Skip to main content
SpringerLink
Log in

On the Weak Ideal Compression Functions

  • Conference paper
Information Security and Privacy (ACISP 2009)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5594))

Included in the following conference series:

  • 635 Accesses

Abstract

In SAC 2006, Liskov introduced the weak ideal compression functions. He proved that a hash construction based on these functions is indifferentiable from the random oracle. In ICALP 2008, Hoch and Shamir applied Liskov’s idea and proved the indifferentiability of another hash construction. However, these proofs of indifferentiability can have gaps in certain situations. In this paper, we formalize these situations and propose the simulation method which covers these situations. In particular, we apply our simulation method to the latter proof of indifferentiability, and concretely analyze the security of the latter hash construction. We can derive a lower bound to find a collision in the concatenated hash construction, which covers the gaps of the original proof.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Brassard, G. (ed.): CRYPTO 1989. LNCS, vol. 435. Springer, Heidelberg (1990)

    MATH  Google Scholar 

  2. Coron, J.-S., Dodis, Y., Malinaud, C., Puniya, P.: Merkle-damgård revisited: How to construct a hash function. In: Shoup [16], pp. 430–448

    Google Scholar 

  3. Cramer, R. (ed.): EUROCRYPT 2005. LNCS, vol. 3494. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  4. Damgård, I.: A design principle for hash functions. In: Brassard [1], pp. 416–427

    Google Scholar 

  5. Hoch, J.J., Shamir, A.: On the strength of the concatenated hash combiner when all the hash functions are weak. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 616–630. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Joux, A.: Multicollisions in iterated hash functions. Application to cascaded constructions. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 306–316. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  7. Kawachi, A., Numayama, A., Tanaka, K., Xagawa, K.: Approximation sampling and its application to security proofs in cryptography. In: Symposium on Cryptography and Information Security, pp. 3D1–1 (2009)

    Google Scholar 

  8. Kelsey, J., Kohno, T.: Herding hash functions and the nostradamus attack. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 183–200. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Kelsey, J., Schneier, B.: Second preimages on n-bit hash functions for much less than 2n work. In: Cramer [3], pp. 474–490

    Google Scholar 

  10. Liskov, M.: Constructing an ideal hash function from weak ideal compression functions. In: Biham, E., Youssef, A.M. (eds.) SAC 2006. LNCS, vol. 4356, pp. 358–375. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  11. Maurer, U.M., Renner, R., Holenstein, C.: Indifferentiability, impossibility results on reductions, and applications to the random oracle methodology. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 21–39. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Merkle, R.C.: One way hash functions and des. In: Brassard [1], pp. 428–446

    Google Scholar 

  13. National Institute of Standards and Technology. Secure hash standard. FIPS 180-2 (August 2002)

    Google Scholar 

  14. Numayama, A., Isshiki, T., Tanaka, K.: Security of digital signature schemes in weakened random oracle models. In: Cramer, R. (ed.) PKC 2008. LNCS, vol. 4939, pp. 268–287. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  15. Rivest, R.L.: The MD5 message-digest algorithm. Internet Request for Comments, RFC 1321 (April 1992)

    Google Scholar 

  16. Shoup, V. (ed.): CRYPTO 2005. LNCS, vol. 3621. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  17. Wang, X., Yin, Y.L., Yu, H.: Finding collisions in the full SHA-1. In: Shoup [16], pp. 17–36

    Google Scholar 

  18. Wang, X., Yu, H.: How to break MD5 and other hash functions. In: Cramer [3], pp. 19–35

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, W8-55, 2-12-1 Ookayama Meguro-ku, Tokyo, 152-8552, Japan

    Akira Numayama & Keisuke Tanaka

Authors
  1. Akira Numayama
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Keisuke Tanaka
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Information Security Institute, Queensland University of Technology, GPO Box 2434, Qld 4001, Brisbane, Australia

    Colin Boyd

  2. Information Security Institute, Queensland Univ. of Technology, GPO Box 2434, QLD, 4001, Brisbane, Australia

    Juan González Nieto

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Numayama, A., Tanaka, K. (2009). On the Weak Ideal Compression Functions. In: Boyd, C., González Nieto, J. (eds) Information Security and Privacy. ACISP 2009. Lecture Notes in Computer Science, vol 5594. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02620-1_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02620-1_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02619-5

  • Online ISBN: 978-3-642-02620-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation