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Multicollisions and Graph-Based Hash Functions

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Trusted Systems (INTRUST 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7222))

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Abstract

In this paper, we present some generalisations of previous multicollision finding methods and apply these against a new type of tree-based hash functions. We also show that the very general class of hash functions first presented by Nandi and Stinson can be understood as graph-based hash functions and a graph theoretical approach can be utilised in studying their properties. Previously, an efficient multicollision attack has been found against the basic iterated hash function construction. This method has been applied to the generalised iterated hash functions and binary tree-based hash functions. We show that similar methods can be utilised also against t-ary tree-based hash functions, simplify some definitions and conjecture a similar result for multicollisions against graph-based hash functions.

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References

  1. Andreeva, E., Bouillaguet, C., Fouque, P.-A., Hoch, J.J., Kelsey, J., Shamir, A., Zimmer, S.: Second Preimage Attacks on Dithered Hash Functions. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 270–288. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  2. Bertoni, G., Daemen, J., Peeters, M., Van Assche, G.: Sponge functions. Sponge Functions website (2007), http://sponge.noekeon.org/SpongeFunctions.pdf

  3. Bertoni, G., Daemen, J., Peeters, M., Van Assche, G.: Sufficient conditions for sound tree and sequential hashing modes. Cryptology ePrint Archive, Report 2009/210 (2009), http://eprint.iacr.org/

  4. Damgård, I.B.: A Design Principle for Hash Functions. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 416–427. Springer, Heidelberg (1990)

    Google Scholar 

  5. Diestel, R.: Graph Theory. Graduate Texts in Mathematics. Springer (2006)

    Google Scholar 

  6. Gauravaram, P., Millan, W., Dawson, E., Viswanathan, K.: Constructing Secure Hash Functions by Enhancing Merkle-Damgård Construction. In: Batten, L.M., Safavi-Naini, R. (eds.) ACISP 2006. LNCS, vol. 4058, pp. 407–420. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Halunen, K., Kortelainen, J., Kortelainen, T.: Combinatorial multicollision attacks on generalized iterated hash functions. In: Boyd, C., Susilo, W. (eds.) Eighth Australasian Information Security Conference (AISC 2010). CRPIT, vol. 105, pp. 86–93. ACS, Brisbane (2010)

    Google Scholar 

  8. Hoch, J.J., Shamir, A.: Breaking the ICE - Finding Multicollisions in Iterated Concatenated and Expanded (ICE) Hash Functions. In: Robshaw, M.J.B. (ed.) FSE 2006. LNCS, vol. 4047, pp. 179–194. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. 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)

    Google Scholar 

  10. 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 

  11. Kortelainen, J., Halunen, K., Kortelainen, T.: Multicollision attacks and generalized iterated hash functions. Journal of Mathematical Cryptology 4 (2010)

    Google Scholar 

  12. Kortelainen, J., Kortelainen, T., Vesanen, A.: Unavoidable Regularities in Long Words with Bounded Number of Symbol Occurrences. In: Fu, B., Du, D.-Z. (eds.) COCOON 2011. LNCS, vol. 6842, pp. 519–530. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  13. Kortelainen, T., Kortelainen, J., Halunen, K.: Variants of Multicollision Attacks on Iterated Hash Functions. In: Lai, X., Yung, M., Lin, D. (eds.) Inscrypt 2010. LNCS, vol. 6584, pp. 139–154. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  14. Lucks, S.: A Failure-Friendly Design Principle for Hash Functions. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 474–494. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  15. Martin, J.W.: ESSENCE: A candidate hashing algorithm for the NIST competition. Submission to NIST (2008), http://www.math.jmu.edu/~martin/essence/Supporting_Documentation/essence_NIST.pdf

  16. Merkle, R.C.: One Way Hash Functions and DES. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 428–446. Springer, Heidelberg (1990)

    Google Scholar 

  17. Nandi, M., Stinson, D.R.: Multicollision attacks on generalized hash functions. Cryptology ePrint Archive, Report 2004/330 (2004), http://eprint.iacr.org/

  18. Rivest, R.L.: The MD6 hash function – a proposal to NIST for SHA-3. Submission to NIST (2008), http://groups.csail.mit.edu/cis/md6/submitted-2008-10-27/Supporting_Documentation/md6_report.pdf

  19. Suzuki, K., Tonien, D., Kurosawa, K., Toyota, K.: Birthday paradox for multi-collisions. IEICE Transactions 91-A(1), 39–45 (2008)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Oulu University Secure Programming Group, P.O. Box 4500, 90014, Finland

    Kimmo Halunen

  2. Department of Computer Science and Engineering, University of Oulu, P.O. Box 4500, 90014, Finland

    Kimmo Halunen

Authors
  1. Kimmo Halunen
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Editor information

Editors and Affiliations

  1. Hewlett-Packard Laboratories, Long Down Avenue, BS34 8QZ, Stoke Gifford, Bristol, UK

    Liqun Chen

  2. Computer Science Department, Columbia University, Room 465, S.W. Mudd Building, 10027, New York, NY, USA

    Moti Yung

  3. Institute of Technology, Beijing Key Lab of Intelligent Information Technology, 100081, Beijing, China

    Liehuang Zhu

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Halunen, K. (2012). Multicollisions and Graph-Based Hash Functions. In: Chen, L., Yung, M., Zhu, L. (eds) Trusted Systems. INTRUST 2011. Lecture Notes in Computer Science, vol 7222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32298-3_11

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  • DOI: https://doi.org/10.1007/978-3-642-32298-3_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32297-6

  • Online ISBN: 978-3-642-32298-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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