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

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.

@article{foreman2025_2506.15547,
  title={ An efficient construction of Raz's two-source randomness extractor with improved parameters },
  author={ Cameron Foreman and Lewis Wooltorton and Kevin Milner and Florian J. Curchod },
  journal={arXiv preprint arXiv:2506.15547},
  year={ 2025 }
}