Security

A Link Between Integrals and Higher-Order Integrals of SPN Ciphers

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Executive Summary

Integral cryptanalysis, which is based on the existence of (higher-order) integral distinguishers, is a powerful cryptographic method that can be used to evaluate the security of modern block ciphers. In this paper, the authors focus on Substitution-Permutation Network (SPN) ciphers and propose a criterion to characterize how an r-round integral distinguisher can be extended to an (r+1)-round higher-order integral distinguisher. This criterion, which builds a link between integrals and higher-order integrals of SPN ciphers, is in fact based on the theory of direct decomposition of a linear space defined by the linear mapping of the cipher.

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