## Cryptology ePrint Archive: Report 2007/347

Lai-Massey Scheme and Quasi-Feistel Networks

Aaram Yun and Je Hong Park and Jooyoung Lee

Abstract: We introduce the notion of quasi-Feistel network, which is generalization of the Feistel network, and contains the Lai-Massey scheme as an instance. We show that some of the works on the Feistel network, including the works of Luby-Rackoff, Patarin, Naor-Reingold and Piret, can be naturally extended to our setting. This gives a new proof for theorems of Vaudenay on the security of the Lai-Massey scheme, and also introduces 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 networks with b branches against CPA and CPCA attacks, respectively. This answers an unsolved problem pointed out by Patarin et al.

Category / Keywords: foundations / Lai-Massey scheme, Feistel network, Luby-Rackoff, block cipher design, pseudorandom function, indistinguishability