In this paper, we first prove beyond-birthyday-bound security for the Misty structure. Specifically, we show that an r-round Misty structure is secure against CCA attacks up to $O(2^{\frac{rn}{r+7}})$ query complexity, where n is the size of each round permutation. So for any ε>0, a sufficient number of rounds would guarantee the security of the Misty structure up to 2n(1-ε) query complexity.
