Layout Graphs, Random Walks and the t-wise Independence of SPN Block Ciphers

ePrint Report: Layout Graphs, Random Walks and the t-wise Independence of SPN Block Ciphers

Tianren Liu, Angelos Pelecanos, Stefano Tessaro, Vinod Vaikuntanathan

We continue the study of $t$-wise independence of substitution-permutation networks (SPNs) initiated by the recent work of Liu, Tessaro, and Vaikuntanathan (CRYPTO 2021).
Our key technical result shows that when the S-boxes are randomly and independently chosen and kept secret, an $r$-round SPN with input length $n = b \cdot k$ is $2^{-\Theta(n)}$-close to $t$-wise independent within $r …

block ciphers continue crypto eprint report graphs key layout networks random report spn study technical work