Skip to main content
Springer Nature Link
Log in

Tweak-Length Extension for Tweakable Blockciphers

  • Conference paper
  • First Online:
Cryptography and Coding (IMACC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9496))

Included in the following conference series:

  • 707 Accesses

Abstract

Tweakable blockcipher (TBC) is an extension of standard blockcipher introduced by Liskov, Rivest and Wagner in 2002. TBC is a versatile building block for efficient symmetric-key cryptographic functions, such as authenticated encryption.

In this paper we study the problem of extending tweak of a given TBC of fixed-length tweak, which is a variant of popular problem of converting a blockcipher into a TBC, i.e., blockcipher mode of operation. The problem is particularly important for known dedicated TBCs since they have relatively short tweak. We propose a simple and efficient solution, called \(\text {XTX}\), for this problem. \(\text {XTX}\) converts a TBC of fixed-length tweak into another TBC of arbitrarily long tweak, by extending the scheme of Liskov, Rivest and Wagner that converts a blockcipher into a TBC. Given a TBC of n-bit block and m-bit tweak, \(\text {XTX}\) provides \((n+m){/}2\)-bit security while conventional methods provide n / 2 or m / 2-bit security. We also show that \(\text {XTX}\) is even useful when combined with some blockcipher modes for building TBC having security beyond the birthday bound.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    The two schemes shown by [17] are also called LRW1 and LRW2, and we refer to LRW2 throughout this paper.

  2. 2.

    Originally proved by [17] with a slightly larger constant, then improved by [22].

  3. 3.

    In some special cases the result obtained by the method of [18] cannot be converted into computational counterparts [19, 25]. However the proof presented here does not have such difficulty. A bug in a theorem of [18] was pointed out by Jetchev, Özen and Stam [14], however we did not use it.

  4. 4.

    The name CLRW2 means it is a chain of the second construction of [17], which we simply call LRW.

  5. 5.

    Originally the constant was 6, however an error in the proof was pointed out by Procter [26]. He fixed the proof with an increased constant, 8.

References

  1. CAESAR: Competition for authenticated encryption: security, applicability, and robustness. http://competitions.cr.yp.to/caesar.html/

  2. Skein Hash Function: SHA-3 submission (2008). http://www.skein-hash.info/

  3. Aoki, K., Yasuda, K.: The security and performance of “GCM” when short multiplications are used instead. In: Kutyłowski, M., Yung, M. (eds.) Inscrypt 2012. LNCS, vol. 7763, pp. 225–245. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  4. Bellare, M., Desai, A., Jokipii, E., Rogaway, P.: A concrete security treatment of symmetric encryption. In: 38th Annual Symposium on Foundations of Computer Science, FOCS 1997, 19–22 Oct 1997, pp. 394–403. IEEE Computer Society, Miami Beach (1997)

    Google Scholar 

  5. 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)

    Chapter  Google Scholar 

  6. 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)

    Chapter  Google Scholar 

  7. Carter, L., Wegman, M.N.: Universal classes of hash functions. J. Comput. Syst. Sci. 18(2), 143–154 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cogliati, B., Lampe, R., Seurin, Y.: Tweaking Even-Mansour ciphers. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015, Part I. LNCS, vol. 9215, pp. 189–208. Springer, Heidelberg (2015). Full version in Cryptology ePrint Archive, Report 2015/539. http://eprint.iacr.org/

    Chapter  Google Scholar 

  9. Coron, J.-S., Dodis, Y., Mandal, A., Seurin, Y.: A domain extender for the ideal cipher. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 273–289. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  10. 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)

    Chapter  Google Scholar 

  11. Even, S., Mansour, Y.: A construction of a cipher from a single pseudorandom permutation. J. Cryptol. 10(3), 151–162 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hirose, S., Sasaki, Y., Yasuda, K.: IV-FV authenticated encryption and triplet-robust decryption. In: Early Symetric Crypto, ESC 2015 (2015)

    Google Scholar 

  13. Jean, J., Nikolic, I., Peyrin, T.: Tweaks and keys for block ciphers: the TWEAKEY framework. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 274–288. Springer, Heidelberg (2014)

    Google Scholar 

  14. 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)

    Chapter  Google Scholar 

  15. Lampe, R., Seurin, Y.: Tweakable blockciphers with asymptotically optimal security. In: Moriai, S. (ed.) FSE 2013. LNCS, vol. 8424, pp. 133–152. Springer, Heidelberg (2014)

    Google Scholar 

  16. 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)

    Chapter  Google Scholar 

  17. 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)

    Chapter  Google Scholar 

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

    Chapter  Google Scholar 

  19. 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)

    Chapter  Google Scholar 

  20. Mennink, B.: Optimally secure tweakable blockciphers. In: Leander, G. (ed.) FSE 2015. LNCS, vol. 9054, pp. 428–448. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  21. Mennink, B.: XPX: generalized tweakable even-mansour with improved security guarantees. IACR Cryptology ePrint Archive 2015, 476 (2015)

    Google Scholar 

  22. Minematsu, K.: Improved security analysis of XEX and LRW modes. In: Biham, E., Youssef, A.M. (eds.) SAC 2006. LNCS, vol. 4356, pp. 96–113. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  23. 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)

    Chapter  Google Scholar 

  24. Patarin, J.: The “coefficients H” technique. In: Avanzi, R.M., Keliher, L., Sica, F. (eds.) SAC 2008. LNCS, vol. 5381, pp. 328–345. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  25. Pietrzak, K.: Composition does not imply adaptive security. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 55–65. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  26. Procter, G.: A note on the CLRW2 tweakable block cipher construction. IACR Cryptology ePrint Archive 2014, 111 (2014)

    Google Scholar 

  27. Procter, G., Cid, C.: On weak keys and forgery attacks against polynomial-based MAC schemes. In: Moriai, S. (ed.) FSE 2013. LNCS, vol. 8424, pp. 287–304. Springer, Heidelberg (2014)

    Google Scholar 

  28. 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)

    Chapter  Google Scholar 

  29. Sasaki, Y., Todo, Y., Aoki, K., Naito, Y., Sugawara, T., Murakami, Y., Matsui, M., Hirose, S.: Minalpher. A submission to CAESAR

    Google Scholar 

  30. Schroeppel, R.: Hasty pudding cipher. AES submission (1998). http://www.cs.arizona.edu/rcs/hpc/

  31. Shrimpton, T., Terashima, R.S.: A modular framework for building variable-input-length tweakable ciphers. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part I. LNCS, vol. 8269, pp. 405–423. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the anonymous reviewers for highly constructive and insightful comments. The work by Tetsu Iwata was supported in part by JSPS KAKENHI, Grant-in-Aid for Scientific Research (B), Grant Number 26280045.

Author information

Authors and Affiliations

  1. NEC Corporation, Kawasaki, Japan

    Kazuhiko Minematsu

  2. Nagoya University, Nagoya, Japan

    Tetsu Iwata

Authors
  1. Kazuhiko Minematsu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tetsu Iwata
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kazuhiko Minematsu .

Editor information

Editors and Affiliations

  1. University College London, Cambridge, United Kingdom

    Jens Groth

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Minematsu, K., Iwata, T. (2015). Tweak-Length Extension for Tweakable Blockciphers. In: Groth, J. (eds) Cryptography and Coding. IMACC 2015. Lecture Notes in Computer Science(), vol 9496. Springer, Cham. https://doi.org/10.1007/978-3-319-27239-9_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-27239-9_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27238-2

  • Online ISBN: 978-3-319-27239-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics