Structure of Pseudorandom Numbers Derived from Fermat Quotients
Structure of Pseudorandom Numbers Derived from Fermat Quotients
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DOI：
10.1007/978-3-642-13797-6_6
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发表时间：
2010-06
影响因子：
2
通讯作者：
Zhixiong Chen;Alina Ostafe;Arne Winterhof
中科院分区：
文献类型：
--
作者：
Zhixiong Chen;Alina Ostafe;Arne Winterhof
研究了模为任意滞后的费马商的三维点的分布。如果没有滞后重合，则采用与文献[21]中相同的方法进行模运算。然而，在另一个案例中有一些有趣的转折。我们证明了一个差异界，它是无条件的，并且需要对s>； 2的滞后进行限制。利用这个界，我们得到了由费马商导出的二元门限序列的伪随机性的结果，这些结果都是由Mauduit和S提出的关于二阶均匀分布测度和相关测度的界的。我们还证明了它的线性复杂性分布的一个下界。这些证明是基于指数和的界，以及Mauduit，Niederreiter和S所证明的上述两个度量与偏差之间的早期关系。此外，我们还分析了任意滞后模费马商的格结构。
We study the distribution ofs-dimensional points of Fermat quotients modulopwith arbitrary lags. If no lags coincide modulopthe same technique as in [21] works. However, there are some interesting twists in the other case. We prove a discrepancy bound which is unconditional fors= 2 and needs restrictions on the lags fors> 2. We apply this bound to derive results on the pseudorandomness of the binary threshold sequence derived from Fermat quotients in terms of bounds on the well-distribution measure and the correlation measure of order 2, both introduced by Mauduit and Sárközy. We also prove a lower bound on its linear complexity profile. The proofs are based on bounds on exponential sums and earlier relations between discrepancy and both measures above shown by Mauduit, Niederreiter and Sárközy. Moreover, we analyze the lattice structure of Fermat quotients modulopwith arbitrary lags.