Abstract

Linear congruential method was one of the first one proposed to generate pseudorandom numbers. However, due to drawbacks arising from linearity nonlinear methods of generating pseudorandom numbers were proposed; however, these methods were mostly nonlinear recurrences of rank 1, i.e., iterations of a univariate map. In this paper we propose a generator which is a recurrence of order \(k\) based on 2-adic 1-Lipschitz bijective functions and find conditions under which generator produces sequences with the period of \(k2^{t}\) of uniformly distributed numbers modulo \(2^{t}\).

中文翻译：

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$$2$$ -基于 Adic 1-Lipschitz 图的具有最长周期的任意阶非线性伪随机生成器

摘要

线性同余方法是最早提出的生成伪随机数的方法之一。然而，由于线性产生的缺点，提出了生成伪随机数的非线性方法；然而，这些方法大多是 1 阶的非线性递归，即单变量映射的迭代。在本文中，我们提出了一种基于 2-adic 1-Lipschitz 双射函数的阶\(k\)递推生成器，并找到生成器生成周期为 \(k2^{t}\) 的序列的条件均匀分布的数字模\(2^{t}\)。