Proving the security of AES substitution-permutation network

In this paper we study the substitution-permutation network (SPN) on which AES is based. We introduce AES*, a SPN identical to AES except that fixed S-boxes are replaced by random and independent permutations. We prove that this construction resists linear and differential cryptanalysis with 4 inner rounds only, despite the huge cumulative effect of multipath characteristics that is induced by the symmetries of AES. We show that the DP and LP terms both tend towards 1/(2 128_ 1) very fast when the number of round increases. This proves a conjecture by Keliher, Meijer, and Tavares. We further show that AES* is immune to any iterated attack of order 1 after 10 rounds only, which substantially improves a previous result by Moriai and Vaudenay.