Developments in generalized Feistel networks

A generalized Feistel networks (GFN) with n parallel bijectives s-boxes per round has proven to be secure against differential and linear cryptanalysis. For n = 1, the maximum average of the differential probability of the GFN with > 3-round is less than or equal to p². For n = 2, it is not difficult to show that the maximum average of differential probability of the GFN with > 6-round is less than or equal to p³. The results indicate that if GFN has n parallel bijective s-boxes per round, the maximum average of differential probability of the GFN with > 3n-round is less than or equal to pⁿ⁺¹.