Cellular Automata based Resource Efficient Maximally Equidistributed Pseudo-Random Number Generators
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910060790153216 |
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| author | A, Bhuvaneswari Bhattacharjee, Kamalika |
| author_facet | A, Bhuvaneswari Bhattacharjee, Kamalika |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19656 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cellular Automata based Resource Efficient Maximally Equidistributed Pseudo-Random Number Generators A, Bhuvaneswari Bhattacharjee, Kamalika Cryptography and Security Formal Languages and Automata Theory Mathematical Software 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. |
| title | Cellular Automata based Resource Efficient Maximally Equidistributed Pseudo-Random Number Generators |
| topic | Cryptography and Security Formal Languages and Automata Theory Mathematical Software |
| url | https://arxiv.org/abs/2603.19656 |