Impossibility of Finding Any Third Family of Server Protocols Integrating Byzantine Quorum Systems with Threshold Signature Schemes

  • Jingqiang Lin
  • Peng Liu
  • Jiwu Jing
  • Qiongxiao Wang
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 50)


In order to tolerate servers’ Byzantine failures, a distributed storage service of self-verifying data (e.g., certificates) needs to make three security properties be Byzantine fault tolerant (BFT): data consistency, data availability, and confidentiality of the (signing service’s) private key. Building such systems demands the integration of Byzantine quorum systems (BQS), which only make data consistency and availability be BFT, and threshold signature schemes (TSS), which only make confidentiality of the private key be BFT. Two families of correct or valid TSS-BQS systems (of which the server protocols carry all the design options) have been proposed in the literature. Motivated by the failures in finding a third family of valid server protocols, we study the reverse problem and formally prove that it is impossible to find any third family of valid TSS-BQS systems. To obtain this proof, we develop a validity theory on server protocols of TSS-BQS systems. It is shown that the only two families of valid server protocols, “predicted” (or deduced) by the validity theory, precisely match the existing protocols.


Byzantine fault tolerance Byzantine quorum systems threshold signature schemes 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alvisi, L., Dahlin, M., et al.: Dynamic Byzantine quorum systems. In: Int’l. Conf. Dependable Systems and Networks, pp. 283–292 (2000)Google Scholar
  2. 2.
    Amir, Y., Coan, B., et al.: Customizable fault tolerance for wide-area replication. In: IEEE Symp. Reliable Distributed Systems, pp. 65–82 (2007)Google Scholar
  3. 3.
    Amir, Y., Danilov, C., et al.: Scaling Byzantine fault-tolerant replication to wide area networks. In: Int’l. Conf. Dependable Systems and Networks, pp. 105–114 (2006)Google Scholar
  4. 4.
    Bazzi, R.: Synchronous Byzantine quorum systems. Distributed Computing 13(1), 45–52 (2000)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Castro, M., Liskov, B.: Practical Byzantine fault tolerance and proactive recovery. ACM Trans. Computer Systems 20(4), 398–461 (2002)CrossRefGoogle Scholar
  6. 6.
    Desmedt, Y.: Society and group oriented cryptography: A new concept. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 120–127. Springer, Heidelberg (1988)Google Scholar
  7. 7.
    Goodson, G., Wylie, J., et al.: Efficient Byzantine-tolerant erasure-coded storage. In: Int’l. Conf. Dependable Systems and Networks, pp. 135–144 (2004)Google Scholar
  8. 8.
    Herzberg, A., Jakobsson, M., et al.: Proactive public key and signature systems. In: ACM Conf. Computer Communications Security, pp. 100–110 (1997)Google Scholar
  9. 9.
    Iyengar, A., Cahn, R., et al.: Design and implementation of a secure distributed data repository. In: IFIP Int’l. Information Security Conference, pp. 123–135 (1998)Google Scholar
  10. 10.
    Jing, J., Wang, J., et al.: Research on server protocols of Byzantine quorum systems implemented utilizing threshold signature schemes (accepted to appear). Chinese Journal of Software Google Scholar
  11. 11.
    Kong, L., Subbiah, A., et al.: A reconfigurable Byzantine quorum approach for the Agile Store. In: IEEE Symp. Reliable Distributed Systems, pp. 219–228 (2003)Google Scholar
  12. 12.
    Lamport, L., Shostak, R., et al.: The Byzantine generals problem. ACM Trans. Programming Languages and Systems 4(3), 382–401 (1982)CrossRefzbMATHGoogle Scholar
  13. 13.
    Malkhi, D., Reiter, M.: Byzantine quorum systems. Distributed Computing 11(4), 203–213 (1998)CrossRefzbMATHGoogle Scholar
  14. 14.
    Malkhi, D., Reiter, M.: Secure and scalable replication in Phalanx. In: IEEE Symp. Reliable Distributed Systems, pp. 51–60 (1998)Google Scholar
  15. 15.
    Marsh, M., Schneider, F.: CODEX: A robust and secure secret distribution system. IEEE Trans. Dependable and Secure Computing 1(1), 34–47 (2004)CrossRefGoogle Scholar
  16. 16.
    Martin, J.-P., Alvisi, L.: A framework for dynamic Byzantine storage. In: Int’l. Conf. Dependable Systems and Networks, pp. 325–334 (2004)Google Scholar
  17. 17.
    Martin, J.-P., Alvisi, L., et al.: Small Byzantine quorum systems. In: Int’l. Conf. Dependable Systems and Networks, pp. 374–383 (2002)Google Scholar
  18. 18.
    Naor, M., Wool, A.: Access control and signatures via quorum secret sharing. IEEE Trans. Parallel and Distributed Systems 9(9), 909–922 (1998)CrossRefGoogle Scholar
  19. 19.
    Ostrovsky, R., Yung, M.: How to withstand mobile virus attacks. In: ACM Symp. Principles of Distributed Computing, pp. 51–59 (1991)Google Scholar
  20. 20.
    Reiter, M., Birman, K.: How to securely replicate services. ACM Trans. Programming Languages and Systems 16(3), 986–1009 (1994)CrossRefGoogle Scholar
  21. 21.
    Reiter, M., Franklin, M., et al.: The Ω key management service. In: ACM Conf. Computer and Communications Security, pp. 38–47 (1996)Google Scholar
  22. 22.
    Rhea, S., Eaton, P., et al.: Pond: the OceanStore prototype. In: USENIX Conf. File and Storage Technologies, pp. 1–14 (2003)Google Scholar
  23. 23.
    Subbiah, A., Ahamad, M., et al.: Using Byzantine quorum systems to manage confidential data. Technical Report GIT-CERCS-04-13, Georgia Institute of Technology (2004)Google Scholar
  24. 24.
    Subbiah, A., Blough, D.: An approach for fault tolerant and secure data storage in collaborative work environments. In: ACM Workshop on Storage Security and Survivability, pp. 84–93 (2005)Google Scholar
  25. 25.
    Wylie, J., Bigrigg, M., et al.: Survivable information storage systems. IEEE Computer 33(8), 61–68 (2000)CrossRefGoogle Scholar
  26. 26.
    Zhou, L., Schneider, F., et al.: COCA: A secure on-line certification authority. ACM Trans. Computer Systems 20(4), 329–368 (2002)CrossRefGoogle Scholar
  27. 27.
    Zhou, L., Schneider, F., et al.: APSS: Proactive secret sharing in asynchronous systems. ACM Trans. Information and System Security 8(3), 259–286 (2005)CrossRefGoogle Scholar

Copyright information

© ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering 2010

Authors and Affiliations

  • Jingqiang Lin
    • 1
    • 2
  • Peng Liu
    • 2
  • Jiwu Jing
    • 1
  • Qiongxiao Wang
    • 1
  1. 1.The State Key Laboratory of Information SecurityGraduate University of CASBeijingChina
  2. 2.The Pennsylvania State UniversityUniversity ParkUSA

Personalised recommendations