Journal of Zhejiang University-SCIENCE A

, Volume 8, Issue 4, pp 511–521 | Cite as

On ASGS framework: general requirements and an example of implementation

  • Kulesza Kamil 
  • Kotulski Zbigniew 


In the paper we propose a general, abstract framework for Automatic Secret Generation and Sharing (ASGS) that should be independent of underlying Secret Sharing Scheme (SSS). ASGS allows to prevent the Dealer from knowing the secret. The Basic Property Conjecture (BPC) forms the base of the framework. Due to the level of abstraction, results are portable into the realm of quantum computing.

Two situations are discussed. First concerns simultaneous generation and sharing of the random, prior nonexistent secret. Such a secret remains unknown until it is reconstructed. Next, we propose the framework for automatic sharing of a known secret. In this case the Dealer does not know the secret and the secret Owner does not know the shares. We present opportunities for joining ASGS with other extended capabilities, with special emphasis on PVSS and pre-positioned secret sharing. Finally, we illustrate framework with practical implementation.

Key words

Secret sharing Security protocols Dependable systems Authentication management 

CLC number



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson, R., 2001. Security Engineering—A Guide to Building Dependable Distributed Systems. John Wiley & Sons, New York.Google Scholar
  2. Asmuth, C., Bloom, J., 1983. A modular approach to key safeguarding. IEEE Trans. Inf. Theory, 29(2):208–211. [doi:10.1109/TIT.1983.1056651]CrossRefMathSciNetGoogle Scholar
  3. Blakley, G.R., 1979. Safeguarding Cryptographic Keys. Proceedings AFIPS 1979 National Computer Conference, p.313–317.Google Scholar
  4. Blundo, C., Stinson, D.R., 1997. Anonymous Secret Sharing Schemes. Discrete Applied Mathematics, 77(1):13–28. [doi:10.1016/S0166-218X(97)89208-6]CrossRefMATHMathSciNetGoogle Scholar
  5. Blundo, C., Giorgio Gaggia, A., Stinson, D.R., 1997. On the dealer’s randomness required in secret sharing schemes. Designs, Codes and Cryptography, 11(2):107–122. [doi:10.1023/A:1008216403325]CrossRefMATHMathSciNetGoogle Scholar
  6. Brickell, E.F., 1989. Some ideal secret sharing schemes. J. Combin. Math. Combin. Comput., 6:105–113.MATHMathSciNetGoogle Scholar
  7. Budd, T., 1997. The Introduction to Object-Oriented Programming. Addison-Wesley, Reading.Google Scholar
  8. Desmedt, Y., Frankel, Y., 1989. Threshold cryptosystems. Crypto’89. LNCS, 435:307–315.Google Scholar
  9. Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T., 1999. Secure distributed key generation for discrete-log based cryptosystems. Eurocrypt’99. LNCS, 1592:295–310.MATHGoogle Scholar
  10. Gruska, J., 1999. Quantum Computing. McGraw Hill, New York.MATHGoogle Scholar
  11. Herstein, I.N., 1964. Topics in Algebra. Blaisdell Publishing, Waltham, Massachusetts.MATHGoogle Scholar
  12. Ito, M., Saito, A., Nishizeki, T., 1987. Secret Sharing Scheme Realizing General Access Structure. Proc. IEEE Globecom’87, p.99–102.Google Scholar
  13. Karnin, E.D., Greene, J.W., Hellman, M.E., 1983. On secret sharing systems. IEEE Trans. Inf. Theory, 29(1):35–41. [doi:10.1109/TIT.1983.1056621]CrossRefMATHMathSciNetGoogle Scholar
  14. Knuth, D.E., 1997. The Art of Computer Programming—Seminumerical Algorithms. Vol. 2, 3rd Ed., Addison-Wesley, Reading.MATHGoogle Scholar
  15. Koblitz, N., 1993. Introduction to Elliptic Curves and Modular Forms. Springer-Verlag, New York.CrossRefMATHGoogle Scholar
  16. Kulesza, K., Kotulski, Z., 2002. On Secret Sharing Schemes with Extended Capabilities. RCMIS’02, 1:79–88.Google Scholar
  17. Kulesza, K., Kotulski, Z., Pieprzyk, J., 2002. On Alternative Approach for Verifiable Secret Sharing. Esorics’02. Available from IACR’s Cryptology ePrint Archive (
  18. Kulesza, K., Kotulski, Z., 2003. On Automatic Secret Generation and Sharing for Karin-Greene-Hellman Scheme. In: Soldek, J., Drobiazgiewicz, L. (Eds.), Artificial Intelligence and Security in Computing Systems Advanced Computer Systems. Kluwer Academic Publisher, Boston, p.281–292.Google Scholar
  19. Li, C., Hwang, T., Lee, N., 1994. (t,n) threshold signature schemes based on discrete logarithm. Eurocrypt’94. LNCS, 950: 191–200.Google Scholar
  20. Menezes, A.J., van Oorschot, P., Vanstone, S.C., 1997. Handbook of Applied Cryptography. CRC Press, Boca Raton.MATHGoogle Scholar
  21. Pedersen, T., 1991. A threshold cryptosystem without a trusted third party. Eurocrypt’99. LNCS, 547:522–526.MATHGoogle Scholar
  22. Pieprzyk, J., Hardjono, T., Seberry, J., 2003. Fundamentals of Computer Security. Springer-Verlag, Berlin.CrossRefMATHGoogle Scholar
  23. Shamir, A., 1979. How to share a secret. Commun. ACM, 22(11):612–613. [doi:10.1145/359168.359176]CrossRefMATHMathSciNetGoogle Scholar
  24. Shoup, V., Gennaro, R., 1998. Securing threshold cryptosystems against chosen ciphertext attack. Crypto’98. LNCS, 1403:1–16.MATHMathSciNetGoogle Scholar
  25. Stadler, M., 1996. Publicly verifiable secret sharing. Eurocrypt’96. LNCS, 1070:190–199.MATHGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Kulesza Kamil 
    • 1
    • 2
  • Kotulski Zbigniew 
    • 2
  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeUK
  2. 2.Institute of Fundamental Technological ResearchPolish Academy of SciencesWarsawPoland

Personalised recommendations