Catalytic-Logspace PRGs from Reversible Cellular Automata

Design pseudorandom generators whose state evolution is governed by reversible cellular automata with local update rules, enabling the generator to use only tiny extra workspace and restore its catalytic memory, consistent with the catalytic space paradigm. Prove indistinguishability against classes such as read-once branching programs and permutation branching programs, and immunize against Hamming-weight–based tests using small-bias weight (anti-)concentration techniques. This approach leverages reversible CA dynamics, indistinguishability analyses, and controlled weight distributions to thwart weight-sensitive distinguishers. It addresses the minimal-memory derandomization frontier and the need for targeted PRGs in catalytic logspace. Reversible CA are highly local and hardware-friendly, making them attractive for constrained platforms like IoT devices with tight memory and energy constraints. The impact is a new family of provable, low-footprint PRGs with both theoretical interest in targeted/catalytic derandomization and practical relevance for secure lightweight devices and streaming.

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