Linear Extension Cube Attack on Stream Ciphers

Basing on the original Cube attack, this paper proposes an improved method of Cube attack on stream ciphers, which makes improvement on the pre-processing phase of the original attack. The new method can induce maxterms of higher-order from those of lower-order by the trade-off between time and space, thus recovering more key bits and reducing the search complexity on higher-dimension. In this paper, the improved attack is applied to Lili-128 algorithm and reduced variants of Trivium algorithm. We can recover 88 key bits of Lili-128 algorithm within time complexity of 14 O(2(14)) and 48 key bits of Trivium algorithm can be recovered by cubes with dimension no larger than 8 when the initialization round is 576, the results are much better than those of the original attacks.