Study On Correlation Property Of Sequence Cipher

Pseudorandom sequences, applied widely in the data encryption, Spread Spectrum Communication and CDMA Communication System, not only can be generated by hardware (shift register) but also by trace function. And it is found that the sequences generated by trace function are much better than by hardware, especially in the aspects of correlation properties. Auto-correlation function of the most of the pseudorandom sequences has been resolved preferably, but cross-correlation function doesn't give a complete description. For example, cross-correlation function of m sequences hasn't been fully resolved. So it restricts our application to the pseudorandom sequences. Correlation function is a important parameter to study the pseudorandom property of sequence cipher. So it is very important to study correlation property of sequence cipher for us.By using the theory and the method of Finite Field and Number, we discuss the correlation property of m sequences, logarithm sequences, GMW sequences, Cascaded GMW sequences, Kasami sequences, and No sequences, and get the auto-correlation of two classes of generalized Jacobi sequences and cross-correlation of some classes of m sequences and the relation of cross-correlation of one class of m sequences. Furthermore, we discuss the correlation values and the distribution of these correlation values of these sequences mentioned presented.