Correlation Analysis With Memory Nonlinear Combination Generator

In this paper, we study the correlation properties with the theory of probability and spectrum for non-linear combiners with memory. Concerning the multi-valued combiners with only 1 digit memory, we firstly analyze the probability distributions of its sequences, then investigate its properties of correlation coefficients and correlation immunity, and finally construct a kind of combiners with 1 digit memory with good cryptographic properties. In regard to the bluetooth combiner, we study the probability distributions between its output and input sequences, with which we analyze its correlation immunity, introduce two representative attack methods and give a whole evaluation on the security of bluetooth combiner.