# ε-close to t-wise inependence of SPN (AES)

According to theorem 3.13, the 6 rounds of AES is 0.472-close to pairwise independence. It is also mentioned t-wise independence used to analyze higher order derivates attacks. it is also mentioned 3-wise indepdent permutations have a potential application in strengthening short encryption keys. My questions are related to the fundamentals of t-wise independence permutations.

Q.1 What does it mean to have 2, 3 or 4-wise independence to a block cipher from a mathematical perspective?

Q.2 what does it mean 6 rounds of AES is 0.472-close to pairwise independence?

Q.3 (assumption) Does higher order independence have opposite relation with key size but same security level?

• Q2: Definition 2.5 explains what it means to be $\delta$-close to t-wise independence. Q1: t-wise independence is Definition 2.5 with $\delta=0$ Jul 22, 2021 at 14:41
• your questions are a bit vague and some answers are embedded in the definitions as in the comment by @Mikero. Also please help readability by stating at least one of these definitions. Jul 23, 2021 at 2:23
• Thanks for pointing to the definition but what implication does it have in term of AES security (number of rounds), secondly, for Q1, is there a relationship between k-wise and higher order derivatives (for example 2-wise means immune against second order differential cryptanlysis) Jul 27, 2021 at 14:47