New Properties of the Double Boomerang Connectivity Table.

The double boomerang connectivity table (DBCT) is a new table proposed recently to capture the behavior of two consecutive S-boxes in boomerang attacks. In this paper, we observe an interesting property of DBCT of S-box that the ladder switch and the S-box switch happen in most cases for two continuous S-boxes, and for some S-boxes only S-box switch and ladder switch are possible. This property implies an additional criterion for S-boxes to resist the boomerang attacks and provides as well a new evaluation direction for an S-box. Using an extension of the DBCT, we verify that some boomerang distinguishers of TweAES and Deoxys are flawed. On the other hand, inspired by the property, we put forward a formula for estimating boomerang cluster probabilities. Furthermore, we introduce the first model to search for boomerang distinguishers with good cluster probabilities. Applying the model to CRAFT, we obtain 9-round and 10-round boomerang distinguishers with a higher probability than that of previous works.