Parsimonious models of high-order Markov chains for evaluation of cryptographic generators

Parsimonious (small-parametric) high-order Markov chains determined by a small number of parameters may be used as models of output sequences in cryptographic generators and their blocks. The paper presents methods of statistical identification (parameter estimation and hypotheses testing) by the observed output sequence for Jacobs–Lewis model, Raftery MTD model, Markov chain with partial connections, Markov chain of conditional order.