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Towards the optimality of Feistel ciphers with substitution-permutation functions

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Abstract

We explore the optimality of balanced Feistel ciphers with SP-type F-functions with respect to their resistance against differential and linear cryptanalysis. Instantiations of Feistel ciphers with the wide class of (SP)\(^u\) and (SP)\(^u\)S F-functions are considered: one F-function can contain an arbitrary number of S-box layers interleaved with linear diffusion. For the matrices with maximum diffusion, it is proven that SPS and SPSP F-functions are optimal in terms of the proportion of active S-boxes in all S-boxes—a common efficiency metric for substitution-permutation ciphers. Interestingly, one SP-layer in the F-function is not enough to attain optimality whereas taking more than two S-box layers does not increase the efficiency either.

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Authors and Affiliations

  1. Sony Corporation, 1-7-1 Konan, Minato-ku, Tokyo , 108-0075, Japan

    Kyoji Shibutani

  2. ESAT/SCD/COSIC, KU Leuven, Kasteelpark Arenberg 10, 3001 , Heverlee, Belgium

    Andrey Bogdanov

Authors
  1. Kyoji Shibutani
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  2. Andrey Bogdanov
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Correspondence to Kyoji Shibutani.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography”.

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Shibutani, K., Bogdanov, A. Towards the optimality of Feistel ciphers with substitution-permutation functions. Des. Codes Cryptogr. 73, 667–682 (2014). https://doi.org/10.1007/s10623-014-9970-4

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