Tweakable Blockciphers with Asymptotically Optimal Security

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8424)

Abstract

We consider tweakable blockciphers with beyond the birthday bound security. Landecker, Shrimpton, and Terashima (CRYPTO 2012) gave the first construction with security up to \(\mathcal {O}(2^{2n/3})\) adversarial queries (\(n\) denotes the block size in bits of the underlying blockcipher), and for which changing the tweak does not require changing the keys for blockcipher calls. In this paper, we extend this construction, which consists of two rounds of a previous proposal by Liskov, Rivest, and Wagner (CRYPTO 2002), by considering larger numbers of rounds \(r>2\). We show that asymptotically, as \(r\) increases, the resulting tweakable blockcipher approaches security up to the information bound, namely \(\mathcal {O}(2^n)\) queries. Our analysis makes use of a coupling argument, and carries some similarities with the analysis of the iterated Even-Mansour cipher by Lampe, Patarin, and Seurin (ASIACRYPT 2012).

Keywords

Tweakable blockcipher Beyond birthday bound Coupling Message authentication code 

References

  1. 1.
    Aldous, D.J.: Random walks on finite groups and rapidly mixing Markov chains. In: Azéma, J., Yor, M. (eds.) Séminaire de Probabilités XVII. Lecture Notes in Mathematics, vol. 986, pp. 243–297. Springer, Heidelberg (1983)Google Scholar
  2. 2.
    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)Google Scholar
  3. 3.
    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 (2001) CrossRefGoogle Scholar
  4. 4.
    Dodis, Y., Steinberger, J.: Domain extension for MACs beyond the birthday barrier. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 323–342. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  5. 5.
    Even, S., Mansour, Y.: A construction of a cipher from a single pseudorandom permutation. J. Cryptol. 10(3), 151–162 (1997)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Ferguson, N., Lucks, S., Schneier, B., Whiting, D., Bellare, M., Kohno, T., Callas, J., Walker, J.: The Skein Hash Function Family. SHA3 Submission to NIST (Round 3) (2010)Google Scholar
  7. 7.
    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
  8. 8.
    Hoang, V.T., Rogaway, P.: On generalized Feistel networks. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 613–630. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  9. 9.
    Jetchev, D., Özen, O., Stam, M.: Understanding adaptivity: random systems revisited. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 313–330. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  10. 10.
    Lampe, R., Patarin, J., Seurin, Y.: An asymptotically tight security analysis of the iterated Even-Mansour cipher. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 278–295. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  11. 11.
    Landecker, W., Shrimpton, T., Terashima, R.S.: Tweakable blockciphers with beyond birthday-bound security. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 14–30. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  12. 12.
    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
  13. 13.
    Maurer, U.M.: Indistinguishability of random systems. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 110–132. Springer, Heidelberg (2002) CrossRefGoogle Scholar
  14. 14.
    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) CrossRefGoogle Scholar
  15. 15.
    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)Google Scholar
  16. 16.
    Minematsu, K.: Beyond-birthday-bound security based on tweakable block cipher. In: Dunkelman, O. (ed.) FSE 2009. LNCS, vol. 5665, pp. 308–326. Springer, Heidelberg (2009)Google Scholar
  17. 17.
    Mironov, I.: (Not so) Random shuffles of RC4. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, p. 304. Springer, Heidelberg (2002) CrossRefGoogle Scholar
  18. 18.
    Morris, B., Rogaway, P., Stegers, T.: How to encipher messages on a small domain. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 286–302. Springer, Heidelberg (2009)Google Scholar
  19. 19.
    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
  20. 20.
    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) CrossRefGoogle Scholar
  21. 21.
    Schroeppel, R.: The Hasty Pudding Cipher. AES Submission to NIST (1998)Google Scholar
  22. 22.
    Shoup, V.: On fast and provably secure message authentication based on universal hashing. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 313–328. Springer, Heidelberg (1996) Google Scholar
  23. 23.
    Steinberger, J.: Improved security bounds for key-alternating ciphers via Hellinger distance. IACR Cryptology ePrint Archive Report 2012/481 (2012). http://eprint.iacr.org/2012/481.pdf
  24. 24.
    Yasuda, K.: The sum of CBC MACs is a secure PRF. In: Pieprzyk, J. (ed.) CT-RSA 2010. LNCS, vol. 5985, pp. 366–381. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  25. 25.
    Yasuda, K.: A new variant of PMAC: beyond the birthday bound. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 596–609. Springer, Heidelberg (2011) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.University of VersaillesVersaillesFrance
  2. 2.ANSSIParisFrance

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