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Pseudorandom permutations based on the DES scheme
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We introduce a new notion called a quasi-Feistel cipher, which is a generalization of the Feistel cipher, and contains the Lai---Massey cipher as an instance. We show that most of the works on the Feistel cipher can be naturally extended to the quasi-Feistel cipher. From this, we give a new proof for Vaudenay's theorems on the security of the Lai---Massey cipher, and also we introduce for Lai---Massey a new construction of pseudorandom permutation, analoguous to the construction of Naor---Reingold using pairwise independent permutations. Also, we prove the birthday security of (2b驴1)- and (3b驴2)-round unbalanced quasi-Feistel ciphers with b branches against CPA and CPCA attacks, respectively.