Skip to main content
SpringerLink
Log in

A New Identification Scheme Based on the Bilinear Diffie-Hellman Problem

  • Conference paper
  • First Online:
Information Security and Privacy (ACISP 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2384))

Included in the following conference series:

Abstract

We construct an interactive identification scheme based on the bilinear Diffie-Hellman problem and analyze its security. This scheme is practical in terms of key size, communication complexity, and availability of identity-variance provided that an algorithm of computing the Weil-pairing is feasible. We prove that this scheme is secure against active attacks as well as passive attacks if the bilinear Diffie-Hellman problem is intractable. Our proof is based on the fact that the computational Diffie-Hellman problem is hard in the additive group of points of an elliptic curve over a finite field, on the other hand, the decisional Diffie-Hellman problem is easy in the multiplicative group of the finite field mapped by a bilinear map. Finally, this scheme is compared with other identification schemes.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Bellare and P. Rogaway, “Random Oracles are Practical: A Paradigm for Designing Efficient Protocols”, ACM Conference on Computer and Communications Security, pp. 62–73, 1993.

    Google Scholar 

  2. D. Boneh and M. Franklin, “ID-based encryption from the Weil-pairing”, Advances in Cryptology-Crypto’ 2001, LNCS 2139, Springer-Verlag, pp. 213–229, 2001.

    Chapter  Google Scholar 

  3. D. Boneh, H. Shacham, and B. Lynn, “Short signatures from the Weil-pairing”, Advances in Cryptology-Asiacrypt’ 2001, LNCS 2248, Springer-Verlag, pp. 514–532, 2001.

    Chapter  Google Scholar 

  4. I. Blake, G. Seroussi and N. Smart, “Elliptic curves in cryptography”, Cambridge University Prress, LNS 265, 1999.

    Google Scholar 

  5. J.-S. Coron, “On the security of full domain hash”, Advances in Cryptology-Crypto’ 2000, LNCS 1880, Springer-Verlag, pp. 229–235, 2000.

    Chapter  Google Scholar 

  6. U. Feige, A. Fiat, and A. Shamir, “Zero-knowledge proofs of identity”, J. Cryptology, 1: 77–94, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  7. A. Fiat and A. Shamir, “How to prove yourself: pratical solutions to identification and signature problems”, Advances in Cryptology — Crypto’ 86, LNCS 263, Springer-Verlag, pp. 186–194, 1987.

    Google Scholar 

  8. O. Goldreich and H. Krawczyk, “On the composition of zero-knowledge proof systems”, In Proceedings of the 17th ICALP, LNCS 443, Springer-Verlag, pp. 268–282, 1990.

    Google Scholar 

  9. S. Goldwasser, S. Micali, and C. Rackoff, “The knowledge complexity of interactive proof systems”, SIAM J. Comput., 18: 186–208, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  10. L. Guillou and J. Quisquater, “A practical zero-knowledge protocol fitted to security microprocessors minimizing both transmission and memory”, Advances in Cryptology — Eurocrypt’ 88, LNCS 330, Springer-Verlag, pp. 123–128, 1989.

    Chapter  Google Scholar 

  11. A. Joux and K. Nguyen, “Seperating decision Diffie-Hellman from Diffie-Hellman in cryptographic groups”, available from eprint.iacr.org.

  12. A. J. Menezes, “Elliptic curve public key cryptosystems”, Kluwer Academic Publishers, 1993.

    Google Scholar 

  13. A. J. Menezes, T. Okamoto, and S. A. Vanstone, “Reducing elliptic curve logarithms to logarithms in a finite field”, IEEE Trans. Inform. Theory, 39(1993), pp. 1639–1646.

    Article  MATH  MathSciNet  Google Scholar 

  14. V. Miller, “Short programs for functions on curves”, unpublished manuscript, 1986.

    Google Scholar 

  15. T. Okamoto, “Provably secure and practical identification schemes and corresponding signature schemes”, Advances in Cryptology — Crypto’ 92, LNCS 740, Springer-Verlag, pp. 31–53, 1993.

    Google Scholar 

  16. T. Okamoto and D. Pointcheval, “The gap-problem: a new class of problems for the security of cryptographic schemes”, PKC 2001, LNCS 1992, Springer-Verlag, pp. 104–118, 2001.

    Google Scholar 

  17. K. Ohta and T. Okamoto, “A modification of the Fiat-Shamir scheme”, Advances in Cryptology-Crypto’ 88, LNCS 403, Springer-Verlag, pp. 232–243, 1990.

    Google Scholar 

  18. C. Popescu, “An identification scheme based on the elliptic curve discrete logarithm problem”, IEEE High Performance Computing in the Asia-Pacific Region, Volume: 2, pp. 624–625, 2000.

    Article  Google Scholar 

  19. A.D. Santis, S. Micali, and G. Persiano, “Non-interactive zero-knowledge proof systems”, Advances in Cryptology — Crypto’ 87, LNCS 293, pp. 52–72, 1988.

    Google Scholar 

  20. C. Schnorr, “Security of 2t-root identification and signatures”, Advances in Cryptology — Crypto’ 96, LNCS 1109, Springer-Verlag, pp. 143–156, 1996.

    Chapter  Google Scholar 

  21. V. Shoup, “On the security of a practical identification scheme”, J. Cryptology 12: 247–260, 1999.

    Article  MATH  Google Scholar 

  22. J. H. Silverman, “The arithmetic of elliptic curves”, Springer-Verlag, GTM 106, 1986.

    Google Scholar 

  23. D.R. Stinson, “Cryptography: Theory and Practice”, CRC Press, Boca Raton, Florida, pp. 236, 1995.

    MATH  Google Scholar 

  24. T. Yamanaka, R. Sakai, and M. Kasahara, “Fast computation of pairings over elliptic curves”, Proc. of SCIS 2002, pp. 709–714, Jan. 29–Feb. 1, 2002, Shirahama, Japan.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. International Research center for Information Security (IRIS), Information and Communications Univ. (ICU), 58-4 Hwaamdong, Yuseong-gu, Daejon, 305-732, Korea

    Myungsun Kim & Kwangjo Kim

Authors
  1. Myungsun Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kwangjo Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Rusden Campus, Deakin University, Burwood Road, Melbourne, Victoria, Australia

    Lynn Batten

  2. Department of Computer Science, University of Wollongong, Northfields Avenue, Wollongong, NSW, Australia

    Jennifer Seberry

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kim, M., Kim, K. (2002). A New Identification Scheme Based on the Bilinear Diffie-Hellman Problem. In: Batten, L., Seberry, J. (eds) Information Security and Privacy. ACISP 2002. Lecture Notes in Computer Science, vol 2384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45450-0_28

Download citation

  • DOI: https://doi.org/10.1007/3-540-45450-0_28

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43861-8

  • Online ISBN: 978-3-540-45450-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation