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Efficient Construction of the Boomerang Connection Table

Recently, the Boomerang Connection Table was introduced by Cid et al. as a tool to better evaluate the probability of a boomerang distinguisher. To compute the BCT of an n-bit to n-bit S-box, the inventors of the BCT proposed an algorithm that takes O(2) time. We show that one can construct the same table in only O(2) time.