Cube Attacks on the Stream Cipher Grain-v1

Abstract

The Cube Attack was introduced by Itai Dinur and Adi Shamir. As a known plaintext attack on symmetric primitives, it is efficient to stream cipher, block cipher and hash functions. In this paper, we proposed a new method to find all the cubes U which could produce linear relations, and it is applied to simplified Grain-v1 variants with 60, 65 initialization rounds, from which we can obtain at least 25, 11 key bits respectively. Our results show that the Grain-v1 with reduced initialization rounds can be broken with Cube Attack, and the complexity is significantly lower than exhaustive search.