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Linear cryptanalysis of substitutionpermutation networks
, 2003
"... The subject of this thesis is linear cryptanalysis of substitutionpermutation networks (SPNs). We focus on the rigorous form of linear cryptanalysis, which requires the concept of linear hulls. First, we consider SPNs in which the sboxes are selected independently and uniformly from the set of al ..."
Abstract

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The subject of this thesis is linear cryptanalysis of substitutionpermutation networks (SPNs). We focus on the rigorous form of linear cryptanalysis, which requires the concept of linear hulls. First, we consider SPNs in which the sboxes are selected independently and uniformly from the set of all bijective n × n sboxes. We derive an expression for the expected linear probability values of such an SPN, and give evidence that this expression converges to the corresponding value for the true random cipher. This adds quantitative support to the claim that the SPN structure is a good approximation to the true random cipher. We conjecture that this convergence holds for a large class of SPNs. In addition, we derive a lower bound on the probability that an SPN with randomly selected sboxes is practically secure against linear cryptanalysis after a given number of rounds. For common block sizes, experimental evidence indicates that this probability rapidly approaches 1 with an increasing number of rounds.