Advertisement

Some Results on Related Key-IV Pairs of Grain

  • Subhadeep Banik
  • Subhamoy Maitra
  • Santanu Sarkar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7644)

Abstract

In this paper we explain how one can obtain Key-IV pairs for Grain family of stream ciphers that can generate output key-streams which are either (i) almost similar in the initial part or (ii) exact shifts of each other throughout the generation of the stream. Let l P be the size of the pad used during the key loading of Grain. For the first case, we show that in expected \(2^{l_P}\) many invocations of the Key Scheduling Algorithm and its reverse routine, one can obtain two related Key-IV pairs that can produce same output bits in 75 (respectively 112 and 115) selected positions among the initial 96 (respectively 160 and 160) bits for Grain v1 (respectively Grain-128 and Grain-128a). Similar idea works for the second case in showing that given any Key-IV, one can obtain another related Key-IV in expected \(2^{l_P}\) many trials such that the related Key-IV pairs produce shifted key-streams. We also provide an efficient strategy to obtain related Key-IV pairs that produce exactly i-bit shifted key-streams for small i. Our technique pre-computes certain equations that help in obtaining such related Key-IV pairs in 2 i many expected trials.

Keywords

Grain v1 Grain-128 Grain-128a LFSR NFSR Related Key-IV pairs Sequences Keystream Stream Cipher 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    The ECRYPT Stream Cipher Project. eSTREAM Portfolio of Stream Ciphers (revised on September 8, 2008)Google Scholar
  2. 2.
    Ågren, M., Hell, M., Johansson, T., Meier, W.: A New Version of Grain-128 with Authentication. In: Symmetric Key Encryption Workshop 2011. DTU, Denmark (2011)Google Scholar
  3. 3.
    Aumasson, J.P., Dinur, I., Henzen, L., Meier, W., Shamir, A.: Efficient FPGA Implementations of High-Dimensional Cube Testers on the Stream Cipher Grain-128. In: SHARCS - Special-purpose Hardware for Attacking Cryptographic Systems (2009)Google Scholar
  4. 4.
    Berbain, C., Gilbert, H., Maximov, A.: Cryptanalysis of Grain. In: Robshaw, M. (ed.) FSE 2006. LNCS, vol. 4047, pp. 15–29. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Bjørstad, T.E.: Cryptanalysis of Grain using Time/Memory/Data tradeoffs (v1.0 / 2008-02-25), http://www.ecrypt.eu.org/stream
  6. 6.
    De Cannière, C., Küçük, Ö., Preneel, B.: Analysis of Grain’s Initialization Algorithm. In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol. 5023, pp. 276–289. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Dinur, I., Güneysu, T., Paar, C., Shamir, A., Zimmermann, R.: An Experimentally Verified Attack on Full Grain-128 Using Dedicated Reconfigurable Hardware. In: Lee, D.H. (ed.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 327–343. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  8. 8.
    Dinur, I., Shamir, A.: Breaking Grain-128 with Dynamic Cube Attacks. In: Joux, A. (ed.) FSE 2011. LNCS, vol. 6733, pp. 167–187. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    Englund, H., Johansson, T., Sönmez Turan, M.: A Framework for Chosen IV Statistical Analysis of Stream Ciphers. In: Srinathan, K., Rangan, C.P., Yung, M. (eds.) INDOCRYPT 2007. LNCS, vol. 4859, pp. 268–281. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. 10.
    Fischer, S., Khazaei, S., Meier, W.: Chosen IV Statistical Analysis for Key Recovery Attacks on Stream Ciphers. In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol. 5023, pp. 236–245. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  11. 11.
    Fredricksen, H.: A survey of full length nonlinear shift register cycle algorithms. SIAM Rev. 24, 195–221 (1982)zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Hell, M., Johansson, T., Meier, W.: Grain - A Stream Cipher for Constrained Environments. ECRYPT Stream Cipher Project Report 2005/001 (2005), http://www.ecrypt.eu.org/stream
  13. 13.
    Hell, M., Johansson, T., Maximov, A., Meier, W.: A Stream Cipher Proposal: Grain-128. In: IEEE International Symposium on Information Theory, ISIT 2006 (2006)Google Scholar
  14. 14.
    Khazaei, S., Hassanzadeh, M., Kiaei, M.: Distinguishing Attack on Grain. ECRYPT Stream Cipher Project Report 2005/071 (2005), http://www.ecrypt.eu.org/stream
  15. 15.
    Knellwolf, S., Meier, W., Naya-Plasencia, M.: Conditional Differential Cryptanalysis of NLFSR-based Cryptosystems. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 130–145. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  16. 16.
    Lee, Y., Jeong, K., Sung, J., Hong, S.: Related-Key Chosen IV Attacks on Grain-v1 and Grain-128. In: Mu, Y., Susilo, W., Seberry, J. (eds.) ACISP 2008. LNCS, vol. 5107, pp. 321–335. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  17. 17.
    Stankovski, P.: Greedy Distinguishers and Nonrandomness Detectors. In: Gong, G., Gupta, K.C. (eds.) INDOCRYPT 2010. LNCS, vol. 6498, pp. 210–226. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  18. 18.
    Stein, W.: Sage Mathematics Software. Free Software Foundation, Inc. (2009), http://www.sagemath.org (Open source project initiated by W. Stein and contributed by many)
  19. 19.
    Zhang, H., Wang, X.: Cryptanalysis of Stream Cipher Grain Family. IACR Cryptology ePrint Archive 2009:109, http://eprint.iacr.org/2009/109

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Subhadeep Banik
    • 1
  • Subhamoy Maitra
    • 1
  • Santanu Sarkar
    • 1
  1. 1.Applied Statistics UnitIndian Statistical InstituteKolkataIndia

Personalised recommendations