Avalanche characteristics of substitution-permutation encryption networks

This paper develops analytical models for the avalanche characteristics of a class of block ciphers usually referred to as substitution-permutation encryption networks or SPNs. An SPN is considered to display good avalanche characteristics if a one bit change in the plaintext input is expected to result in close to half the ciphertext output bits changing. Good avalanche characteristics are important to ensure that a cipher is not susceptible to statistical attacks and the strength of an SPN´s avalanche characteristics may be considered as a measure of the randomness of the ciphertext. The results presented in this paper demonstrate that the avalanche behavior of encryption networks can be improved by using larger S-boxes. As well, it is shown that increasing the diffusion properties of the S-boxes or replacing the permutations by diffusive linear transformations is effective in improving the network avalanche characteristics