On Lai-Massey and quasi-Feistel ciphers

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-1)- and (3b-2)-round unbalanced quasi-Feistel ciphers with b branches against CPA and CPCA attacks, respectively.