Cube Attack

Abstract

Cube attack is a recent addition in the area of cryptanalysis applicable to a wide range of symmetric key algorithms. The attack was proposed by Itai Dinur and Adi Shamir in 2009. Cryptographic schemes may be represented by tweakable polynomials in GF(2) in terms of secret and public variables. Cube attack is a major improvement over existing techniques used for solving such polynomial equations. LBlock is a new light weight block cipher, that has been tested against different cryptanalytic techniques including differential cryptanalysis, linear cryptanalysis, impossible differential cryptanalysis, integral attack and the related key attack but its resistance for cube attack is not tested yet. In this research, LBlock has been evaluated against the cube attack. Moreover, Trivium and A5/1 have also been analyzed. 33 out of 80 key bits have been recovered for 9/32 round LBlock. 69 out of 80 key bits for Trivium have been recovered having 576/1152 initialization rounds and 20 linearly independent relations have been found for A5/1 encryption algorithm having 5/100 setup rounds. A software tool has also been developed which can evaluate both the stream and block ciphers against the cube attack. Code of any cipher may be loaded into the tool to check its resistivity against the attack. The tool is independent of the ciphers and treats them as a black box by sending them chosen inputs and analyzing the outputs. The results include the recovered key bits for the attacked number of rounds of the target cipher.