Statistical analysis of DH1 cryptosystem

In this paper we shall use some standard statistical methods to test the avalanche effect of a previously introduced cryptosystem based on automata compositions, called DH1 cryptosystem. We have generated sample data of encryption and decryption. In our first set of analysis we simply estimated the probabilities of the atoms of the discrete distribution separately in order to compare them with those of the binomial test distribution. In the second statistical analysis, we turned to a goodness-of-fit test. For this we used the χ2-test. Thirdly, we assumed that the sample comes from a binomial distribution and we calculated the maximum likelihood estimation of the two parameters. Finally we discuss some well-known further tests on randomness and related results. Our main conclusions based on the statistics all confirm that the avalanche effect is fulfilled