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

TL;DR

This paper presents an improved, efficient version of Raz's two-source randomness extractor with quasi-linear runtime and reduced entropy requirements, along with practical implementation and quantum-proof features.

Contribution

It introduces a faster, more practical Raz's extractor with lower entropy thresholds and quantum-proof guarantees, plus open-source code for real-world use.

Findings

Achieved quasi-linear computation time for Raz's extractor

Reduced entropy requirements compared to previous constructions

Provided open-source implementation and quantum-proof variants

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.