Pseudorandomness and Dynamics of Fermat Quotients
Pseudorandomness and Dynamics of Fermat Quotients
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DOI：
10.1137/100798466
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发表时间：
2010-01
期刊：
影响因子：
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通讯作者：
Alina Ostafe;I. Shparlinski
中科院分区：
文献类型：
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作者：
Alina Ostafe;I. Shparlinski
我们获得了一些有关动态系统的各种属性，图像分布，周期长度的数量（图像分布的数量）自然与Fermat商相关的动力学系统的一些理论和实验结果。特别是，我们改善了Vandiver的局部[Bull。阿米尔。数学。 Soc。，22（1915），pp。61-67]关于上述FERMAT商的图像大小（从$ P^{1/2} -1 $到$（1+O（1））P（ \ log p）^{ - 2} $）。我们还考虑了Fermat商的伪特性，例如均匀分布和线性复杂性。
We obtain some theoretical and experimental results concerning various properties (the number of fixed points, image distribution, cycle lengths) of the dynamical system naturally associated with Fermat quotients acting on the set $\{0,\dots,p-1\}$. In particular, we improve the lower bound of Vandiver [Bull. Amer. Math. Soc., 22 (1915), pp. 61-67] on the image size of Fermat quotients on the above set (from $p^{1/2}-1$ to $(1+o(1))p(\log p)^{-2}$). We also consider pseudorandom properties of Fermat quotients such as uniform distribution and linear complexity.