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伪随机序列在保密通信、扩频通信和码分多址通信系统中具有广泛的应用,常用来作为保密通信中的密钥流序列、扩频通信中的扩展频谱序列和码分多址通信系统中地址序列。在流密码的设计理论中,需要在严格的数学框架内使用复杂性度量方法来判断密钥流的不可预测性,也就是由特定加密系统所能提供的安全级别,最重要的度量标准是线性复杂度,线性复杂度是指生成作为密钥流序列的最短的LFSR的长度。本文研究了一类使用迹函数构造的p元d型序列的线性复杂度,给出了在特定条件下这类序列的线性复杂度的上界,并构造了线性复杂度达到上界的d型序列,从而表明这个上界是紧的。
Pseudo-random sequences are widely used in secure communication, spread spectrum communication and code division multiple access communication systems. They are often used as key stream sequences in secure communication, spread spectrum sequences in spread spectrum communication and code division multiple access communication systems Middle address sequence. In the design theory of streaming cipher, complexity measure method is needed to judge the unpredictability of key stream in strict mathematical framework, that is, the security level provided by a particular cipher system. The most important metric is linear Complexity, linear complexity refers to the length of the shortest LFSR that is generated as a keystream sequence. In this paper, the linear complexity of a class of p-type d-type sequences constructed by using trace function is studied. The upper bound of the linear complexity of such sequences under given conditions is given and the d-type whose linear complexity reaches the upper bound Sequence, indicating that the upper bound is tight.