Trace Representation Of Two Classes Of Sequences Derived From Fermat Quotients

Pseudorandom sequences play an important role in cryptography,and are widely used in simulation、ranging system、spread spectrum communication system,radar navigation system,especially in stream cipher systems.Many literatures indicate that families of the pseudorandom sequences derived from Fermat quotients and Euler quotients possess sound cryptographic properties.The trace function,as a linear transform from an extension field to its base field,is not only a method to study the sequences generation on the finite field,but also one of the effective tools to research the properties of the periodic sequences on the field.In this paper,we will focus on investigating the trace representation of two classes of sequences derived from Fermat quotients and Euler quotients.The main results obtained are as follows:1.Based on the theory of finite field and defining pairs,firstly,we examine the defining pairs of the sequence over F2 constructed by Ye et al.,and then from which the sequences' trace representation is determined.Finally we obtain the linear complexity of the sequence.2.Based on the theory of coset,we determine the discrete Fourier transform(DFT)of the r-ary sequences over Fr(r>2 is prime)derived from Fermat quo-tients constructed by Du et al.,and then from which we obtain the sequences-trace representation,Our results provide the theoretics basis for the analysis of the se-quences'pseudorandom properties.