Analysis And Application Of Nonlinear Combination Sequence

Nonlinear combined sequences as a kind of the important key sequence generators,its design and analysis are always hotspot and difficulty of stream cipher. Linear approaching analysis and correlation analysis are the two most important and effective methods which attack the nonlinear combined stream cipher.The paper discusses research actuality of nonlinear combining sequences at present. We present a new method which can break some nonlinear combined sequences. The basic idea is to solve a series of equations by calculating the maximum Walsh spectra of a Boolean function attained by the recurrence relation of the linear feedback shift register (LFSR). The method extreamely utilizes the linear relationship between the output and input sequences, and the original state of LFSR can be attained directly. We consider a plaintext being encrypted by a nonlinear combined sequence. By surveying the differential properties of the plaintext and the ciphertext, we give out a kind of differential probability of the ciphertext and find a weak difference between the right and wrong original state of LFSR. Finally, an algorithm is described to attack the nonlinear combined stream cipher system.As a special kind of nonlinear combined sequences, we consider a type of filter generators. For these filter generators, the input bits of the filter functions is less than the degree of the LFSRs. According to the particularities of this kind of filter generators and the properties of the LFSRs, we construct an equivalent system. By analyzing the relationship between the input states of the filter function and the states of the LFSR in the equivalent system, we get numbers of linear equations to attack this kind of filter generators.