T Wise Independence

Almost t-wise independence of concrete block-cipher constructions, as a provable-security target that rules out differential and linear cryptanalysis.

Status	Statement	Tags
	192-Round AES Pairwise Independence Theorem 7 proves the bound for 192-round censored AES – real AES S-boxes and mixing layer, but a subset of the mixing layers removed. The source conjectures the same round count suffices for AES itself, and calls proving it an outstanding open problem. The best proved bound for actual AES is Liu, Tessaro and Vaikuntanathan’s, which needs more than 9000 rounds. 4 open	Block Ciphers Limited Independence Pseudorandom Permutations T Wise Independencetight-bound
	AES t-Wise Independence, t > 2 Named by the source as the first of the two outstanding open problems that come of its work. It proves almost pairwise independence (t = 2) for multi-round AES with independent round keys, and an existential t-wise result for key-alternating ciphers with most permutations, but nothing for concrete AES beyond t = 2. Its Appendix B attacks 4-wise independence in the width-1 case with the same S-box. 4 open	Block Ciphers Limited Independence Pseudorandom Permutations T Wise Independencecharacterizationbarrier (ai)