Paper 2013/674

Cryptanalysis of Iterated Even-Mansour Schemes with Two Keys

Itai Dinur, Orr Dunkelman, Nathan Keller, and Adi Shamir

Abstract

The iterated Even-Mansour (EM) scheme is a generalization of the original 1-round construction proposed in 1991, and can use one key, two keys, or completely independent keys. In this paper, we methodically analyze the security of all the possible iterated Even-Mansour schemes with two $n$-bit keys and up to four rounds, and show that none of them provides more than $n$-bit security. Our attacks are based on a new cryptanalytic technique called \emph{multibridge} which splits the cipher to different parts in a novel way, such that they can be analyzed independently, exploiting its self-similarity properties. After the analysis of the parts, the key suggestions are efficiently joined using a meet-in-the-middle procedure. As a demonstration of the multibridge technique, we devise a new attack on 4 steps of the LED-128 block cipher, reducing the time complexity of the best known attack on this scheme from $2^{96}$ to $2^{64}$. Furthermore, we show that our technique can be used as a generic key-recovery tool, when combined with some statistical distinguishers (like those recently constructed in reflection cryptanalysis of GOST and PRINCE).