Malaysian Journal of Mathematical Sciences, June 2015, Vol. 9(S)
Special Issue: The 4th International Cryptology and Information Security Conference 2014 (Cryptology 2014)

Linear Extension Cube Attack on Stream Ciphers

Liren Ding, Yongjuan Wang and Zhufeng Li

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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 $O(2^{14})$ 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.

Keywords: Cube Attack, Stream Cipher, Linear Extension, Pre-processing, Trivium, Lili-128



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