Advertisement

Estimating the Probabilities of Low-Weight Differential and Linear Approximations on PRESENT-Like Ciphers

  • Mohamed Ahmed Abdelraheem
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7839)

Abstract

We use large but sparse correlation and transition-difference-probability submatrices to find the best linear and differential approximations respectively on PRESENT-like ciphers. This outperforms the branch and bound algorithm when the number of low-weight differential and linear characteristics grows exponentially which is the case in PRESENT-like ciphers. We found linear distinguishers on 23 rounds of the SPONGENT permutation. We also found better linear approximations on PRESENT using trails covering at most 4 active Sboxes which give us 24-round statistical saturation distinguishers which could be used to break 26 rounds of PRESENT.

Keywords

block cipher differential difference matrix linear hull correlation matrix statistical saturation attack PRESENT SPONGENT 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aumasson, J.-P., Henzen, L., Meier, W., Naya-Plasencia, M.: Quark: A lightweight hash. In: Mangard, S., Standaert, F.-X. (eds.) CHES 2010. LNCS, vol. 6225, pp. 1–15. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Blondeau, C., Gérard, B.: Multiple differential cryptanalysis: Theory and practice. In: Joux (ed.) [19], pp. 35–54Google Scholar
  3. 3.
    Bogdanov, A., Knezevic, M., Leander, G., Toz, D., Varici, K., Verbauwhede, I.: Spongent: The design space of lightweight cryptographic hashing. IEEE Transactions on Computers PP(99), 1 (2012)Google Scholar
  4. 4.
    Bogdanov, A., Knežević, M., Leander, G., Toz, D., Varıcı, K., Verbauwhede, I.: spongent: A lightweight hash function. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 312–325. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Bogdanov, A., Knudsen, L.R., Leander, G., Paar, C., Poschmann, A., Robshaw, M.J.B., Seurin, Y., Vikkelsoe, C.: PRESENT: An ultra-lightweight block cipher. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 450–466. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Borghoff, J., Knudsen, L.R., Leander, G., Thomsen, S.S.: Cryptanalysis of present-like ciphers with secret s-boxes. In: Joux (ed.) [19], pp. 270–289Google Scholar
  7. 7.
    De Cannière, C., Dunkelman, O., Knežević, M.: KATAN and KTANTAN — A family of small and efficient hardware-oriented block ciphers. In: Clavier, C., Gaj, K. (eds.) CHES 2009. LNCS, vol. 5747, pp. 272–288. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    De Cannière, C., Preneel, B.: Trivium. In: Robshaw, Billet (eds.) [26], pp. 244–266Google Scholar
  9. 9.
    Cho, J.Y.: Linear cryptanalysis of reduced-round present. In: Pieprzyk, J. (ed.) CT-RSA 2010. LNCS, vol. 5985, pp. 302–317. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Collard, B., Standaert, F.-X.: A statistical saturation attack against the block cipher PRESENT. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 195–210. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Daemen, J., Govaerts, R., Vandewalle, J.: Correlation matrices. In: Preneel, B. (ed.) FSE 1994. LNCS, vol. 1008, pp. 275–285. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  12. 12.
    Daemen, J., Rijmen, V.: The Design of Rijndael: AES - The Advanced Encryption Standard. Springer (2002)Google Scholar
  13. 13.
    Daemen, J., Rijmen, V.: Probability distributions of correlation and differentials in block ciphers. IACR Cryptology ePrint Archive, 2005:212 (2005)Google Scholar
  14. 14.
    Guo, J., Peyrin, T., Poschmann, A.: The PHOTON family of lightweight hash functions. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 222–239. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  15. 15.
    Hell, M., Johansson, T., Maximov, A., Meier, W.: The grain family of stream ciphers. In: Robshaw, Billet (eds.) [26], pp. 179–190Google Scholar
  16. 16.
    Hermelin, M., Cho, J.Y., Nyberg, K.: Multidimensional extension of matsui’s algorithm 2. In: Dunkelman, O. (ed.) FSE 2009. LNCS, vol. 5665, pp. 209–227. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  17. 17.
    Hermelin, M., Nyberg, K.: Linear cryptanalysis using multiple linear approximations. Cryptology ePrint Archive, Report 2011/093 (2011)Google Scholar
  18. 18.
    ISO/IEC 29192-2:2012. Information technology Security techniques Lightweight cryptography. Part 2: Block ciphers (2012)Google Scholar
  19. 19.
    Joux, A. (ed.): FSE 2011. LNCS, vol. 6733. Springer, Heidelberg (2011)zbMATHGoogle Scholar
  20. 20.
    Lai, X., Massey, J.L.: Markov ciphers and differential cryptanalysis. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 17–38. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  21. 21.
    Leander, G.: On linear hulls, statistical saturation attacks, present and a cryptanalysis of puffin. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 303–322. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  22. 22.
    Matsui, M.: On correlation between the order of s-boxes and the strength of des. In: Santis (ed.) [28], pp. 366–375Google Scholar
  23. 23.
    Nyberg, K.: Linear approximation of block ciphers. In: Santis (ed.) [28], pp. 439–444Google Scholar
  24. 24.
    O’Connor, L., Golić, J.D.: A unified markov approach to differential and linear cryptanalysis. In: Pieprzyk, J., Safavi-Naini, R. (eds.) ASIACRYPT 1994. LNCS, vol. 917, pp. 387–397. Springer, Heidelberg (1995)Google Scholar
  25. 25.
    Ohkuma, K.: Weak keys of reduced-round PRESENT for linear cryptanalysis. In: Jacobson Jr., M.J., Rijmen, V., Safavi-Naini, R. (eds.) SAC 2009. LNCS, vol. 5867, pp. 249–265. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  26. 26.
    Robshaw, M., Billet, O. (eds.): New Stream Cipher Designs. LNCS, vol. 4986. Springer, Heidelberg (2008)zbMATHGoogle Scholar
  27. 27.
    Saad, Y.: SPARSKIT: A basic tool kit for sparse matrix computation. Research Institute for Advanced Computer Science, NASA Ames Research Center (1990)Google Scholar
  28. 28.
    De Santis, A. (ed.): EUROCRYPT 1994. LNCS, vol. 950. Springer, Heidelberg (1995)zbMATHGoogle Scholar
  29. 29.
    Wang, M.: Differential cryptanalysis of reduced-round PRESENT. In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol. 5023, pp. 40–49. Springer, Heidelberg (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Mohamed Ahmed Abdelraheem
    • 1
  1. 1.Department of MathematicsTechnical University of DenmarkLyngbyDenmark

Personalised recommendations