Beyond-Birthday-Bound Security Based on Tweakable Block Cipher

  • Kazuhiko Minematsu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5665)

Abstract

This paper studies how to build a 2n-bit block cipher which is hard to distinguish from a truly random permutation against attacks with q ≈ 2n/2 queries, i.e., birthday attacks. Unlike previous approaches using pseudorandom functions, we present a simple and efficient proposal using a tweakable block cipher as an internal module. Our proposal is provably secure against birthday attacks, if underlying tweakable block cipher is also secure against birthday attacks. We also study how to build such tweakable block ciphers from ordinary block ciphers, which may be of independent interest.

Keywords

Block Cipher Mode Birthday Bound Tweakable Block Cipher 

References

  1. 1.
    Aiello, W., Venkatesan, R.: Foiling Birthday Attacks in Length-Doubling Transformations - Benes: A Non-Reversible Alternative to Feistel. 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. In: Proceedings of the 38th Annual Symposium on Foundations of Computer Science, FOCS 1997, pp. 394–403 (1997)Google Scholar
  3. 3.
    Bellare, M., Krovetz, T., Rogaway, P.: Luby-Rackoff Backwards: Increasing Security by Making Block Ciphers Non-invertible. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 266–280. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    Bernstein, D.J.: Stronger Security Bounds for Wegman-Carter-Shoup Authenticators. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 164–180. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Bertoni, G., Breveglieri, L., Fragneto, P., Macchetti, M., Marchesin, S.: Efficient Software Implementation of AES on 32-Bit Platforms. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 159–171. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Carter, L., Wegman, M.: Universal Classes of Hash Functions. Journal of Computer and System Science 18, 143–154 (1979)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Schroeppel, R.: Hasty Pudding Cipher (1998), http://www.cs.arizona.edu/rcs/hpc
  9. 9.
    Crowley, P.: Mercy: A Fast Large Block Cipher for Disk Sector Encryption. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 49–63. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  10. 10.
    Goldenberg, D., Hohenberger, S., Liskov, M., Schwartz, E.C., Seyalioglu, H.: On Tweaking Luby-Rackoff Blockciphers. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 342–356. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Goldreich, O.: Modern Cryptography, Probabilistic Proofs and Pseudorandomness. Algorithms and Combinatorics, vol. 17. Springer, Heidelberg (1998)Google Scholar
  12. 12.
    Halevi, S., Rogaway, P.: A Tweakable Enciphering Mode. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 482–499. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Iwata, T., Yagi, T., Kurosawa, K.: On the Pseudorandomness of KASUMI Type Permutations. In: Safavi-Naini, R., Seberry, J. (eds.) ACISP 2003. LNCS, vol. 2727. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. 14.
    Iwata, T., Kurosawa, K.: OMAC: One-Key CBC MAC. In: Johansson, T. (ed.) FSE 2003. LNCS, vol. 2887, pp. 129–153. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  15. 15.
    Iwata, T.: New Blockcipher Modes of Operation with Beyond the Birthday Bound Security. In: Robshaw, M.J.B. (ed.) FSE 2006. LNCS, vol. 4047, pp. 310–327. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Liskov, M., Rivest, R.L., Wagner, D.: Tweakable Block Ciphers. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 31–46. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  17. 17.
    Luby, M., Rackoff, C.: How to Construct Pseudo-random Permutations from Pseudo-random functions. SIAM J. Computing 17(2), 373–386 (1988)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Patarin, J.: Security of Random Feistel Schemes with 5 or More Rounds. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 106–122. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  19. 19.
    Maurer, U.: Indistinguishability of Random Systems. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 110–132. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  20. 20.
    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
  21. 21.
    Mitsuda, A., Iwata, T.: Tweakable Pseudorandom Permutation from Generalized Feistel Structure. In: Baek, J., Bao, F., Chen, K., Lai, X. (eds.) ProvSec 2008. LNCS, vol. 5324, pp. 22–37. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  22. 22.
    Naor, M., Reingold, O.: On the Construction of Pseudorandom Permutations: Luby-Rackoff Revisited. Journal of Cryptology 12(1), 29–66 (1999)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Patel, S., Ramzan, Z., Sundaram, G.: Towards Making Luby-Rackoff Ciphers Optimal and Practical. In: Knudsen, L.R. (ed.) FSE 1999. LNCS, vol. 1636, pp. 171–185. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  24. 24.
    Rogaway, P.: Efficient Instantiations of Tweakable Blockciphers and Refinements to Modes OCB and PMAC. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 16–31. Springer, Heidelberg (2004), http://www.cs.ucdavis.edu/~rogaway/papers/offsets.pdfCrossRefGoogle Scholar
  25. 25.
    Krovetz, T.: Message Authentication on 64-Bit Architectures. In: Biham, E., Youssef, A.M. (eds.) SAC 2006. LNCS, vol. 4356, pp. 327–341. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  26. 26.
    Vaudenay, S.: On the Lai-Massey scheme. In: Lam, K.-Y., Okamoto, E., Xing, C. (eds.) ASIACRYPT 1999. LNCS, vol. 1716, pp. 8–19. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  27. 27.
    Wegman, M., Carter, L.: New Hash Functions and Their Use in Authentication and Set Equality. Journal of Computer and System Sciences 22, 265–279 (1981)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Yasuda, K.: A One-Pass Mode of Operation for Deterministic Message Authentication- Security beyond the Birthday Barrier. In: Nyberg, K. (ed.) FSE 2008. LNCS, vol. 5086, pp. 316–333. Springer, Heidelberg (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Kazuhiko Minematsu
    • 1
  1. 1.NEC CorporationKawasakiJapan

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