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/(2128 −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.

• Type: Conference
• Year: 2005
• Where: SACRYPT
• Authors: Thomas Baignères, Serge Vaudenay
• Keywords: Construction Resists Linear, Huge Cumulative Effect, SACRYPT 2005, Substitution-permutation Network