This paper discusses the cryptographical characteristic of output sequence of the additive combined generator,and points out the Output sequence has long period,large linear complexities,correlation-immunity,strong auto correlation and weak cross correlation.

This paper discusses the cryptographical characteristic of output sequence of the generator,points out that the Output sequence has long period,large linear complexities,correlation-immunity,strong auto correlation and weak cross correlation.

First, this paper gives non-linearity and balanced correlation-immunity of Bent functions and non-repeated homogeneous functions with k degree respectively; second, deeply studies the applications of the two kinds of functions in constructing nonlinear combining functions.

The necessary and sufficient conditions of balanced ,correlation-immune and propagating partially-Bent functions are presented respectively, the nonlinear degree of partially-Bent functions and the equivalent probability of a partially-Bent function and an affine function are given in the paper.

The cryptographic properties of the k -order quasi-Bent functions, such as balancedness, correlation immunity, propagation criterion and the highest algebraic degree can all be easily decided only by the distributions of 0 and 1 in the character matrix, which is different from the spectrum method and the auto-correlation method.

Both balancedness and correlation immunity is one of the most important cryptographic characteristics of a Boolean function to which have gotten many researches respectively.

The relation between combining design and correlation immunity is discussed.

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