Proof Beyond the Birthday Bound with the Coupling Technique

The coupling technique originates from the theory of Markov chains, and allows to upper bound the rate at which a Markov chain approaches its stationary distribution. Recasting the encryption process of a tuple of plaintexts through an iterative block cipher as a Markov chain, it is possible to use this tool to upper bound the advantage of a distinguisher against various kinds of Feistel schemes.