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Computational Soundness of Uniformity Properties for Multi-party Computation Based on LSSS

  • Hui ZhaoEmail author
  • Kouichi Sakurai
Conference paper
  • 326 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9565)

Abstract

We provide a symbolic model for multi-party computation based on linear secret-sharing scheme, and prove that this model is computationally sound: if there is an attack in the computational world, then there is an attack in the symbolic (abstract) model. Our original contribution is that we deal with the uniformity properties, which cannot be described using a single execution trace, while considering an unbounded number of sessions of the protocols in the presence of active and adaptive adversaries.

Keywords

Multi-party computation Uniformity properties Universally composable 

References

  1. 1.
    Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Feldman, P.: A practical scheme for non-interactive verifiable secret sharing. In: Proceedings of the 28th Annual IEEE Symposium on Foundations of Computer Science, pp. 427–437 (1987)Google Scholar
  3. 3.
    Shoup, V.: Practical threshold signatures. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 207–220. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  4. 4.
    He, A.J., Dawson, E.: Multistage secret sharing based on one-way function. Electron. Lett. 30(9), 1591–1592 (1994)CrossRefGoogle Scholar
  5. 5.
    Chien, H.-Y., Tseng, J.K.: A practical (t, n) multi-secret sharing scheme. IEICE Trans. Fundam. Electron. Commun. Comput. 83–A(12), 2762–2765 (2000)Google Scholar
  6. 6.
    Shao, J., Cao, Z.F.: A new efficient (t, n) verifiable multi-secret sharing (VMSS) based on YCH scheme. Appl. Math. Comput. 168(1), 135–140 (2005)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Zhao, J., Zhang, J., Zhao, R.: A practical verifiable multi-secret sharing scheme. Comput. Stand. Interfaces 29(1), 138–141 (2007)CrossRefGoogle Scholar
  8. 8.
    Yang, C.C., Chang, T.Y., Hwang, M.S.: A (t, n) multi-secret sharing scheme. Appl. Math. Comput. 151, 483–490 (2004)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Cramer, R., Damgård, I.B., Maurer, U.M.: General secure multi-party computation from any linear secret-sharing scheme. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 316–334. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  10. 10.
    Abadi, M., Baudet, M., Warinschi, B.: Guessing attacks and the computational soundness of static equivalence. In: Aceto, L., Ingólfsdóttir, A. (eds.) FOSSACS 2006. LNCS, vol. 3921, pp. 398–412. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Abadi, M., Fournet, C.: Mobile values, new names, and secure communication. In: Proceedings of the 28th Symposium on Principles of Programming Languages (POPL), pp. 104–115. ACM Press (2001)Google Scholar
  12. 12.
    Abadi, M., Rogaway, P.: Reconciling two views of cryptography (the computational soundness of formal encryption). J. Crypt. 15(2), 103–127 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Backes, M., Maffei, M., Mohammadi, E.: Computationally sound abstraction and verification of secure multi-party computations. In: Proceedings of ARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS) (2010)Google Scholar
  14. 14.
    Backes, M., Hofheinz, D., Unruh, D.: A general framework for computational soundness proofs or the computational soundness of the applied pi-calculus. IACR ePrint Archive 2009/080 (2009)Google Scholar
  15. 15.
    Backes, M., Bendun, F., Unruh, D.: Computational soundness of symbolic zero-knowledge proofs: weaker assumptions and mechanized verification. In: Basin, D., Mitchell, J.C. (eds.) POST 2013 (ETAPS 2013). LNCS, vol. 7796, pp. 206–225. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  16. 16.
    Backes, M., Malik, A., Unruh, D.: Computational soundness without protocol restrictions. In: CCS, pp. 699–711. ACM Press (2012)Google Scholar
  17. 17.
    Kusters, R., Tuengerthal, M.: Computational soundness for key exchange protocols with symmetric encryption. In: Proceedings of the 16th ACM Conference on Computer and Communications Security (CCS), pp. 91–100. ACM Press (2009)Google Scholar
  18. 18.
    Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multiparty secure computation. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computing (STOC), pp. 494–503. ACM Press (2002)Google Scholar
  19. 19.
    Comon-Lundh, H., Cortier, V.: Computational soundness of observational equivalence. In: Proceedings of the 16th ACM Conference on Computer and Communications Security (CCS), pp. 109–118. ACM Press (2008)Google Scholar
  20. 20.
    Comon-Lundh, H., Cortier, V., Scerri, G.: Security proof with dishonest keys. In: Degano, P., Guttman, J.D. (eds.) Principles of Security and Trust. LNCS, vol. 7215, pp. 149–168. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  21. 21.
    Canetti, R.: Herzog: universally composable symbolic security analysis. J. Cryptol. 24(1), 83–147 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Backes, M., Mohammadi, E., Ruffing, T.: Computational soundness results for ProVerif. bridging the gap from trace properties to uniformity. In: Kremer, S., Abadi, M. (eds.) POST 2014 (ETAPS 2014). LNCS, vol. 8414, pp. 42–62. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  23. 23.
    Canetti, R., Feige, U., Goldreich, O., Naor, M.: Adaptively secure multi-party computation. In: Proceedings of 28th STOC, pp. 639–648 (1996)Google Scholar
  24. 24.
    Canetti, R., Fischlin, M.: Universally composable commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  25. 25.
    Canetti, R., Rabin, T.: Universal composition with joint state. Cryptology ePrint Archive. Report 2002/047 (2002). http://eprint.iacr.org/

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Kyushu UniversityFukuokaJapan
  2. 2.Shandong University of TechnologyZiboChina

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