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In this paper, the authors combine ideas from two different proof techniques: the Coupling technique and the H Coefficients technique. They introduce a new Theorem: the "H Coefficients Composition Theorem". From this new theorem, they are able to obtain security proofs that combine the efficiency of the H Coefficients for small rounds Feistel schemes and the geometric gain of the Coupling technique. They apply these results only on the classical balanced generic Feistel schemes but the technique can also be applied to many different schemes like unbalanced Feistel schemes or Misty schemes for example.
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