基于细胞自动机的资源高效最大等分布伪随机数生成器
Cellular Automata based Resource Efficient Maximally Equidistributed Pseudo-Random Number Generators
AI总结：
本文提出轻量级组合细胞自动机伪随机数生成器，通过时间间隔和最大长度细胞自动机实现最大周期和等分布特性，性能接近梅尔斯enne扭振器。
摘要：
等分布是衡量线性伪随机数生成器均匀性的理论标准。本文首先证明现有所有线性细胞自动机基于伪随机数生成器在等分布特性上较弱。然后提出一组轻量级组合细胞自动机基于伪随机数生成器，使用线性最大长度细胞自动机（度数31≤k≤128，接近计算机字长）和时间间隔（2≤s≤10）。证明这些生成器实现最大周期并满足最大等分布属性。最后证明这些组合最大长度细胞自动机基于伪随机数生成器通过几乎所有经验测试集，速度和性能与梅尔斯enne扭振器相当。
英文摘要：
An equidistribution is a theoretical quality criteria that measures the uniformity of a linear pseudo-random number generator (PRNG). In this work, we first show that all existing linear cellular automaton (CA) based pseudo-random number generators (PRNGs) are weak in the equidistribution characteristic. Then we propose a list of light-weight combined CA-based PRNGs with time spacing ($2 \leq s \leq 10$) using linear maximal length cellular automata of degree $31 \leq k \leq 128$ (close to computer word size). We show that these PRNGs achieve maximal period as well as satisfy the maximal equidistribution property. Finally, we show that these combined maximal length CA-based PRNGs pass almost all the empirical testbeds, with speed and performance comparable to the Mersenne Twister.
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