中文摘要：

基于费马商和欧拉商构造的伪随机序列均具有良好的密码学性质.本文基于有限域理论及定义对思想,确定了基于欧拉商的二元序列的定义对,并由此出发得到该序列的迹函数表示,从而确定了序列的线性复杂度.所给序列的迹函数表示为分析序列的伪随机性质提供了新的工具.

英文摘要：

Families of pseudorandom sequences derived from Fermat quotients and Euler quotients possess good cryptographic properties. In this paper, based on the theory of finite fields and defining pairs, the defining pairs of binary sequence based on Euler quotient are determined firstly, and then from which the sequences＇ trace representation is obtained. Finally the linear complexity of the sequence is given. The trace representation can provide a new tool for analyzing other pseudorandom properties of the sequence.