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A note on some algebraic trapdoors for block ciphers

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  • We provide sufficient conditions to guarantee that a translation based cipher is not vulnerable with respect to the partition-based trapdoor. This trapdoor has been introduced, recently, by Bannier et al. (2016) and it generalizes that introduced by Paterson in 1999. Moreover, we discuss the fact that studying the group generated by the round functions of a block cipher may not be sufficient to guarantee security against these trapdoors for the cipher.

    Mathematics Subject Classification: Primary: 94A60, 20B15; Secondary: 20B35.

    Citation:

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  • Table 1.  AES state

    $V_1$$V_2$$V_3$$V_4$
    $V_5$$V_6$$V_7$$V_8$
    $V_9$$V_{10}$$V_{11}$$V_{12}$
    $V_{13}$$V_{14}$$V_{15}$$V_{16}$
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    Table 2.  AES wall

    $ \color{orange}{V_1}$$V_2$$V_3$$V_4$ $\color{orange}{V_1}$$V_2$$V_3$$V_4$ $\color{orange}{V_1}$$V_2$$V_3$$V_4$
    $V_5$$\color{orange}{V_6}$$V_7$$V_8$$\mathop {SR}\limits_ \mapsto $ $\color{orange}{V_5}$$V_6$$V_7$$V_8$ $\mathop {MC}\limits_ \mapsto $ $\color{orange}{V_5}$$V_6$$V_7$$V_8$
    $V_9$$V_{10}$$\color{orange}{V_{11}}$$V_{12}$ $\color{orange}{V_9}$$V_{10}$$V_{11}$$V_{12}$ $\color{orange}{V_9}$$V_{10}$$V_{11}$$V_{12}$
    $V_{13}$$V_{14}$$V_{15}$$\color{orange}{V_{16}}$ $\color{orange}{V_{13}}$$V_{14}$$V_{15}$$V_{16}$ $\color{orange}{V_{13}}$$V_{14}$$V_{15}$$V_{16}$
     | Show Table
    DownLoad: CSV
  • [1] R. Anderson, E. Biham and L. Knudsen, SERPENT: A new block cipher proposal, in: Fast Software Encryption, LNCS, Springer, Berlin, 1372 (1998), 222–238.
    [2] R. Aragona, M. Calderini, A. Tortora and M. Tota, Primitivity of PRESENT and other lightweight ciphers, Journal of Algebra and Its Applications, 17 (2018), 1850115, 16pp. doi: 10.1142/S0219498818501153.
    [3] R. AragonaM. CalderiniD. Maccauro and M. Sala, On weak differential uniformity of vectorial Boolean functions as a cryptographic criterion, Appl. Algebra Engrg. Comm. Comput., 27 (2016), 359-372.  doi: 10.1007/s00200-016-0285-8.
    [4] R. AragonaA. Caranti and M. Sala, The group generated by the round functions of a GOST-like cipher, Ann. Mat. Pura Appl., 196 (2016), 1-17.  doi: 10.1007/s10231-016-0559-6.
    [5] A. Bannier, N. Bodin and E. Filiol, Partition-Based Trapdoor Ciphers, preprint, https://eprint.iacr.org/2016/493.pdf.
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