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International Conference on Cryptology in India

INDOCRYPT 2008: Progress in Cryptology - INDOCRYPT 2008 pp 67–77Cite as

Faster Multicollisions

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5365))

Abstract

Joux’s multicollision attack is one of the most striking results on hash functions and also one of the simplest: it computes a k-collision on iterated hashes in time \(\lceil \log_2 k\rceil\cdot 2^{n/2}\), whereas k!1/k·2n(k − 1)/k was thought to be optimal. Kelsey and Schneier improved this to 3·2n/2 if storage 2n/2 is available and if the compression functions admits easily found fixed-points. This paper presents a simple technique that reduces this cost to 2n/2 and negligible memory, when the IV can be chosen by the attacker. Additional benefits are shorter messages than the Kelsey/Schneier attack and cost-optimality.

Article previously accepted to SECRYPT 2008, but withdrawn by the author because unable to attend the conference. This author was supported by the Swiss National Science Foundation under project no. 113329.

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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. Aumasson, J.-P., Phan, R.C.-W.: How (not) to efficiently dither blockcipher-based hash functions? In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol. 5023, pp. 308–324. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  3. Biham, E., Dunkelman, O.: A framework for iterative hash functions - HAIFA. In: Second NIST Cryptographic Hash Workshop (2006)

    Google Scholar 

  4. Biham, E., Dunkelman, O.: A framework for iterative hash functions - HAIFA. Cryptology ePrint Archive, Report 2007/278 (2007); Extended version of [3]

    Google Scholar 

  5. Brassard, G. (ed.): CRYPTO 1989. LNCS, vol. 435. Springer, Heidelberg (1990)

    MATH  Google Scholar 

  6. Coron, J.-S., Dodis, Y., Malinaud, C., Puniya, P.: Merkle-Damgård revisited: How to construct a hash function. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 430–448. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Damgård, I.: A design principle for hash functions. In: Brassard [5], pp. 416–427

    Google Scholar 

  8. Dean, R.D.: Formal Aspects of Mobile Code Security. PhD thesis, Princeton University (1999)

    Google Scholar 

  9. Hoch, 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 

  10. 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 

  11. 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 

  12. Kelsey, J., Schneier, B.: Second preimages on n-bit hash functions for much less than 2n work. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 474–490. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  13. Knudsen, L.R., Mathiassen, J.E.: Preimage and collision attacks on MD2. In: Gilbert, H., Handschuh, H. (eds.) FSE 2005. LNCS, vol. 3557, pp. 255–267. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  14. Lai, X., Massey, J.: Hash functions based on block ciphers. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 55–70. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  15. Lucks, S.: Design principles for iterated hash functions. Cryptology ePrint Archive, Report 2004/253 (2004)

    Google Scholar 

  16. Maurer, U.M., Tessaro, S.: Domain extension of public random functions: Beyond the birthday barrier. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 187–204. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  17. Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)

    Book  MATH  Google Scholar 

  18. Merkle, R.: One way hash functions and DES. In: Brassard [5], pp. 428–446

    Google Scholar 

  19. Nandi, M., Stinson, D.: Multicollision attacks on generalized hash functions. Cryptology ePrint Archive, Report 2004/330 (2004); Later published in [20]

    Google Scholar 

  20. Nandi, M., Stinson, D.: Multicollision attacks on a class of hash functions. IEEE Transactions on Information Theory 53, 759–767 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. Preneel, B.: Analysis and Design of Cryptographic Hash Functions. PhD thesis, Katholieke Universiteit Leuven (1993)

    Google Scholar 

  22. Preneel, B., Govaerts, R., Vandewalle, J.: Hash functions based on block ciphers: A synthetic approach. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 368–378. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  23. Quisquater, J.-J., Delescaille, J.-P.: How easy is collision search? Application to DES (extended summary). In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 429–434. Springer, Heidelberg (1990)

    Chapter  Google Scholar 

  24. Rabin, M.: Digitalized signatures. In: Lipton, R., DeMillo, R. (eds.) Foundations of Secure Computation, pp. 155–166. Academic Press, London (1978)

    Google Scholar 

  25. Rabin, M.: Digitalized signatures and public-key functions as intractable as factorization. Technical Report MIT/LCS/TR-212, MIT (1979)

    Google Scholar 

  26. Rivest, R.: Abelian square-free dithering for iterated hash functions. In: ECRYPT Conference on Hash Functions (2005); Also presented in [27]

    Google Scholar 

  27. Rivest, R.: Abelian square-free dithering for iterated hash functions. In: First NIST Cryptographic Hash Workshop (2005)

    Google Scholar 

  28. Schneier, B.: Applied Cryptography, 2nd edn. John Wiley & Sons, Chichester (1996)

    MATH  Google Scholar 

  29. Sedgewick, R., Szymanski, T.G., Chi-Chih Yao, A.: The complexity of finding cycles in periodic functions. SIAM Journal of Computing 11(2), 376–390 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  30. Suzuki, K., Tonien, D., Kurosawa, K., Toyota, K.: Birthday paradox for multi-collisions. In: Rhee, M.S., Lee, B. (eds.) ICISC 2006. LNCS, vol. 4296, pp. 29–40. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  31. Yu, H., Wang, X.: Multi-collision attack on the compression functions of MD4 and 3-pass HAVAL. In: Nam, K.-H., Rhee, G. (eds.) ICISC 2007. LNCS, vol. 4817, pp. 206–226. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. FHNW, Windisch, Switzerland

    Jean-Philippe Aumasson

Authors
  1. Jean-Philippe Aumasson
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Editor information

Editors and Affiliations

  1. Dept. of Computer Science and Engineering, Indian Institute of Technology, 721 302, Kharagpur, India

    Dipanwita Roy Chowdhury

  2. K.U. Leuven, ESAT/COSIC Kasteelpark, Arenberg 10, B-3001, Leuven-Heverlee, Belgium

    Vincent Rijmen

  3. Department of Computer Science and Engineering, Indian Institute of Technology, 721 302, Kharagpur, India

    Abhijit Das

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Aumasson, JP. (2008). Faster Multicollisions. In: Chowdhury, D.R., Rijmen, V., Das, A. (eds) Progress in Cryptology - INDOCRYPT 2008. INDOCRYPT 2008. Lecture Notes in Computer Science, vol 5365. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89754-5_6

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  • DOI: https://doi.org/10.1007/978-3-540-89754-5_6

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  • Print ISBN: 978-3-540-89753-8

  • Online ISBN: 978-3-540-89754-5

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