Skip to main content
Book cover

International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 1999: Advances in Cryptology — EUROCRYPT ’99 pp 295–310Cite as

Secure Distributed Key Generation for Discrete-Log Based Cryptosystems

Part of the Lecture Notes in Computer Science book series (LNCS,volume 1592)

Abstract

Distributed key generation is a main component of threshold cryptosystems and distributed cryptographic computing in general. Solutions to the distributed generation of private keys for discrete-log based cryptosystems have been known for several years and used in a variety of protocols and in many research papers. However, these solutions fail to provide the full security required and claimed by these works. We show how an active attacker controlling a small number of parties can bias the values of the generated keys, thus violating basic correctness and secrecy requirements of a key generation protocol. In particular, our attacks point out to the places where the proofs of security fail.

Based on these findings we designed a distributed key generation protocol which we present here together with a rigorous proof of security. Our solution, that achieves optimal resiliency, can be used as a drop-in replacement for key generation modules as well as other components of threshold or proactive discrete-log based cryptosystems.

Keywords

  • Threshold Cryptography
  • Distributed Key Generation
  • VSS
  • Discrete Logarithm

Download conference paper PDF

References

  1. R. Canetti, R. Gennaro, S. Jarecki, H. Krawczyk, and T. Rabin. Adaptive Security for Threshold Cryptosystems. Mansuscript, 1999.

    Google Scholar 

  2. R. Cramer, R. Gennaro, and B. Schoenmakers. A secure and optimally efficient multi-authority election scheme. In Advances in Cryptology — Eurocrypt’ 97, pages 103–118. LNCS No. 1233.

    Google Scholar 

  3. M. Cerecedo, T. Matsumoto, and H. Imai. Efficient and secure multiparty generation of digital signatures based on discrete logarithms. IEICE Trans. Fundamentals, E76-A(4):532–545, 1993.

    Google Scholar 

  4. Yvo Desmedt and Yair Frankel. Threshold cryptosystems. In Advances in Cryptology — Crypto’ 89, pages 307–315. LNCS No. 435.

    Google Scholar 

  5. T. ElGamal. A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. IEEE Trans. Info. Theory, IT 31:469–472, 1985.

    CrossRef  MathSciNet  Google Scholar 

  6. P. Feldman. A Practical Scheme for Non-Interactive Verifiable Secret Sharing. In Proc. 28th FOCS, pages 427–437.

    Google Scholar 

  7. Y. Frankel, P. Gemmell, P. Mackenzie, and M. Yung. Optimal resilience proactive public-key cryptosystems. In Proc. 38th FOCS, pages 384–393. IEEE, 1997.

    Google Scholar 

  8. R. Gennaro, S. Jarecki, H. Krawczyk, and T. Rabin. Robust threshold DSS signatures. In Advances in Cryptology — Eurocrypt’ 96, pages 354–371. LNCS No. 1070.

    Google Scholar 

  9. R. Gennaro, S. Jarecki, H. Krawczyk, and T. Rabin. Secure Distributed Key Generation for Discrete-Log Based Cryptosystems http://www.research.ibm.com/security/dkg.ps

  10. L. Harn. Group oriented (t; n) digital signature scheme. IEE Proc.-Comput.Digit.Tech, 141(5):307–313, Sept 1994.

    MATH  CrossRef  Google Scholar 

  11. A. Herzberg, M. Jakobsson, S. Jarecki, H. Krawczyk, and M. Yung. Proactive public key and signature systems. In 1997 ACM Conference on Computers and Communication Security, 1997.

    Google Scholar 

  12. A. Herzberg, S. Jarecki, H. Krawczyk, and M. Yung. Proactive secret sharing, or: How to cope with perpetual leakage. In Advances in Cryptology — Crypto’ 95, pages 339–352. LNCS No. 963.

    Google Scholar 

  13. C.-H. Li, T. Hwang, and N.-Y. Lee. (t; n) threshold signature schemes ased on discrete logarithm. In Advances in Cryptology — Eurocrypt’ 94, pages 191–200. LNCS No. 950.

    Google Scholar 

  14. T. Pedersen. A threshold cryptosystem without a trusted party. In Advances in Cryptology — Eurocrypt’ 91, pages 522–526. LNCS No. 547.

    Google Scholar 

  15. T. Pedersen. Non-interactive and information-theoretic secure verifiable secret sharing. In Advances in Cryptology — Crypto’ 91, pages 129–140. LNCS No. 576.

    Google Scholar 

  16. C. Park and K. Kurosawa. New ElGamal Type Threshold Digital Signature Scheme. IEICE Trans. Fundamentals, E79-A(1):86–93, January 1996.

    Google Scholar 

  17. C. P. Schnorr. Efficient signature generation by smart cards. Journal of Cryptology, 4:161–174, 1991.

    MATH  CrossRef  Google Scholar 

  18. V. Shoup and R. Gennaro. Securing threshold cryptosystems against chosen ciphertext attack. In Advances in Cryptology — Eurocrypt’ 98, pages 1–16. LNCS No. 1403.

    Google Scholar 

  19. A. Shamir. How to Share a Secret. Communications of the ACM, 22:612–613, 1979.

    MATH  CrossRef  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IBM T.J.Watson Research Center, PO Box 704, Yorktown Heights, NY, 10598, USA

    Rosario Gennaro & Tal Rabin

  2. MIT Laboratory for Computer Science, 545 Tech Square, Cambridge, MA, 02139, USA

    Stanisław Jarecki

  3. Department of Electrical Engineering, Technion, Haifa, 32000, Israel

    Hugo Krawczyk

  4. IBM T.J. Watson Research Center, New York, USA

    Hugo Krawczyk

Authors
  1. Rosario Gennaro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stanisław Jarecki
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hugo Krawczyk
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tal Rabin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Ecole Normale Supérieure, 45, rue d’Ulm, F-75230, Paris 05, France

    Jacques Stern

Rights and permissions

Reprints and Permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T. (1999). Secure Distributed Key Generation for Discrete-Log Based Cryptosystems. In: Stern, J. (eds) Advances in Cryptology — EUROCRYPT ’99. EUROCRYPT 1999. Lecture Notes in Computer Science, vol 1592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48910-X_21

Download citation

  • DOI: https://doi.org/10.1007/3-540-48910-X_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65889-4

  • Online ISBN: 978-3-540-48910-8

  • eBook Packages: Springer Book Archive