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Abstract

This paper presents a new construction of a lattice-based verifiable secret sharing scheme. Our proposal is based on lattices and the usage of linear hash functions to enable each participant to verify its received secret share. The security of this scheme relies on the hardness of some well known approximation problems in lattices such as n c -approximate SVP. Different to protocols proposed by Pedersen this scheme uses efficient matrix vector operations instead of exponentiation to verify the secret shares.

Keywords

Secret Sharing Lattice-based Cryptography Shortest Vector Problem Hash Functions 

References

  1. 1.
    Ajtai, M.: Generating hard instances of lattice problems (extended abstract). In: Proceedings of the Twenty-Eighth Annual ACM Symposium on the Theory of Computing, pp. 99–108. ACM (1996)Google Scholar
  2. 2.
    Asmuth, C., Bloom, J.: A modular approach to key safeguarding. IEEE Transactions on Information Theory 29(2), 208–210 (1983)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Blakley, G.R.: Safeguarding cryptographic keys. In: Proceedings of the National Computer Conference, pp. 313–317. American Federation of Information Processing Societies (1979)Google Scholar
  4. 4.
    Cramer, R., Damgård, I., Maurer, U.: 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
  5. 5.
    Lyubashevsky, V., Micciancio, D.: Generalized Compact Knapsacks Are Collision Resistant. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006, Part II. LNCS, vol. 4052, pp. 144–155. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Mahimkar, A.: Securedav: A secure data aggregation and verification protocol for sensor networks. In: Proceedings of the IEEE Global Telecommunications Conference, pp. 2175–2179 (2004)Google Scholar
  7. 7.
    Mignotte, M.: How to Share a Secret? In: Beth, T. (ed.) Cryptography - EUROCRYPT 1982. LNCS, vol. 149, pp. 371–375. Springer, Heidelberg (1983)CrossRefGoogle Scholar
  8. 8.
    Pedersen, T.P.: Non-interactive and Information-Theoretic Secure Verifiable Secret Sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)Google Scholar
  9. 9.
    Peikert, C., Rosen, A.: Efficient Collision-Resistant Hashing from Worst-Case Assumptions on Cyclic Lattices. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 145–166. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM 56(6), 34:1–34:40 (2009)Google Scholar
  11. 11.
    Shamir, A.: How to share a secret. Commun. ACM 22, 612–613 (1979)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Smith, H.J.S.: On systems of linear indeterminate equations and congruences. Philosophical Transactions of the Royal Society of London 151, 293–326 (1861)CrossRefGoogle Scholar
  14. 14.
    Sorin, Iftene: General secret sharing based on the chinese remainder theorem with applications in e-voting. Electronic Notes in Theoretical Computer Science 186, 67–84 (2007)CrossRefGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2012

Authors and Affiliations

  • Rachid El Bansarkhani
    • 1
  • Mohammed Meziani
    • 2
  1. 1.Fachbereich Informatik, Kryptographie und ComputeralgebraTechnische Universität DarmstadtDarmstadtGermany
  2. 2.CASED – Center for Advanced Security Research DarmstadtDarmstadtGermany

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