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d-Multiplicative Secret Sharing for Multipartite Adversary Structures

Authors Reo Eriguchi, Noboru Kunihiro



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Reo Eriguchi
  • Graduate School of Information Science and Technology, The University of Tokyo, Japan
Noboru Kunihiro
  • Department of Computer Science, University of Tsukuba, Japan

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Reo Eriguchi and Noboru Kunihiro. d-Multiplicative Secret Sharing for Multipartite Adversary Structures. In 1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 2:1-2:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.ITC.2020.2

Abstract

Secret sharing schemes are said to be d-multiplicative if the i-th shares of any d secrets s^(j), j∈[d] can be converted into an additive share of the product ∏_{j∈[d]}s^(j). d-Multiplicative secret sharing is a central building block of multiparty computation protocols with minimum number of rounds which are unconditionally secure against possibly non-threshold adversaries. It is known that d-multiplicative secret sharing is possible if and only if no d forbidden subsets covers the set of all the n players or, equivalently, it is private with respect to an adversary structure of type Q_d. However, the only known method to achieve d-multiplicativity for any adversary structure of type Q_d is based on CNF secret sharing schemes, which are not efficient in general in that the information ratios are exponential in n. In this paper, we explicitly construct a d-multiplicative secret sharing scheme for any 𝓁-partite adversary structure of type Q_d whose information ratio is O(n^{𝓁+1}). Our schemes are applicable to the class of all the 𝓁-partite adversary structures, which is much wider than that of the threshold ones. Furthermore, our schemes achieve information ratios which are polynomial in n if 𝓁 is constant and hence are more efficient than CNF schemes. In addition, based on the standard embedding of 𝓁-partite adversary structures into ℝ^𝓁, we introduce a class of 𝓁-partite adversary structures of type Q_d with good geometric properties and show that there exist more efficient d-multiplicative secret sharing schemes for adversary structures in that family than the above general construction. The family of adversary structures is a natural generalization of that of the threshold ones and includes some adversary structures which arise in real-world scenarios.

Subject Classification

ACM Subject Classification
  • Security and privacy → Information-theoretic techniques
Keywords
  • Secret sharing scheme
  • multiplicative secret sharing scheme
  • multipartite adversary structure

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References

  1. Omer Barkol, Yuval Ishai, and Enav Weinreb. On d-multiplicative secret sharing. Journal of cryptology, 23(4):580-593, 2010. Google Scholar
  2. Amos Beimel. Secret-sharing schemes: A survey. In Coding and Cryptology, pages 11-46, 2011. Google Scholar
  3. Michael Ben-Or, Shafi Goldwasser, and Avi Wigderson. Completeness theorems for non-cryptographic fault-tolerant distributed computation. In Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, pages 1-10, 1988. Google Scholar
  4. G. R. Blakley. Safeguarding cryptographic keys. In 1979 International Workshop on Managing Requirements Knowledge (MARK), pages 313-318, 1979. Google Scholar
  5. Elette Boyle, Niv Gilboa, and Yuval Ishai. Breaking the circuit size barrier for secure computation under ddh. In Advances in Cryptology - CRYPTO 2016, pages 509-539, 2016. Google Scholar
  6. Elette Boyle, Lisa Kohl, and Peter Scholl. Homomorphic secret sharing from lattices without fhe. In Advances in Cryptology - EUROCRYPT 2019, pages 3-33, 2019. Google Scholar
  7. I. Cascudo, R. Cramer, and C. Xing. The arithmetic codex. In 2012 IEEE Information Theory Workshop, pages 75-79, 2012. Google Scholar
  8. Hao Chen and Ronald Cramer. Algebraic geometric secret sharing schemes and secure multi-party computations over small fields. In Advances in Cryptology - CRYPTO 2006, pages 521-536, 2006. Google Scholar
  9. Ronald Cramer, Ivan Damgård, and Ueli Maurer. General secure multi-party computation from any linear secret-sharing scheme. In Advances in Cryptology - EUROCRYPT 2000, pages 316-334, 2000. Google Scholar
  10. Ivan Damgård and Jesper Buus Nielsen. Scalable and unconditionally secure multiparty computation. In Advances in Cryptology - CRYPTO 2007, pages 572-590, 2007. Google Scholar
  11. Oriol Farràs, Jaume Martí-Farré, and Carles Padró. Ideal multipartite secret sharing schemes. Journal of cryptology, 25(3):434-463, 2012. Google Scholar
  12. Oriol Farràs and Carles Padró. Ideal secret sharing schemes for useful multipartite access structures. In Coding and Cryptology, pages 99-108, 2011. Google Scholar
  13. P. M. Gruber. Convex and Discrete Geometry. Springer-Verlag, 2007. Google Scholar
  14. Martin Hirt and Daniel Tschudi. Efficient general-adversary multi-party computation. In Advances in Cryptology - ASIACRYPT 2013, pages 181-200, 2013. Google Scholar
  15. Mitsuru Ito, Akira Saito, and Takao Nishizeki. Secret sharing scheme realizing general access structure. Electronics and Communications in Japan (Part III: Fundamental Electronic Science), 72(9):56-64, 1989. Google Scholar
  16. E. Karnin, J. Greene, and M. Hellman. On secret sharing systems. IEEE Transactions on Information Theory, 29(1):35-41, 1983. Google Scholar
  17. Emilia Käsper, Ventzislav Nikov, and Svetla Nikova. Strongly multiplicative hierarchical threshold secret sharing. In International Conference on Information Theoretic Security, pages 148-168, 2007. Google Scholar
  18. M. Liu, L. Xiao, and Z. Zhang. Multiplicative linear secret sharing schemes based on connectivity of graphs. IEEE Transactions on Information Theory, 53(11):3973-3978, 2007. Google Scholar
  19. Ueli Maurer. Secure multi-party computation made simple. Discrete Applied Mathematics, 154(2):370-381, 2006. Google Scholar
  20. A. Shamir. How to share a secret. Communications of the ACM, 22(11):612-613, 1979. Google Scholar
  21. D. R. Stinson. Decomposition constructions for secret-sharing schemes. IEEE Transactions on Information Theory, 40(1):118-125, 1994. Google Scholar
  22. Vladimir Vapnik. Pattern recognition using generalized portrait method. Automation and remote control, 24:774-780, 1963. Google Scholar
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