Advertisement

Cryptanalysis of CTC2

  • Orr Dunkelman
  • Nathan Keller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5473)

Abstract

CTC is a toy cipher designed in order to assess the strength of algebraic attacks. While the structure of CTC is deliberately weak with respect to algebraic attacks, it was claimed by the designers that CTC is secure with respect to statistical attacks, such as differential and linear cryptanalysis. After a linear attack on CTC was presented, the cipher’s linear transformation was tweaked to offer more diffusion, and specifically to prevent the existence of 1-bit to 1-bit approximations (and differentials) through the linear transformation. The new cipher was named CTC2, and was analyzed by the designers using algebraic techniques.

In this paper we analyze the security of CTC2 with respect to differential and differential-linear attacks. The data complexities of our best attacks on 6-round, 7-round, and 8-round variants of CTC2 are 64, 215, and 237 chosen plaintexts, respectively, and the time complexities are dominated by the time required to encrypt the data.

Our findings show that the diffusion of CTC2 is relatively low, and hence variants of the cipher with a small number of rounds are relatively weak, which may explain (to some extent) the success of the algebraic attacks on these variants.

Keywords

Time Complexity Linear Approximation Linear Transformation Block Cipher Stream Cipher 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Biham, E.: On matsui’s linear cryptanalysis. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 341–355. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  2. 2.
    Biham, E., Dunkelman, O., Keller, N.: Enhancing differential-linear cryptanalysis. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 254–266. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Biham, E., Dunkelman, O., Keller, N.: Differential-linear cryptanalysis of serpent. In: Johansson, T. (ed.) FSE 2003. LNCS, vol. 2887, pp. 9–21. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Biryukov, A., De Cannière, C., Quisquater, M.: On multiple linear approximations. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 1–22. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Buchmann, J., Pyshkin, A., Weinmann, R.-P.: Block ciphers sensitive to gröbner basis attacks. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 313–331. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Collard, B., Standaert, F.-X., Quisquater, J.-J.: Improved and multiple linear cryptanalysis of reduced round serpent. In: Pei, D., Yung, M., Lin, D., Wu, C. (eds.) Inscrypt 2007. LNCS, vol. 4990, pp. 51–65. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    Nicolas, T.: Courtois, How Fast can be Algebraic Attacks on Block Ciphers?, IACR ePrint report 2006/168 (2006)Google Scholar
  9. 9.
    Courtois, N.T.: Algebraic Attacks On Block Ciphers. In: Dagstuhl seminar on Symmetric Cryptography (January 2007)Google Scholar
  10. 10.
    Courtois, N.T.: CTC2 and Fast Algebraic Attacks on Block Ciphers Revisited, IACR ePrint report 2007/152 (2007)Google Scholar
  11. 11.
    Courtois, N.T., Bard, G.V., Wagner, D.: Algebraic and slide attacks on keeLoq. In: Nyberg, K. (ed.) FSE 2008. LNCS, vol. 5086, pp. 97–115. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Courtois, N.T., Meier, W.: Algebraic Attacks on Stream Ciphers with Linear Feedback. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 345–359. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Courtois, N.T., Pieprzyk, J.: Cryptanalysis of block ciphers with overdefined systems of equations. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 267–287. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. 14.
    Dunkelman, O., Keller, N.: Linear Cryptanalysis of CTC, IACR ePrint report 2006/250 (2006)Google Scholar
  15. 15.
    Dunkelman, O., Sekar, G., Preneel, B.: Improved meet-in-the-middle attacks on reduced-round DES. In: Srinathan, K., Rangan, C.P., Yung, M. (eds.) INDOCRYPT 2007. LNCS, vol. 4859, pp. 86–100. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    Faugére, J.-C., Perret, L.: Algebraic Cryptanalysis of Curry and Flurry using Correlated Messages, IACR ePrint report 2008/402 (2008)Google Scholar
  17. 17.
    Langford, S.K.: Differential-Linear Cryptanalysis and Threshold Signatures, Ph.D. thesis (1995)Google Scholar
  18. 18.
    Selçuk, A.A.: On Probability of Success in Linear and Differential Cryptanalysis. Journal of Cryptology 21(1), 131–147 (2008)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Orr Dunkelman
    • 1
  • Nathan Keller
    • 2
  1. 1.Département d’InformatiqueÉcole normale supérieureParisFrance
  2. 2.Einstein Institute of MathematicsHebrew UniversityJerusalemIsrael

Personalised recommendations