Cellular Automata based Resource Efficient Maximally Equidistributed Pseudo-Random Number Generators
This work addresses the need for resource-efficient and high-quality PRNGs in applications requiring uniform randomness, though it appears incremental as it builds on existing CA-based methods.
The paper tackled the problem of weak equidistribution in existing linear cellular automaton-based pseudo-random number generators (PRNGs) by proposing new combined CA-based PRNGs that achieve maximal period and satisfy maximal equidistribution, with performance comparable to the Mersenne Twister.
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.