On unbalanced Feistel networks with contracting MDS diffusion

  • Authors:
  • Andrey Bogdanov

  • Affiliations:
  • Department of Electrical Engineering ESAT/SCD-COSIC, Katholieke Universiteit Leuven, Leuven-Heverlee, Belgium 3001 and Interdisciplinary Center for Broad Band Technologies, Leuven-Heverlee, Belgiu ...

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2011

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Abstract

Though unbalanced Feistel networks (UFN) are widely considered as an alternative to balanced Feistel networks (BFN) and substitution---permutation networks (SPN) in symmetric cryptography, little has been known yet about their resistance against differential and linear cryptanalysis. In this work, we tackle the problem at the example of d-branch SP-type UFNs with contracting MDS diffusion (dCUFN-SP). Under some restrictions on the contracting MDS matrices over multiple rounds, we prove lower bounds on the number of differentially active S-boxes for dCUFN-SP with $${d\in\{3,4\}}$$ and on the number of linearly active S-boxes for dCUFN-SP with d 驴 3. As opposed to SPNs and BFNs, the number of differentially active S-boxes for such constructions does not directly translate to an upper bound on the probability of differential trails. So we provide a thorough analysis of single-round differentials that yields an upper bound on the probability of a differential trail. It is also shown that the efficiency level of dCUFN-SP is comparable to that of BFNs and SPNs with respect to differential and linear cryptanalysis.