An efficient construction of Raz's two-source randomness extractor with improved parameters
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.