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Several generalizations of linear cryptanalysis have been pro- posed in the past, as well as very similar attacks in a statistical point of view. In this paper, we deflne a rigorous general statistical framework which allows to interpret most of these attacks in a simple and unifled way. Then, we explicitely construct optimal distinguishers, we evaluate their performance, and we prove that a block cipher immune to classical linear cryptanalysis possesses some resistance to a wide class of general- ized versions, but not all. Finally, we derive tools which are necessary to set up more elaborate extensions of linear cryptanalysis, and to general- ize the notions of bias, characteristic, and piling-up lemma.

How Far Can We Go Beyond Linear Cryptanalysis?