An efficient construction of Raz's two-source randomness extractor with improved parameters
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918062989508608 |
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| author | Foreman, Cameron Wooltorton, Lewis Milner, Kevin Curchod, Florian J. |
| author_facet | Foreman, Cameron Wooltorton, Lewis Milner, Kevin Curchod, Florian J. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15547 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An efficient construction of Raz's two-source randomness extractor with improved parameters Foreman, Cameron Wooltorton, Lewis Milner, Kevin Curchod, Florian J. Cryptography and Security Computational Complexity Quantum Physics 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. |
| title | An efficient construction of Raz's two-source randomness extractor with improved parameters |
| topic | Cryptography and Security Computational Complexity Quantum Physics |
| url | https://arxiv.org/abs/2506.15547 |