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.

翻译：均衡分布是衡量线性伪随机数生成器均匀性的理论质量标准。本文首先指出现有基于线性元胞自动机的伪随机数生成器在均衡分布特性上存在显著不足。随后我们提出一系列采用时间间隔(2≤s≤10)的轻量级组合型元胞自动机伪随机数生成器,其使用次数为31≤k≤128(接近计算机字长)的线性最大长度元胞自动机。研究表明,这些生成器既能实现最大周期,又能满足最大均衡分布特性。最后,实验证明这些基于组合型最大长度元胞自动机的伪随机数生成器能通过几乎所有经验性测试基准,其运行速度和性能与梅森旋转算法相当。