A Threshold Pseudorandom Function Construction and Its Applications

  • Jesper Buus Nielsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2442)


We give the first construction of a practical threshold pseudo- random function.The protocol for evaluating the function is efficient enough that it can be used to replace random oracles in some protocols relying on such oracles. In particular, we show how to transform the efficient cryptographically secure Byzantine agreement protocol by Cachin, Kursawe and Shoup for the random oracle model into a cryptographically secure protocol for the complexity theoretic model without loosing efficiency or resilience,thereby constructing an efficient and optimally resilient Byzantine agreement protocol for the complexity theoretic model.


Random Oracle Function Family Ideal Functionality Random Oracle Model Pseudorandom Function 
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. BCF00.
    Ernest F. Brickell, Giovanni Di Crescenzo, and Yair Frankel. Sharing blockciphers.In Ed Dawson, Andrew Clark, and Colin Boyd,editors,Information Security and Privacy, 5th Australasian Conference, ACISP 2000, Brisbane, Australia, July 10–12,2000, Proceedings, pages 457–470.Springer, 2000.Google Scholar
  2. BDJR97.
    M. Bellare, A. Desai, E. Jokipii, and P. Rogaway. A concrete security treatment of symmetric encryption.In 38th Annual Symposium on Foundations of Computer Science [IEE97].Google Scholar
  3. Can01.
    Ran Canetti. Universally composable security:A new paradigm for cryptographic protocols.In 42th Annual Symposium on Foundations of Computer Science.IEEE, 2001.Google Scholar
  4. CGH98.
    Ran Canetti, Oded Goldreich, and Shai Halevi.The random oracle methodology, revisited (preliminary version).In Proceedings of the Thirtieth Annual ACM Symposium on the Theory of Computing,pages 209–218, Dallas, TX,USA, 24–26 May 1998.Google Scholar
  5. CHH00.
    Ran Canetti, Shai Halevi, and Amir Herzberg. Maintaining authenticated communication in the presence of break-ins.Journal of Cryptology,13(1):61–106,winter 2000.MATHCrossRefMathSciNetGoogle Scholar
  6. CKS00.
    Christian Cachin, Klaus Kursawe, and Victor Shoup. Random oracles in constantinople:Practical asynchronous byzantine agreement using cryptography.In Proceedings of the 19th ACM Symposium on Principles of Distributed Computing (PODC 2000),pages 123–132.ACM, July 2000.Google Scholar
  7. CP92.
    D. Chaum and T.P. Pedersen.Wallet databases with observers.InErnest F. Brickell,editor,Advances in Cryptology-Crypto’ 92,pages 89–105,Berlin,1992.Springer-Verlag.Lecture Notes in Computer ScienceVolume 740.Google Scholar
  8. GGM86.
    Oded Goldreich, Shafi Goldwasser, and Silvio Micali. How to construct random functions. Journal of the ACM, 33(4):792–807,1986.CrossRefMathSciNetGoogle Scholar
  9. Gol01.
    Oded Goldreich.The Foundations of Cryptography, volume 1.Cambridge University Press, 2001.Google Scholar
  10. IEE97.
    IEEE. 38th Annual Symposium on Foundations of Computer Science,Miami Beach,FL,19-22 October 1997.Google Scholar
  11. MS95.
    Silvio Micali and Ray Sidney. A simple method for generating and sharing pseudo-random functions,with applications to clipper-like escrow systems.In Don Coppersmith,editor, Advances in Cryptology-Crypto’ 95,pages 185–196, Berlin,1995.Springer-Verlag. Lecture Notes in Computer ScienceVolume 963.Google Scholar
  12. Nie02.
    Jesper B. Nielsen. Separating random oracle proofs from complexity theoretic proofs: the non-committing encryption case.In Advances in Cryptology-Crypto’ 02, 2002.Google Scholar
  13. NPR99.
    Moni Naor, Benny Pinkas, and Omer Reingold. Distributed pseudo-random functions and KDCs.In Jacques Stern,editor, Advances in Cryptology-EuroCrypt’ 99,pages 327–346, Berlin,1999.Springer-Verlag.Lecture Notes in Computer Science Volume 1592.Google Scholar
  14. NR97.
    Moni Naor and Omer Reingold. Number-theoretic constructions of efficient pseudo-random functions (extended abstract).In 38th Annual Symposium on Foundations of Computer Science [IEE97],pages 458–467.Google Scholar
  15. Sho00.
    Victor Shoup.Practical threshold signatures.In Bart Preneel,editor,Advances in Cryptology-EuroCrypt 2000,pages 207–220, Berlin, 2000.Springer-Verlag. Lecture Notes in Computer ScienceVolume 1807.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jesper Buus Nielsen
    • 1
  1. 1.BRICS Department of Computer ScienceUniversity of AarhusArhus CDenmark

Personalised recommendations