Key Recovery Attacks on 3-round Even-Mansour, 8-step LED-128, and Full AES(2)

The Even-Mansour (EM) encryption scheme received a lot of attention in the last couple of years due to its exceptional simplicity and tight security proofs. The original 1-round construction was naturally generalized into r-round structures with one key, two alternating keys, and completely independent keys. In this paper we describe the first key recovery attack on the one-key 3-round version of EM which is asymptotically faster than exhaustive search (in the sense that its running time is o(2(n)) rather than O(2(n)) for an n-bit key). We then use the new cryptanalytic techniques in order to improve the best known attacks on several concrete EM-like schemes. In the case of LED-128, the best previously known attack could only be applied to 6 of its 12 steps. In this paper we develop a new attack which increases the number of attacked steps to 8, is slightly faster than the previous attack on 6 steps, and uses about a thousand times less data. Finally, we describe the first attack on the full AES(2) (which uses two complete AES-128 encryptions and three independent 128-bit keys, and looks exceptionally strong) which is about 7 times faster than a standard meet-in-the-middle attack, thus violating its security claim.