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International Conference on the Theory and Application of Cryptology and Information Security

ASIACRYPT 2012: Advances in Cryptology – ASIACRYPT 2012 pp 313–330Cite as

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Understanding Adaptivity: Random Systems Revisited

Understanding Adaptivity: Random Systems Revisited

  • Dimitar Jetchev18,
  • Onur Özen18 &
  • Martijn Stam19 
  • Conference paper
  • 3692 Accesses

  • 9 Citations

Part of the Lecture Notes in Computer Science book series (LNSC,volume 7658)

Abstract

We develop a conceptual approach for probabilistic analysis of adaptive adversaries via Maurer’s methodology of random systems (Eurocrypt’02). We first consider a well-known comparison theorem of Maurer according to which, under certain hypotheses, adaptivity does not help for achieving a certain event. This theorem has subsequently been misinterpreted, leading to a misrepresentation with one of Maurer’s hypotheses being omitted in various applications. In particular, the only proof of (a misrepresentation of) the theorem available in the literature contained a flaw. We clarify the theorem by pointing out a simple example illustrating why the hypothesis of Maurer is necessary for the comparison statement to hold and provide a correct proof. Furthermore, we prove several technical statements applicable in more general settings where adaptivity might be helpful, which can be seen as the random system analogue of the game-playing arguments recently proved by Jetchev, Özen and Stam (TCC’12).

Keywords

  • Hash Function
  • Random Permutation
  • Full Version
  • Monotone Condition
  • Conditional Probability Distribution

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.

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References

  1. Armknecht, F., Fleischmann, E., Krause, M., Lee, J., Stam, M., Steinberger, J.: The Preimage Security of Double-Block-Length Compression Functions. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 233–251. Springer, Heidelberg (2011)

    Google Scholar 

  2. Bellare, M., Rogaway, P.: The Security of Triple Encryption and a Framework for Code-Based Game-Playing Proofs. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 409–426. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  3. Blum, M., Micali, S.: How to generate cryptographically strong sequences of pseudo random bits. In: FOCS, pp. 112–117. IEEE Computer Society (1982)

    Google Scholar 

  4. Bogdanov, A., Knudsen, L.R., Leander, G., Standaert, F.-X., Steinberger, J., Tischhauser, E.: Key-Alternating Ciphers in a Provable Setting: Encryption Using a Small Number of Public Permutations (Extended Abstract). In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 45–62. Springer, Heidelberg (2012)

    CrossRef  Google Scholar 

  5. Gaži, P., Maurer, U.: Free-Start Distinguishing: Combining Two Types of Indistinguishability Amplification. In: Kurosawa, K. (ed.) ICITS 2009. LNCS, vol. 5973, pp. 28–44. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  6. Hirose, S.: Some Plausible Constructions of Double-Block-Length Hash Functions. In: Robshaw, M. (ed.) FSE 2006. LNCS, vol. 4047, pp. 210–225. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  7. Jetchev, D., Özen, O., Stam, M.: Collisions Are Not Incidental: A Compression Function Exploiting Discrete Geometry. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 303–320. Springer, Heidelberg (2012)

    CrossRef  Google Scholar 

  8. Kilian, J., Rogaway, P.: How to Protect DES Against Exhaustive Key Search (an Analysis of DESX). J. Cryptology 14(1), 17–35 (2001)

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Lee, J., Stam, M., Steinberger, J.: The Collision Security of Tandem-DM in the Ideal Cipher Model. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 561–577. Springer, Heidelberg (2011)

    Google Scholar 

  10. Lucks, S.: A collision-resistant rate-1 double-block-length hash function. In: Biham, E., Handschuh, H., Lucks, S., Rijmen, V. (eds.) Symmetric Cryptography. No. 07021 in Dagstuhl Seminar Proceedings, Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany, Dagstuhl, Germany (2007), http://drops.dagstuhl.de/opus/volltexte/2007/1017

  11. Maurer, U.M.: Indistinguishability of Random Systems. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 110–132. Springer, Heidelberg (2002)

    CrossRef  Google Scholar 

  12. Maurer, U., Pietrzak, K.: The Security of Many-Round Luby–Rackoff Pseudo-Random Permutations. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 544–561. Springer, Heidelberg (2003)

    CrossRef  Google Scholar 

  13. Maurer, U.M., Pietrzak, K.: Composition of Random Systems: When Two Weak Make One Strong. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 410–427. Springer, Heidelberg (2004)

    CrossRef  Google Scholar 

  14. Maurer, U.M., Pietrzak, K., Renner, R.S.: Indistinguishability Amplification. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 130–149. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  15. Pietrzak, K.: Indistinguishability and Composition of Random Systems. ETH Zurich, Ph.D. thesis (2005), http://homepages.cwi.nl/%7Epietrzak/publications/thesis05.ps

  16. Shoup, V.: Sequences of Games: A Tool for Taming Complexity in Security Proofs. Cryptology ePrint Archive, Report 2004/332 (2004), http://eprint.iacr.org/

  17. Steinberger, J.P.: The Collision Intractability of MDC-2 in the Ideal-Cipher Model. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 34–51. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  18. Steinberger, J.P.: Improved security bounds for key-alternating ciphers via hellinger distance. Cryptology ePrint Archive, Report 2012/481 (2012), http://eprint.iacr.org/

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Author information

Authors and Affiliations

  1. EPFL IC IIF LACAL, Station 14, CH-1015, Lausanne, Switzerland

    Dimitar Jetchev & Onur Özen

  2. Department of Computer Science, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, UK

    Martijn Stam

Authors
  1. Dimitar Jetchev
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  2. Onur Özen
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  3. Martijn Stam
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Editor information

Editors and Affiliations

  1. Tsinghua University, 30 Shuangqing Road, 100084, Beijing, China

    Xiaoyun Wang

  2. Central Research Laboratories, NEC, 1754 Shimonumabe Nakahara, 211-8666, Kawasaki, Japan

    Kazue Sako

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© 2012 International Association for Cryptologic Research

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Cite this paper

Jetchev, D., Özen, O., Stam, M. (2012). Understanding Adaptivity: Random Systems Revisited. In: Wang, X., Sako, K. (eds) Advances in Cryptology – ASIACRYPT 2012. ASIACRYPT 2012. Lecture Notes in Computer Science, vol 7658. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34961-4_20

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  • DOI: https://doi.org/10.1007/978-3-642-34961-4_20

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