论文标题
关于循环多项式和线性反馈转移寄存器的注释
A note on cyclotomic polynomials and Linear Feedback Shift Registers
论文作者
论文摘要
线性反馈移位寄存器（LFRS）是在许多不同上下文中通常使用的工具，例如，作为伪随机数生成器。在本文中，我们表征具有某些对称特性的LFR。与这个问题有关，我们还对n的多项式f进行了分类，即满足属性，如果a是f的根，则$ f（a^n）= 0 $。分类在很大程度上取决于多项式系数的磁场的选择；我们考虑$ k = \ mathbb {f} _p $和$ k = \ mathbb {q} $。
Linear Feedback Shift Registers (LFRS) are tools commonly used in cryptography in many different context, for example as pseudo-random numbers generators. In this paper we characterize LFRS with certain symmetry properties. Related to this question we also classify polynomials f of degree n satisfying the property that if a is a root of f then $f(a^n)=0$. The classification heavily depends on the choice of the fields of coefficients of the polynomial; we consider the cases $K=\mathbb{F}_p$ and $K=\mathbb{Q}$.
