Integral Property Analysis on the Structure of SP-GFS

The paper propose the definition of diffusion order and described the diffusion property of the linear permutation. Moreover, by analyzing effect of the linear permutation on the integral distinguisher length, the lower bounds for the round number of the Substitute Permutation-Generalized Feistel Structure (SP-GFS) integral distinguisher with different linear permutations P are obtained. Using this method，the integral distinguishers of two block ciphers Camellia and CLEFIA are improved, hence verifying the correctness of the conclusion.