Security of the MISTY Structure in the Luby-Rackoff Model: Improved Results

In this paper we consider the security of the Misty structure in the Luby-Rackoff model, if the inner functions are replaced by involutions without fixed point. In this context we show that the success probability in distinguishing a 4-round L-scheme from a random function is O(m2/2n) (where m is the number of queries and 2n the block size) when the adversary is allowed to make adaptively chosen encryption queries. We give a similar bound in the case of the 3-round R-scheme. Finally, we show that the advantage in distinguishing a 5-round scheme from a random permutation when the adversary is allowed to adaptively chosen encryption as well as decryption queries is also O(m2/2n). This is to our knowledge the first time involutions are considered in the context of the Luby-Rackoff model.

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