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. We will present some results proving the security of block ciphers against important and well-studied classes of attacks. In particular, we will introduce a concrete block cipher construction paradigm called the substitution-permutation network (SPN) and study its (almost) t-wise independence as a relevant and meaningful property that captures security. We will also survey some recent t-wise independence results that are not limited to the SPN paradigm.

Based on works with Tianren Liu, Stefano Tessaro, Vinod Vaikuntanathan (https://eprint.iacr.org/2021/507, https://eprint.iacr.org/2024/083), and Lucas Gretta, William He (https://eprint.iacr.org/2024/847).