Cryptanalysis of SP Networks with Partial Non-Linear Layers

  • Achiya Bar-On
  • Itai DinurEmail author
  • Orr Dunkelman
  • Virginie Lallemand
  • Nathan Keller
  • Boaz Tsaban
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9056)


Design of SP networks in which the non-linear layer is applied to only a part of the state in each round was suggested by Gérard et al. at CHES 2013. Besides performance advantage on certain platforms, such a design allows for more efficient masking techniques that can mitigate side-channel attacks with a small performance overhead.

In this paper we present generic techniques for differential and linear cryptanalysis of SP networks with partial non-linear layers, including an automated characteristic search tool and dedicated key-recovery algorithms. Our techniques can be used both for cryptanalysis of such schemes and for proving their security with respect to basic differential and linear cryptanalysis, succeeding where previous automated analysis tools seem to fail.

We first apply our techniques to the block cipher Zorro (designed by Gérard et al. following their methodology), obtaining practical attacks on the cipher which where fully simulated on a single desktop PC in a few days. Then, we propose a mild change to Zorro, and formally prove its security against basic differential and linear cryptanalysis. We conclude that there is no inherent flaw in the design strategy of Gérard et al., and it can be used in future designs, where our tools should prove useful.


Block cipher Lightweight Zorro Differential cryptanalysis Linear cryptanalysis 


  1. 1.
    Albrecht, M., Cid, C.: Algebraic Techniques in Differential Cryptanalysis. In: Dunkelman, O. (ed.) FSE 2009. LNCS, vol. 5665, pp. 193–208. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  2. 2.
    Bar-On, A., Dinur, I., Dunkelman, O., Lallemand, V., Keller, N., Tsaban, B.: Cryptanalysis of SP Networks with Partial Non-Linear Layers. Cryptology ePrint Archive, Report 2014/228 (2014).
  3. 3.
    Biryukov, A., Nikolić, I.: Automatic Search for Related-key Differential Characteristics in Byte-oriented Block Ciphers: Application to AES, Camellia, Khazad and Others. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 322–344. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  4. 4.
    Biryukov, A., Nikolić, I.: Search for Related-Key Differential Characteristics in DES-Like Ciphers. In: Joux, A. (ed.) FSE 2011. LNCS, vol. 6733, pp. 18–34. Springer, Heidelberg (2011). CrossRefGoogle Scholar
  5. 5.
    Bogdanov, A., Tischhauser, E.: On the Wrong Key Randomisation and Key Equivalence Hypotheses in Matsui’s Algorithm 2. In: Moriai, S. (ed.) FSE 2013. LNCS, vol. 8424, pp. 19–38. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  6. 6.
    Collard, B., Standaert, F.-X., Quisquater, J.-J.: Improving the Time Complexity of Matsui’s Linear Cryptanalysis. In: Nam, K.-H., Rhee, G. (eds.) ICISC 2007. LNCS, vol. 4817, pp. 77–88. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  7. 7.
    Daemen, J., Rijmen, V.: The Design of Rijndael: AES - The Advanced Encryption Standard. Information Security and Cryptography, Springer (2002).
  8. 8.
    Derbez, P., Fouque, P.-A., Jean, J.: Improved Key Recovery Attacks on Reduced-Round AES in the Single-Key Setting. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 371–387. Springer, Heidelberg (2013). CrossRefGoogle Scholar
  9. 9.
    Ferguson, N., Kelsey, J., Lucks, S., Schneier, B., Stay, M., Wagner, D., Whiting, D.L.: Improved Cryptanalysis of Rijndael. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 213–230. Springer, Heidelberg (2001) CrossRefGoogle Scholar
  10. 10.
    Gérard, B., Grosso, V., Naya-Plasencia, M., Standaert, F.-X.: Block Ciphers that Are Easier to Mask: How Far Can We Go? In: Bertoni, G., Coron, J.-S. (eds.) CHES 2013. LNCS, vol. 8086, pp. 383–399. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  11. 11.
    Guo, J., Nikolic, I., Peyrin, T., Wang, L.: Cryptanalysis of Zorro. Cryptology ePrint Archive, Report 2013/713 (2013).
  12. 12.
    Matsui, M.: On Correlation Between the Order of S-boxes and the Strength of DES. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 366–375. Springer, Heidelberg (1995). CrossRefGoogle Scholar
  13. 13.
    Mouha, N., Wang, Q., Gu, D., Preneel, B.: Differential and Linear Cryptanalysis Using Mixed-Integer Linear Programming. In: Wu, C.-K., Yung, M., Lin, D. (eds.) Inscrypt 2011. LNCS, vol. 7537, pp. 57–76. Springer, Heidelberg (2012). CrossRefGoogle Scholar
  14. 14.
    Rasoolzadeh, S., Ahmadian, Z., Salmasizadeh, M., Aref, M.R.: Total Break of Zorro using Linear and Differential Attacks. Cryptology ePrint Archive, Report 2014/220 (2014).
  15. 15.
    Selçuk, A.A.: On Probability of Success in Linear and Differential Cryptanalysis. J. Cryptology 21(1), 131–147 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Wang, Y., Wu, W., Guo, Z., Yu, X.: Differential Cryptanalysis and Linear Distinguisher of Full-Round Zorro. In: Boureanu, I., Owesarski, P., Vaudenay, S. (eds.) ACNS 2014. LNCS, vol. 8479, pp. 308–323. Springer, Heidelberg (2014). CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  • Achiya Bar-On
    • 1
  • Itai Dinur
    • 2
    Email author
  • Orr Dunkelman
    • 3
    • 5
  • Virginie Lallemand
    • 4
  • Nathan Keller
    • 1
    • 5
  • Boaz Tsaban
    • 1
  1. 1.Department of MathematicsBar-Ilan UniversityRamat GanIsrael
  2. 2.Département d’InformatiqueÉcole Normale SupérieureParisFrance
  3. 3.Computer Science DepartmentUniversity of HaifaHaifaIsrael
  4. 4.InriaParisFrance
  5. 5.Computer Science DepartmentThe Weizmann InstituteRehovotIsrael

Personalised recommendations