An Algorithm to Analyze Non-injective S-Boxes

Abstract : We present an algorithm for constructing pairs of an invertible mapping A and an affine mapping B such that AS = SB for a given S-box. For doing we so, we introduce and analyse the link graph of an S-box. We apply the algorithm to the eight DES S-boxes. All obtained pairs (A,B) are those reported in previous work, in which it was required that both A and B are invertible affine mappings. In particular, the relaxation that A need not be affine does not yield new pairs.
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Leandro Marin, Ludo Tolhuizen. An Algorithm to Analyze Non-injective S-Boxes. 2nd Information and Communication Technology - EurAsia Conference (ICT-EurAsia), Apr 2014, Bali, Indonesia. pp.576-585, ⟨10.1007/978-3-642-55032-4_59⟩. ⟨hal-01397273⟩

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