Real Time Cryptanalysis of Bluetooth Encryption with Condition Masking

(Extended Abstract)
  • Bin Zhang
  • Chao Xu
  • Dengguo Feng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8042)

Abstract

The Bluetooth standard authorized by IEEE 802.15.1 adopts the two-level E0 stream cipher to protect short range privacy in wireless networks. The best published attack on it at Crypto 2005 requires 238 on-line computations, 238 off-line computations and 233 memory (which amount to about 19-hour, 37-hour and 64GB storage in practice) to restore the original encryption key, given the first 24 bits of 223.8 frames. In this paper, we describe more threatening and real time attacks against two-level E0 based on condition masking, a new cryptanalytic technique that characterizes the conditional correlation attacks on stream ciphers. The idea is to carefully choose the condition to get better tradeoffs on the time/memory/data complexity curve. It is shown that if the first 24 bits of 222.7 frames is available, the secret key can be reliably found with 227 on-line computations, 221.1 off-line computations and 4MB memory. Our attacks have been fully implemented on one core of a single PC. It takes only a few seconds to restore the original encryption key. This is the best known-IV attack on the real Bluetooth encryption scheme so far.

Keywords

Stream ciphers Correlation Condition masking Bluetooth two-level E0 

References

  1. 1.
    Armknecht, F., Krause, M.: Algebraic attacks on combiners with memory. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 162–175. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Baignères, T., Junod, P., Vaudenay, S.: How far can we go beyond linear cryptanalysis? In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 432–450. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    SIG Bluetooth. Specification of the bluetooth system. volume 4.0 (2010)Google Scholar
  4. 4.
    Canteaut, A., Trabbia, M.: Improved fast correlation attacks using parity-check equations of weight 4 and 5. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 573–588. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Chose, P., Joux, A., Mitton, M.: Fast correlation attacks: An algorithmic point of view. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 209–221. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Courtois, N.T.: Fast algebraic attacks on stream ciphers with linear feedback. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 176–194. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Fluhrer, S.R., Lucks, S.: Analysis of the E0 encryption system. In: Vaudenay, S., Youssef, A.M. (eds.) SAC 2001. LNCS, vol. 2259, pp. 38–48. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Fluhrer, S.R., Cisco Systems Inc.: Improved key recovery of level 1 of the bluetooth encryption system. Cambridge University Press (2002), http://eprint.iacr.org/2002/068
  9. 9.
    Golić, J.: Correlation properties of a general binary combiner with memory. Journal of Cryptology 9, 111–126 (1996)CrossRefMATHGoogle Scholar
  10. 10.
    Golić, J.D., Bagini, V., Morgari, G.: Linear cryptanalysis of bluetooth stream cipher. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 238–255. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Hermelin, M., Nyberg, K.: Correlation properties of the bluetooth combiner. In: Song, J.S. (ed.) ICISC 1999. LNCS, vol. 1787, pp. 17–29. Springer, Heidelberg (2000)Google Scholar
  12. 12.
    Johansson, T., Jönsson, F.: Improved fast correlation attacks on stream ciphers via convolutional codes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 347–362. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  13. 13.
    Johansson, T., Jönsson, F.: Fast correlation attacks through reconstruction of linear polynomials. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 300–315. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  14. 14.
    Krause, M.: BDD-based cryptanalysis of keystream generators. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 222–237. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Lee, S., Chee, S., Park, S., Park, S.: Conditional correlation attack on nonlinear filter generators. In: Kim, K.-C., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 360–367. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  16. 16.
    Löhlein, B.: Attacks based on conditional correlations against the nonlinear filter generator, http://eprint.iacr.org/2003/020
  17. 17.
    Lu, Y., Meier, W., Vaudenay, S.: The conditional correlation attack: A practical attack on bluetooth encryption. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 97–117. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  18. 18.
    Lu, Y., Vaudenay, S.: Cryptanalysis of bluetooth keystream generator two-level E0. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 483–499. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  19. 19.
    Lu, Y., Vaudenay, S.: Faster correlation attack on bluetooth keystream generator E0. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 407–425. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  20. 20.
    Lu, Y., Vaudenay, S.: Cryptanalysis of an e0-like combiner with memory. Journal of Cryptology 21, 430–457 (2008)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Matsui, M.: Linear cryptanalysis method for DES cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  22. 22.
    Meier, W., Staffelbach, O.: Fast correlation attacks on certain stream ciphers. Journal of Cryptology 1, 159–176 (1989)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Meier, W., Staffelbach, O.: Correlation properties of combiners with memory in stream ciphers. Journal of Cryptology 5, 67–86 (1992)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Petrakos, N., Dinolt, G.W., Michael, J.B., Stanica, P.: Cube-type algebraic attacks on wireless encryption protocols. Computer 42(10), 103–105 (2009)CrossRefGoogle Scholar
  25. 25.
    Preneel, B.: Stream ciphers: Past, present and future (2010)Google Scholar
  26. 26.
    Saarinen, M.: Re: Bluetooth and E0. Posting to Sci. Crypt. Research 2(09) (2000)Google Scholar
  27. 27.
    Shaked, Y., Wool, A.: Cryptanalysis of the bluetooth E0 cipher using oBDD’s. In: Katsikas, S.K., López, J., Backes, M., Gritzalis, S., Preneel, B. (eds.) ISC 2006. LNCS, vol. 4176, pp. 187–202. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  28. 28.
    Siegenthaler, T.: Decrypting a class of stream ciphers using ciphertext only. IEEE Transactions on Computers C-34, 81–85 (1985)CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Bin Zhang
    • 1
  • Chao Xu
    • 2
  • Dengguo Feng
    • 2
  1. 1.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingP.R. China
  2. 2.Institute of SoftwareChinese Academy of SciencesBeijingP.R. China

Personalised recommendations