The t-wise Independence of Substitution-Permutation Networks

Abstract

Block ciphers such as the Advanced Encryption Standard (Rijndael) are used extensively in practice, yet our understanding of their security continues to be highly incomplete. This paper promotes and continues a research program aimed at proving the security of block ciphers against important and well-studied classes of attacks. In particular, we initiate the study of (almost) t-wise independence of concrete block-cipher construction paradigms such as substitution-permutation networks and key-alternating ciphers. Sufficiently strong (almost) pairwise independence already suffices to resist (truncated) differential attacks and linear cryptanalysis, and hence this is a relevant and meaningful target. Our results are two-fold.