耗散动力系统在伪随机数生成中的应用：等分布性和距离为网格尺寸对数的比特的统计独立性
Applying dissipative dynamical systems to pseudorandom number generation: Equidistribution property and statistical independence of bits at distances up to logarithm of mesh size
摘要：
在离散格点上研究了二维环面变换的一类耗散动力系统的行为，并与环面的保守双曲自同构的行为进行了比较.应用耗散动力系统产生的伪随机数是有利的，可以实现的比特序列的概率的均匀分布。提出了一种新的产生均匀伪随机数的算法。的理论的生成器，其中包括周期性的属性和统计独立的位在距离的网格大小的对数的证明，提出。使用可用的测试包进行的广泛的统计测试表明了出色的结果，而发电机的速度与其他现代发电机相当。
英文摘要：
The behavior of a family of dissipative dynamical systems representing transformations of two-dimensional torus is studied on a discrete lattice and compared with that of conservative hyperbolic automorphisms of the torus. Applying dissipative dynamical systems to generation of pseudorandom numbers is shown to be advantageous and equidistribution of probabilities for the sequences of bits can be achieved. A new algorithm for generating uniform pseudorandom numbers is proposed. The theory of the generator, which includes proofs of periodic properties and of statistical independence of bits at distances up to logarithm of mesh size, is presented. Extensive statistical testing using available test packages demonstrates excellent results, while the speed of the generator is comparable to other modern generators.
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