The Study Of Cryptographic Characters Of Sequences Generated By Trace Function On Finite Field

Applied widely in the data encryption, pseudorandom sequences can be generated not only by hardware (shift register) but also by trace function, and it is found that the sequences generated by trace function are much better than those generated by hardware, especially in the aspects of correlation properties. In recent years, the trace function, as a linear transform from an extension victor space to its basic victor space, has been comprehensively employed to do researches concerning the algebra construction of finite field and the property of sequences. It has been proved to be a powerful tool to study the sequence cipher by numerous documents.By using the properties of trace function, the cryptographic characters of GMW sequences, Cascaded GMW sequences, No sequences and Kasami sequences are discussed in this thesis. All these characters include the periodic of sequence, the trinomial property, periodic correlation function and so on. Based on these characters, all those sequences mentioned above are proved to have regular trinomial pairs. Furthermore, the cross-correlation values and the distribution of these correlation values of these sequences are presented.The linear complexity of periodic sequence is an important index to depict the security of the sequence cipher. Based on discussing the properties of the Hasse derivative and the Hasse matrix, this thesis presents a recursive expression of Hasse matrix, the relation between the Hasse modular matrix and the linear complexity of periodic sequence, and another deduction of the Games-Chan algorithm on the finite field of characteristic p on which base another extension are given additionally.