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在流密码的设计中,通常要用一个随机源。常用线性反馈移位寄存器作为随机源。在Klimov A和Shamir A提出单圈T函数的概念后,许多学者在设计流密码时用单圈T函数作为随机源。为了得到新的随机源,单圈T函数的概念被扩展,单圈函数和单圈函数序列的概念被定义,单圈函数序列的最小周期被计算,有限域上分圆多项式的表达式被给出,与分圆多项式相关的两个定理被介绍。以这两个定理为基础,单圈函数序列的线性复杂度的下界被推导,猜测在许多情况下,单圈函数序列的线性复杂度远远大于这个下界。
In the design of streaming cipher, it is usually to use a random source. Common linear feedback shift register as a random source. After Klimov A and Shamir A proposed the concept of a lap T function, many scholars used a lap T function as a random source in the design of the stream cipher. In order to obtain a new random source, the concept of a single-turn T function is extended. The concepts of the single-turn function and the single-turn function sequence are defined. The minimum period of the single-turn function sequence is calculated. The expression of the circular polynomial on the finite field is given Out, the two theorems related to the circular polynomials are introduced. Based on these two theorems, the lower bound of the linear complexity of a single lap function sequence is derived, and it is suspected that in many cases the linear complexity of a single lap function sequence is much larger than this lower bound.