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Conclusions

We have shown two forms of bias in the output of the LEVIATHAN keystream generator, either of which distinguish it from a random function with \( 2^{36} \) known bytes of output; we have not as yet found a way to recover key material using these distinguishers. These distinguishers can both be applied to the same portion of keystream for greater statistical significance. Both make use of compression in the PairCom function.

Despite these attacks, LEVIATHAN demonstrates that a tree-based cipher could offer many advantages. It is to be hoped that similar designs, offering the same speed and flexibility but resistant to this and other attacks, will be forthcoming.



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