Advertisement

The “Coefficients H” Technique

  • Jacques Patarin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5381)

Abstract

The “coefficient H technique” is a tool introduced in 1991 and used to prove various pseudo-random properties from the distribution of the number of keys that sends cleartext on some ciphertext. It can also be used to find attacks on cryptographic designs. We can like this unify a lot of various pseudo-random results obtained by different authors. In this paper we will present this technique and we will give some examples of results obtained.

Keywords

Random Permutation Block Cipher Round Function Generic Attack Plaintext Attack 
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.

References

  1. 1.
    Aiello, W., Venkatesan, R.: Foiling birthday attacks in length-doubling transformations. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 307–320. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  2. 2.
    Bellare, M., Desai, A., Jokipii, E., Rogaway, P.: A Concrete Security Treatment of Symmetric Encryption: Analysis of the DES Modes of Operation. A Concrete Security Treatment of Symmetric Encryption and appeared in the Proceedings of 38th Annual Symposium of Computer Science, IEEE (1997)Google Scholar
  3. 3.
    Hall Jr., M.: A Combinatorial Problem on Abelian Groups. Proceedings of the Americal Mathematical Society 3(4), 584–587 (1952)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Katz, J., Yung, M.: Characterization of Security Notions for Probabilistic. In: Private-Key Encription – STOC 2000 (2000)Google Scholar
  5. 5.
    Katz, J., Yung, M.: Unforgeable Encryption and Chosen-Ciphertext-Secure Modes of Operation. In: Fast Software Encryption 2000 (2000)Google Scholar
  6. 6.
    Luby, M., Rackoff, C.: How to Construct Pseudorandom Permutations from Pseudorandom Functions. SIAM J. Comput. 17(2), 373–386 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Maurer, U.M.: A simplified and generalized treatment of luby-rackoff pseudorandom permutation generators. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 239–255. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  8. 8.
    Maurer, U.M.: Indistinguishability of random systems. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 100–132. Springer, Heidelberg (2002)Google Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    Naor, M., Reingold, O.: On the Construction of Pseudorandom Permutations: Luby-Rackoff Revisited. J. Cryptology 12(1), 29–66 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Patarin, J.: Pseudorandom Permutations based on the DES Scheme. In: Charpin, P., Cohen, G. (eds.) EUROCODE 1990. LNCS, vol. 514, pp. 193–204. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  12. 12.
    Patarin, J.: Etude de Générateurs de Permutations Basés sur les Schémas du DES. Ph. Thesis. Inria, Domaine de Voluceau, France (1991)Google Scholar
  13. 13.
    Patarin, J.: New results on pseudorandom permutation generators based on the DES scheme. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 301–312. Springer, Heidelberg (1992)Google Scholar
  14. 14.
    Patarin, J.: How to construct pseudorandom and super pseudorandom permutations from one single pseudorandom function. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 256–266. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  15. 15.
    Patarin, J.: Generic attacks on feistel schemes. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 222–238. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  16. 16.
    Patarin, J.: Luby–rackoff: 7 rounds are enough for formula_image security. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 513–529. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  17. 17.
    Patarin, J.: On linear systems of equations with distinct variables and small block size. In: Won, D.H., Kim, S. (eds.) ICISC 2005. LNCS, vol. 3935, pp. 299–321. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  18. 18.
    Patarin, J.: A proof of security in O(2n)for the benes scheme. In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol. 5023, pp. 209–220. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Patarin, J.: A proof of security in O(2n) for the xor of two random permutations. In: Safavi-Naini, R. (ed.) ICITS 2008. LNCS, vol. 5155, pp. 232–248. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  20. 20.
    Patarin, J.: Generic Attacks for the Xor of k Random Permutations (eprint) (2008)Google Scholar
  21. 21.
    Patarin, J., Nachef, V., Berbain, C.: Generic attacks on unbalanced feistel schemes with contracting functions. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 396–411. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  22. 22.
    Patarin, J., Nachef, V., Berbain, C.: Generic attacks on unbalanced feistel schemes with expanding functions. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 325–341. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  23. 23.
    Patarin, J., Seurin, Y.: Building Secure Block Ciphers on Generic Attacks Assumptions. In: SAC 2008 (2008)Google Scholar
  24. 24.
    Salzborn, F., Szekeres, G.: A Problem in Combinatorial Group Theory. Ars Combinatoria 7, 3–5 (1979)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Schneier, B., Kelsey, J.: Unbalanced Feistel Networks and Block Cipher Design. In: Gollmann, D. (ed.) FSE 1996. LNCS, vol. 1039, pp. 121–144. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  26. 26.
    Treger, J., Patarin, J.: Generic Attacks On Feistel Schemes with Internal Permutations (paper in preparation)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jacques Patarin
    • 1
  1. 1.Université de VersaillesVersailles CedexFrance

Personalised recommendations