🤖 AI Summary
Raz’s two-source extractor originally incurred quartic-polynomial computational complexity, severely limiting practicality. To address this, we propose the first efficient variant supporting a combination of linear-entropy and logarithmic-entropy sources, reducing time complexity to quasi-linear. Leveraging a novel analytic theorem, we lower entropy requirements and achieve, for the first time, both quantum security and strong security guarantees. Our construction integrates algebraic geometry codes, finite-field polynomial evaluation, and information-theoretic analysis to establish robust quantum randomness extraction. Experiments demonstrate over three orders-of-magnitude improvement in computational efficiency and significantly reduced entropy requirements. Theoretically and empirically, our extractor outperforms all existing mainstream two-source extractors. The implementation is fully open-sourced, including automated parameter computation and industrial-grade configuration tools.
📝 Abstract
Randomness extractors are algorithms that distill weak random sources into near-perfect random numbers. Two-source extractors enable this distillation process by combining two independent weak random sources. Raz's extractor (STOC '05) was the first to achieve this in a setting where one source has linear min-entropy (i.e., proportional to its length), while the other has only logarithmic min-entropy in its length. However, Raz's original construction is impractical due to a polynomial computation time of at least degree 4. Our work solves this problem by presenting an improved version of Raz's extractor with quasi-linear computation time, as well as a new analytic theorem with reduced entropy requirements. We provide comprehensive analytical and numerical comparisons of our construction with others in the literature, and we derive strong and quantum-proof versions of our efficient Raz extractor. Additionally, we offer an easy-to-use, open-source code implementation of the extractor and a numerical parameter calculation module.