A New Distinguisher on Grain v1 for 106 Rounds

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9478)

Abstract

In Asiacrypt 2010, Knellwolf, Meier and Naya-Plasencia proposed distinguishing attacks on Grain v1 when (i) Key Scheduling process is reduced to 97 rounds using \(2^{27}\) chosen IVs and (ii) Key Scheduling process is reduced to 104 rounds using \(2^{35}\) chosen IVs. Using similar idea, Banik obtained a new distinguisher for 105 rounds. In this paper, we show similar approach can work for 106 rounds. We present a new distinguisher on Grain v1 for 106 rounds with success probability 63 %.

Keywords

Differential cryptanalysis Distinguisher Grain v1 Stream cipher 

References

  1. 1.
    Aumasson, J.-P., Dinur, I., Meier, W., Shamir, A.: Cube testers and key recovery attacks on reduced-round MD6 and trivium. In: Dunkelman, O. (ed.) FSE 2009. LNCS, vol. 5665, pp. 1–22. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  2. 2.
    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
  3. 3.
    Banik, S.: Some insights into differential cryptanalysis of grain v1. In: Susilo, W., Mu, Y. (eds.) ACISP 2014. LNCS, vol. 8544, pp. 34–49. Springer, Heidelberg (2014) Google Scholar
  4. 4.
    Banik, S.: A Dynamic Cube Attack on 105 round Grain v1. IACR Cryptology ePrint Archive 2014: 652. http://eprint.iacr.org/2014/652
  5. 5.
    Ben-Aroya, I., Biham, E.: Differential cryptanalysis of lucifer. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 187–199. Springer, Heidelberg (1994) Google Scholar
  6. 6.
    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
  7. 7.
    Bjørstad, T.E.: Cryptanalysis of Grain using Time/Memory/Data tradeoffs (v1.0/2008–02-25). http://www.ecrypt.eu.org/stream
  8. 8.
    Daemen, J., Govaerts, R., Vandewalle, J.: Resynchronization weaknesses in synchronous stream ciphers. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 159–167. Springer, Heidelberg (1994) CrossRefGoogle Scholar
  9. 9.
    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
  10. 10.
  11. 11.
    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., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 327–343. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  12. 12.
    Dinur, I., Shamir, A.: Cube attacks on tweakable black box polynomials. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 278–299. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  13. 13.
    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
  14. 14.
    The ECRYPT Stream Cipher Project. eSTREAM Portfolio of Stream Ciphers. Accepted 8 September 2008Google Scholar
  15. 15.
    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
  16. 16.
    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
  17. 17.
    Fredricksen, H.: A survey of full length nonlinear shift register cycle algorithms. SIAM Rev. 24(1982), 195–221 (1982)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    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
  19. 19.
    Khazaei, S., Hassanzadeh, M., Kiaei, M.: Distinguishing Attack on Grain. ECRYPT Stream Cipher Project Report 2005/071 (2005). http://www.ecrypt.eu.org/stream
  20. 20.
    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
  21. 21.
    Knellwolf, S., Meier, W., Naya-Plasencia, M.: Conditional differential cryptanalysis of trivium and KATAN. In: Miri, A., Vaudenay, S. (eds.) SAC 2011. LNCS, vol. 7118, pp. 200–212. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  22. 22.
    Knellwolf, S., Meier, W.: High order differential attacks on stream ciphers. Crypt. Commun. 4(3–4), 203–215 (2012)CrossRefMATHMathSciNetGoogle Scholar
  23. 23.
    Lehmann, M., Meier, W.: Conditional differential cryptanalysis of grain-128a. In: Pieprzyk, J., Sadeghi, A.-R., Manulis, M. (eds.) CANS 2012. LNCS, vol. 7712, pp. 1–11. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  24. 24.
    Lee, Y., Jeong, K., Sung, J., Hong, S.H.: 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
  25. 25.
    Mihaljevic, M.J., Gangopadhyay, S., Paul, G., Imai, H.: Internal state recovery of grain-v1 employing normality order of the filter function. IET Inf. Secur. 6(2), 55–64 (2012)CrossRefGoogle Scholar
  26. 26.
    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)
  27. 27.
    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
  28. 28.
    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 International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of TechnologyChennaiIndia

Personalised recommendations