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An Experimentally Verified Attack on Full Grain-128 Using Dedicated Reconfigurable Hardware

  • Itai Dinur
  • Tim Güneysu
  • Christof Paar
  • Adi Shamir
  • Ralf Zimmermann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7073)

Abstract

In this paper we describe the first single-key attack which can recover the full key of the full version of Grain-128 for arbitrary keys by an algorithm which is significantly faster than exhaustive search (by a factor of about 238). It is based on a new version of a cube tester, which uses an improved choice of dynamic variables to eliminate the previously made assumption that ten particular key bits are zero. In addition, the new attack is much faster than the previous weak-key attack, and has a simpler key recovery process. Since it is extremely difficult to mathematically analyze the expected behavior of such attacks, we implemented it on RIVYERA, which is a new massively parallel reconfigurable hardware, and tested its main components for dozens of random keys. These tests experimentally verified the correctness and expected complexity of the attack, by finding a very significant bias in our new cube tester for about 7.5% of the keys we tested. This is the first time that the main components of a complex analytical attack are successfully realized against a full-size cipher with a special-purpose machine. Moreover, it is also the first attack that truly exploits the configurable nature of an FPGA-based cryptanalytical hardware.

Keywords

Grain-128 stream cipher cryptanalysis cube attacks cube testers RIVYERA experimental verification 

References

  1. 1.
    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
  2. 2.
    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
  3. 3.
    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
  4. 4.
    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: Workshop on Special-purpose Hardware for Attacking Cryptographic Systems – SHARCS 2009, September 9-10 (2009)Google Scholar
  5. 5.
    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
  6. 6.
    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
  7. 7.
    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
  8. 8.
    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
  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.
    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
  11. 11.
    Lai, X.: Higher Order Derivatives and Differential Cryptanalysis. In: ”Symposium on Communication, Coding and Cryptography”, in Honor of James L. Massey on the Occasion of his 60th Birthday, pp. 227–233 (1994)Google Scholar
  12. 12.
    Joux, A.: Algorithmic Cryptanalysis. Chapman & Hall, pp. 285–286Google Scholar
  13. 13.
    Güneysu, T., Kasper, T., Novotný, M., Paar, C., Rupp, A.: Cryptanalysis with COPACOBANA. IEEE Transactions on Computers 57(11), 1498–1513 (2008)CrossRefGoogle Scholar
  14. 14.
    Güneysu, T., Pfeiffer, G., Paar, C., Schimmler, M.: Three Years of Evolution: Cryptanalysis with COPACOBANA. In: Workshop on Special-purpose Hardware for Attacking Cryptographic Systems – SHARCS 2009, September 9-10 (2009)Google Scholar
  15. 15.
    Budiansky, S.: Battle of Wits: the Complete Story of Codebreaking in World War II. Free Press (2000) ISBN: 9780684859323 Google Scholar
  16. 16.
    Gilmore, J.: Cracking DES: Secrets of Encryption Research. Wiretap Politics & Chip Design. O’Reilly (July 1998)Google Scholar
  17. 17.
    Matsui, M.: The First Experimental Cryptanalysis of the Data Encryption Standard. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 1–11. Springer, Heidelberg (1994)Google Scholar
  18. 18.
    Vielhaber, M.: Breaking ONE.FIVIUM by AIDA an Algebraic IV Differential Attack. Cryptology ePrint Archive, Report 2007/413 (2007)Google Scholar
  19. 19.
    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

Copyright information

© International Association for Cryptologic Research 2011

Authors and Affiliations

  • Itai Dinur
    • 1
  • Tim Güneysu
    • 2
  • Christof Paar
    • 2
  • Adi Shamir
    • 1
  • Ralf Zimmermann
    • 2
  1. 1.Computer Science DepartmentThe Weizmann InstituteRehovotIsrael
  2. 2.Horst Görtz Institute for IT SecurityRuhr-UniversityBochumGermany

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