Skip to main content
Download book PDF
View expanded cover

International Workshop on Public Key Cryptography

PKC 2003: Public Key Cryptography — PKC 2003 pp 1–17Cite as

Efficient Construction of (Distributed) Verifiable Random Functions

Part of the Lecture Notes in Computer Science book series (LNCS,volume 2567)

Abstract

We give the first simple and efficient construction of verifiable random functions (VRFs). VRFs, introduced by Micali et al. [13], combine the properties of regular pseudorandom functions (PRFs) (i.e., indistinguishability from a random function) and digital signatures (i.e., one can provide an unforgeable proof that the VRF value is correctly computed). The efficiency of our VRF construction is only slightly worse than that of a regular PRF construction of Naor and Reingold [16]. In contrast to our direct construction, all previous VRF constructions [13],[12] involved an expensive generic transformation from verifiable unpredictable functions (VUFs).

We also provide the first construction of distributed VRFs. Our construction is more efficient than the only known construction of distributed (non-verifiable) PRFs [17], but has more applications than the latter. For example, it can be used to distributively implement the random oracle model in a publicly verifiable manner, which by itself has many applications.

Our construction is based on a new variant of decisional Diffie-Hellman (DDH) assumption on certain groups where the regular DDH assumption does not hold [10],[9]. Nevertheless, this variant of DDH seems to be plausible based on our current understanding of these groups. We hope that the demonstrated power of our assumption will serve as a motivation for its closer study.

Keywords

  • Random Function
  • Random Oracle
  • Random Oracle Model
  • Oracle Access
  • Round Complexity

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.

Download conference paper PDF

References

  1. Noga Alon and Joel Spencer. Probabilistic Method. Wiley, John and Sons, 2000. 9

    Google Scholar 

  2. Mihir Bellare and Phillip Rogaway. Random oracles are practical: A paradigm for designing efficient protocols. In Proceedings of the 1st ACM Conference on Computer and Communication Security, pages 62–73, November 1993. Revised version appears in http://www-cse.ucsd.edu/users/mihir/papers/crypto-papers.html. 1

  3. Dan Boneh and Matthew Franklin. Identity based encryption from the weil pairing. In Kilian [11], pages 213–229. 7

    Google Scholar 

  4. Dan Boneh and Alice Silverberg. Applications of multilinear forms to cryptography. IACR E-print Archive. Available from http://eprint.iacr.org/2002/080/ 2002. 7

  5. Ran Canetti, Oded Goldreich, and Shai Halevi. The random oracle methodology, revisited. In Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, pages 209–218, Dallas, Texas, 23–26 May 1998. 1

    Google Scholar 

  6. Yevgeniy Dodis. Efficient construction of (distributed) verifiable random functions. IACR E-print Archive. Available from http://eprint.iacr.org/2002/133/, 2002. 10

  7. O. Goldreich and L. Levin. A hard-core predicate for all one-way functions. In Proceedings of the Twenty First Annual ACM Symposium on Theory of Computing, pages 25–32, Seattle, Washington, 15–17 May 1989. 3

    Google Scholar 

  8. Oded Goldreich, Sha. Goldwasser, and Silvio Micali. How to construct random functions. Journal of the ACM, 33(4):792–807, October 1986. 2, 5

    CrossRef  MathSciNet  Google Scholar 

  9. Antoine Joux. A one-round protocol for tripartite diffie-hellman. In ANTS-IV Conference, volume 1838 of Lecture Notes in Computer Science, pages 385–394. Spring-Verlag, 2000. 1

    Google Scholar 

  10. Antoine Joux and Kim Nguyen. Separating decision Diffie-Hellman from Diffie-Hellman in cryptographic groups. IACR E-print Archive. Available from http://eprint.iacr.org/2001/003/, 2001. 1, 4, 7

  11. Joe Kilian, editor. Advances in Cryptology—CRYPTO 2001, volume 2139 of Lecture Notes in Computer Science. Springer-Verlag, 19–23 August 2001. 16

    MATH  Google Scholar 

  12. Anna Lysyanskaya. Unique signatures and verifiable random functions from the dh-ddh separation. In Yung [21]. 1, 2, 3, 5, 6, 7, 10

    Google Scholar 

  13. Silvio Micali, Michael Rabin, and Salil Vadhan. Verifiable random functions. In 40th Annual Symposium on Foundations of Computer Science, pages 120–130, New York, October 1999. IEEE. 1, 2, 3

    Google Scholar 

  14. Silvio Micali and Ray Sidney. A simple method for generating and sharing pseudo-random functions. In Don Coppersmith, editor, Advances in Cryptology—CRYPTO’ 95, volume 963 of Lecture Notes in Computer Science, pages 185–196. Springer-Verlag, 27–31 August 1995. 3

    CrossRef  Google Scholar 

  15. Moni Naor, Benny Pinkas, and Omer Reingold. Distributed pseudo-random functions and KDCs. In Stern [20], pages 327–346. 3

    Google Scholar 

  16. Moni Naor and Omer Reingold. Number-theoretic constructions of efficient pseudo-random functions. In 38th Annual Symposium on Foundations of Computer Science, pages 458–467, Miami Beach, Florida, 20–22 October 1997. IEEE. 1, 2, 4, 5, 6, 9

    Google Scholar 

  17. Jesper Nielsen. Threshold pseudorandom function construction and its applications. In Yung [21]. 1, 4, 5, 13

    Google Scholar 

  18. Adi Shamir. How to share a secret. Communications of the ACM, 22(11):612–613, 1979. 15

    MATH  CrossRef  MathSciNet  Google Scholar 

  19. Michael Steiner, Gene Tsudik, and Michael Waidner. Diffie-hellman key distribution extended to group communicatio. In Third ACM Conference on Computer and Communication Security, pages 31–37. ACM, March 14–16 1996. 7, 9

    Google Scholar 

  20. Jacques Stern, editor. Advances in Cryptology—EUROCRYPT’ 99, volume 1592 of Lecture Notes in Computer Science. Springer-Verlag, 2–6 May 1999. 16

    MATH  Google Scholar 

  21. Moti Yung, editor. Advances in Cryptology—CRYPTO 2002, Lecture Notes in Computer Science. Springer-Verlag, 18–22 August 2002. 16, 17

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, New York University, USA

    Yevgeniy Dodis

Authors
  1. Yevgeniy Dodis
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Florida State University, 253 Love Building, 32306-4530, Tallahassee, FL, USA

    Yvo G. Desmedt

Rights and permissions

Reprints and Permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dodis, Y. (2003). Efficient Construction of (Distributed) Verifiable Random Functions. In: Desmedt, Y.G. (eds) Public Key Cryptography — PKC 2003. PKC 2003. Lecture Notes in Computer Science, vol 2567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36288-6_1

Download citation

  • DOI: https://doi.org/10.1007/3-540-36288-6_1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00324-3

  • Online ISBN: 978-3-540-36288-3

  • eBook Packages: Springer Book Archive