Unconditionally Secure Proactive Secret Sharing Scheme with Combinatorial Structures

  • Douglas R. Stinson
  • R. Wei
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1758)


Verifiable secret sharing schemes (VSS) are secret sharing schemes dealing with possible cheating by the participants. In this paper, we propose a new unconditionally secure VSS. Then we construct a new proactive secret sharing scheme based on that VSS. In a proactive scheme, the shares are periodically renewed so that an adversary cannot get any information about the secret unless he is able to access a specified number of shares in a short time period. Furthermore, we introduce some combinatorial structure into the proactive scheme to make the scheme more efficient. The combinatorial method might also be used to improve some of the previously constructed proactive schemes.


Secret Sharing Good Server Combinatorial Structure Secret Information Proactive Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    N. Alon, Z. Galil and M. Yung, Efficient dynamic-resharing “verifiable secret sharing” against mobile adversary, European Symposium on Algorithms (ESA) 95, LNCS 979, 523–537.Google Scholar
  2. 2.
    J. C. Benaloh, Secret sharing homomorphisms: keeping shares of a secret secret, Advances in Cryptology-Crypto’86, LNCS 263, 1987, 251–260.Google Scholar
  3. 3.
    M. Ben-Or, S. Goldwasser and A. Wigderson, Completeness Theorems for Noncryptographic Fault-Tolerant Distributed Computations, Proc. 20th Annual Symp. on the Theory of Computing, ACM, 1988, 1–10.Google Scholar
  4. 4.
    G.R. Blackley, Safeguarding cryptographic keys. Proc. Nat. Computer Conf. AFIPS Conf. Proc., 1979, 313–317.Google Scholar
  5. 5.
    R. Blom, An optimal class of symmetric key generation systems, Eurocrypt’84, LNCS 209, (1985), 335–338.Google Scholar
  6. 6.
    R. Canetti and A. Herzberg, Maintaining security in the presence of transient faults, Crypto’94, LNCS 839, 1994.Google Scholar
  7. 7.
    D. Chaum, C. Crepeau and I. Damgard, Multiparty Unconditionally Secure Protocols, Proc. 20th Annual Symp. on the Theory of Computing, ACM, 1988, 11–19.Google Scholar
  8. 8.
    B. Chor, S. Goldwasser, S. Micali and B. Awerbuch, Verifiable Secret Sharing and Achieving Simultaneity in Presence of Faults, Proc. 26th Annual Symp. on the Foundations of Computing Science, IEEE, 1985, 383–395.Google Scholar
  9. 9.
    P. Feldman, A Practical Scheme for Non-Interactive Verifiable Secret sharing, Proc. 28th Annual Symp. on the Foundations of Computing Science, IEEE, 1987, 427–437.Google Scholar
  10. 10.
    P. Feldman and S. Micali, An Optimal Algorithm for Synchronous Byzantine Agreement, Proc. 20th Annual Symp. on Theory of Computing, ACM, 1988, 148–161.Google Scholar
  11. 11.
    Y. Frankel, P. Gemmel, P. D. MacKenzie and M. Yung, Proactive RSA, Crypto’97, LNCS 1294, 440–452.Google Scholar
  12. 12.
    R. Gennaro, M. O. Rabin and T. Rabin, Simplified VSS and fast-track multiparty computations with applications to threshold cryptography, Proc. of 17th ACM Symp. on Principles of Distributed Computing, (1998), 101–111.Google Scholar
  13. 13.
    O. Goldreich, S. Micali and A. Wigderson, Proofs that Yield Nothing But Their Validity or All Languages in NP Have Zero-Knowledge Proof Systems, Journal of the ACM, 38 (1991) 691–729.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    A. Herzberg, M. Jakobsson, S. Jarecki, H. Krawczyk and M. Yung, Proactive public key and signature systems, The 4th ACM Symp. on Comp. and Comm. Security, April 1997.Google Scholar
  15. 15.
    A. Herzberg, S. Jarecki, H. Krawczyk and M. Yung, Proactive secret sharing or: How to cope with perpetual leakage, Crypto’95, LNCS 963339-352.Google Scholar
  16. 16.
    I. Ingemarsson and G. J. Simmons, A protocol to set up shared secret schemes without the assistance of a mutually trusted party, Eurocrypt’90, LNCS 473, 1990, 266–282.Google Scholar
  17. 17.
    R. J. McEliece and D. V. Sarwate, On Sharing Secrets and Reed-Solomon Codes, Communications of the ACM, 24 (1981), 583–584.CrossRefMathSciNetGoogle Scholar
  18. 18.
    R. Ostrovsky and M. Yung, How to withstand mobile virus attacks, ACM Symposium on principles of distributed computing, 1991, 51–59.Google Scholar
  19. 19.
    T. P. Pedersen, Non-interactive and information-theoretic secret sharing, Advances in Cryptology-Crypto’91, LNCS 576, 1991, 129–140.Google Scholar
  20. 20.
    T. Rabin, Robust sharing of secrets when the dealer is honest or faulty, Journal of the ACM, 41 (1994), 1089–1109.CrossRefGoogle Scholar
  21. 21.
    T. Rabin, A simplified approach to threshold and proactive RSA, Crypto’98, LNCS 1462, 1998, 89–104.Google Scholar
  22. 22.
    T. Rabin and M. Ben-Or, Verifiable secret sharing and multiparty protocols with honest majority, Proc. 21st Annual Sympo. on the Theory of Computing, ACM, 1989, 73–85.Google Scholar
  23. 23.
    A. Shamir, How to share a secret, Commun. ACM, 22 (1979), 612–613.zbMATHMathSciNetGoogle Scholar
  24. 24.
    R. S. Rees, D. R. Stinson, R. Wei and G. H. J. van Rees, An application of covering designs: determining the maximum consistent set of shares in a threshold scheme, Ars Combin., to appear.Google Scholar
  25. 25.
    D. R. Stinson, Cryptography Theory and Practice, CRC Press, 1995.Google Scholar
  26. 26.
    M. Tompa and H. Woll, How to share a secret with cheaters, Journal of Cryptology, 1 (1988), 133–138.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Douglas R. Stinson
    • 1
  • R. Wei
    • 1
  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

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