Cryptanalysis of the Full MMB Block Cipher

  • Meiqin Wang
  • Jorge NakaharaJr.
  • Yue Sun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5867)


The block cipher MMB was designed by Daemen, Govaerts and Vandewalle, in 1993, as an alternative to the IDEA block cipher. We exploit and describe unusual properties of the modular multiplication in \({\mathbb Z}_{2^{32}-1}\), which lead to a differential attack on the full 6-round MMB cipher (both versions 1.0 and 2.0). Further contributions of this paper include detailed square and linear cryptanalysis of MMB. Concerning differential cryptanalysis (DC), we can break the full MMB with 2118 chosen plaintexts, 295.91 6-round MMB encryptions and 264 counters, effectively bypassing the cipher’s countermeasures against DC. For the square attack, we can recover the 128-bit user key for 4-round MMB with 234 chosen plaintexts, 2126.32 4-round encryptions and 264 memory blocks. Concerning linear cryptanalysis, we present a key-recovery attack on 3-round MMB requiring 2114.56 known-plaintexts and 2126 encryptions. Moreover, we detail a ciphertext-only attack on 2-round MMB using 293.6 ciphertexts and 293.6 parity computations. These attacks do not depend on weak-key or weak-subkey assumptions, and are thus independent of the key schedule algorithm.


MMB block cipher differential cryptanalysis square cryptanalysis linear cryptanalysis modular multiplication 


  1. 1.
    Biryukov, A., Shamir, A.: Structural Cryptanalysis of SASAS. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 394–405. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  2. 2.
    Biham, E., Shamir, A.: Differential Cryptanalysis of DES-like Cryptosystems. Journal of Cryptology 4(1), 3–72 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Daemen, J., Govaerts, R., Vandewalle, J.: Block Ciphers Based on Modular Multiplication. In: Wolfowicz, W. (ed.) Proceedings of 3rd Symposium on State and Progress of Research in Cryptography, Fondazione Ugo Bordoni, pp. 80–89 (1993)Google Scholar
  4. 4.
    Daemen, J., Van Linden, L., Govaerts, R., Vandewalle, J.: Propagation Properties of Multiplication Modulo 2n − 1. In: Proceedings of the 13th Symposium on Information Theory in the Benelux, Werkgemeenschap voor informatie- en Communicatietheorie, Enschede, The Netherlands, pp. 111–118 (1992)Google Scholar
  5. 5.
    Daemen, J.: Cipher and Hash Function Design – Strategies based on Linear and Differential Cryptanalysis. PhD Thesis, Dept. Elektrotechniek, Katholieke Universiteit Leuven, Belgium (1995)Google Scholar
  6. 6.
    Daemen, J., Knudsen, L.R., Rijmen, V.: The Block Cipher SQUARE. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 149–165. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  7. 7.
    Lai, X.: On the Design and Security of Block Ciphers. In: Massey, J.L. (ed.) ETH Series in Information Processing, vol. 1. Hartung-Gorre Verlag, Konstanz (1995)Google Scholar
  8. 8.
    Matsui, M.: Linear Cryptanalysis Method for DES Cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994)Google Scholar
  9. 9.
    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
  10. 10.
    Rijmen, V., Daemen, J., Preneel, B., Bosselaers, A., De Win, E.: The Cipher SHARK. In: Gollmann, D. (ed.) FSE 1996. LNCS, vol. 1039, pp. 99–111. Springer, Heidelberg (1996)Google Scholar
  11. 11.
    Selçuk, A.A., Biçak, A.: On Probability of Success in Linear and Differential Cryptanalysis. In: Cimato, S., Galdi, C., Persiano, G. (eds.) SCN 2002. LNCS, vol. 2576, pp. 174–185. Springer, Heidelberg (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Meiqin Wang
    • 1
  • Jorge NakaharaJr.
    • 2
  • Yue Sun
    • 1
  1. 1.Key Laboratory of Cryptologic Technology and Information Security, Ministry of EducationShandong UniversityJinanChina
  2. 2.EPFLLausanneSwitzerland

Personalised recommendations