Two Classes Of Trace Represention Of R-ary Sequences Derived From Euler Quotients

Pseudorandom sequences are widely used in ranging systems,spread spectrum communication and stream cipher,the construction of pseudorandom sequences with good properties and the analysis of the properties of existing sequences have become a research topic for scholars at home and abroad,expecially the emerging research on the cryptographic application of Fermat sequences in 2011.In recent years,the sequences are based on Euler quotients,as an extension of Fermat quotients function,have attracted many scholars because of their important roles in secret communica-tion,radar navigation and other fields.This paper is based on the study of the Fermat quotients sequences of the modulus an odd prime p,it mainly studies the function representation of two types of sequences by use of number theory and the theory of polynomial and trace function in finite fields,details as follows:(1).Let p be an odd prime,?? 1 be an arbitrary positive integer,an odd prime r|(p-1),the trace representation of r-ary sequences constructed by Euler quotients based on the power of modulus odd prime p? is studied.(2).Let p be an odd prime,?? 1 be an arbitrary positive integer,an odd prime r|(p-1).Firstly,a class of new r-ary sequences are constructed by Euler quotients of modulus 2p?.Secondly,the linear complexity of sequences is studied by utilizing polynomial decomposition theory over finite fields,the results show that the new sequence has good linear complexity and can resist the attack of B-M algorithm.Finally,the trace representation of the sequences has been presented.The trace representation that has been shown in the study,not only provides a theoretical basis for analyzing other pseudorandom properties of sequences,butalso has positive significance for the engineering realization of sequences.