With Memory Nonlinear Combination Generator Probability Model And Correlation Analysis

In this paper, we build up a reasonable probabilistic model for the nonlinear combiner with memory and analyze its correlation properties with the theory of probability and spectrum. Concerning the combiner with only 1 bit memory, we firstly study the probability distributions of its sequences, then analyze its properties of conditional correlation and correlation immunity, and finally construct a kind of combiners with 1 bit memory with good cryptographic properties.In regard to the combiner with an arbitrary number of bits memory, we get the correlation coefficients between its output and input sequences, with which we analyze its correlation immunity, generalizing the situation of 1 bit memory. To resist "divide and conquer correlation attacks" based on the "linear sequential circuit approximation"(LSCA) method, the concept of l-grade and border correlation immunity is introduced. And it's shown that any grade and high order correlation-immune combimers with memory can be constructed with resilient functions. Finally, the "generalized conservation of energy conjecture" on combiners with an arbitrary number of bits memory is brought up, and a part proof is given.