2015: 8-11.
[3]	MA Jie, QI Bin, LYU Kewei. BSA: Enabling Biometric-Based Storage and Authorization on Blockchain[C]// IEEE. IEEE TrustCom 2021. New York: IEEE, 2021: 1077-1084.
[4]	BEAVER D. Efficient Multiparty Protocols Using Circuit Randomization[C]// Springer.Annual International Cryptology Conference. Berlin:Springer, 1991: 420-432.
[5]	LINDELL Y. Secure Multiparty Computation[J]. Communications of the ACM, 2020, 64(1): 86-96.
[6]	HIRT M, MAURER U. Robustness for Free in Unconditional Multi-Party Computation[C]// ACM. Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology. New York: ACM, 2001: 101-118.
[7]	SEO M. Fair and Secure Multi-Party Computation with Cheater Detection[EB/OL]. (2021-08-12) [2022-05-02]. https://doi.org/10.3390/cryptography5030019.
[8]	CANETTI R, Damgaard I, DZIEMBOWSKI S, et al. On Adaptive vs. Non-Adaptive Security of Multiparty Protocols[C]// Springer. International Conference on the Theory and Applications of Cryptographic Techniques. Berlin:Springer, 2001: 262-279.
[9]	CUNNINGHAM R, FULLER B, YAKOUBOV S. Catching MPC Cheaters: Identification and Openability[C]// Springer. International Conference on Information Theoretic Security. Berlin:Springer, 2017: 110-134.
[10]	AUMANN Y, LINDELL Y. Security Against Covert Adversaries: Efficient Protocols for Realistic Adversaries[C]// Springer.Theory of Cryptography Conference. Berlin:Springer, 2010: 281-343.
[11]	HE Yunxiao, XU Haixia, LYU Kewei, et al. Secure Constant Round Protocols for Determining Co-Prime of Polynomials[J]. Journal of Graduate School of Chinese Academy of Sciences, 2004, 21(2): 179-184.
	何云筱, 徐海霞, 吕克伟, 等. 常数轮多项式互素多方安全判定协议[J]. 中科院研究生院学报, 2004, 21(2):179-184.
[12]	HERZBERG A, JARECKI S, KRAWCZYK H, et al. Proactive Secret Sharing or: How to Cope with Perpetual Leakage[C]// Springer. Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology. Berlin:Springer, 1995: 339-352
[13]	NIKOV V, NIKOVA S, PRENEEL B, et al. Applying General Access Structure to Proactive Secret Sharing Schemes[C]// Springer. Proceedings of the 23rd Symposium on Information Theory. Berlin:Springer, 2002: 197-206.
[14]	MARAM S, ZHANG F, WANG L, et al. CHURP: Dynamic-Committee Proactive Secret Sharing[C]// ACM. Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security. New York: ACM, 2019: 2369-2386.
[15]	PAILLIER P. Public-Key Cryptosystems Based on Composite Degree Residuosity Classes[C]// Springer. International Conference on the Theory and Applications of Cryptographic Techniques. Berlin:Springer, 1999: 223-238.
[16]	SU Dong, LYU Kewei. Paillier's Trapdoor Function Hides Θ(n) bits[J]. Science China Information Sciences, 2011, 54(9): 1827-1836. doi: 10.1007/s11432-011-4269-9 URL