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I am reading the "Biclique cryptanalysis of the full AES" paper. What do they mean by "sharing active S-boxes"? How can this concept can be advantageous to make a bicycle? If there is someone who reads this paper, please explain it to me.

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    $\begingroup$ @e-sushi I don't think this is a reference request. It's asking for for clarification of certain concepts used in a notable paper. It's limited in scope and doesn't lead to link-only answers. So I consider it on topic. $\endgroup$
    – CodesInChaos
    Jul 20, 2013 at 19:09
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    $\begingroup$ Can you please provide a link to the paper and quote the relevant section here? $\endgroup$
    – rath
    Jul 24, 2013 at 19:46

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We talk about cryptanalytic tools here. A differential trail describes how a certain difference evolutes throughout the cipher, which helps to find out a key in a standard differential cryptanalysis. Each trail activates certain non-linear operations (S-boxes), which contribute to its probability (a difference goes through a nonlinear operation probabilistically).

The biclique key search method works with a pair of such trails in a small part of the cipher. For the method to work, these trails must activate non-interleaving groups of S-boxes, otherwise more sophisticated conditions come into play.

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