The Probability Model Of Key Stream Generators And Research On Logic Functions

Using the idea of probability theory and spectral theory, we investigate the probability model of key stream generators and some related characteristics of logic functions in cryptography.The main results are following three aspects:In the second chapter, it constructs the probability model of the multi-value clock controlled stop-and-go generator, the probability model of the generalized shrinking generator and the probability model of the general multi-valued shrinking generator. It discusses the probability properties of their output sequences, and gets the formulae of the coincidence of the output sequences with the original input sequences. It also analyzes the properties and gains and losses of the three kinds of generators in the view of probability theory.In the third chapter, in regard to the combiner with r bits of memory, the correlation coefficients between its output sequences and input sequences with memory states are analyzed and all the computational formulae are derived. The formulae are used in doing correlation analysis of the combiner with an arbitrary number of bits memory. The problem of "generalized conservation of energy" is also analyzed, and it is shown that the condition under which the "generalized conservation of energy theorem" is hold.In the fourth chapter, firstly it introduces the Boolean functions' algebraic expressions of the 2-value clock-controlled stop-and-go generator and Gunther generator. It reveals the balanced property of the two kinds of Boolean functions, and studies the Walsh cycle spectrum and the autocorrelation function. It also obtains the coincidence rate of their output sequences with affine sum of some bits of input sequences, and analyzes their ability of resisting the best affine approximation cryptanalysis and differential cryptanalysis. Secondly, we properly present a new definition of the Best Affine Approximation, namely BAA on the Boolean vector functions, followed by the spectral characteristic of such defined BAA attacks through using the decomposition formula of the union distribution for random variables. A lower bound of such BAA attacks is proposed. Finally, we also study the spectral characteristic of the second kind of nonlinearity of Boolean vector functions, followed by a higher bound of such nonlinearity. Furthermore, the limited relationship between the second kind of nonlinearity of Boolean vector functions and the linear structure of the linear combination of every component is analyzed.