More Efficient $k$-wise Independent Permutations from Random Reversible Circuits via log-Sobolev Inequalities
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909223002046464 |
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| author | Gretta, Lucas He, William Pelecanos, Angelos |
| author_facet | Gretta, Lucas He, William Pelecanos, Angelos |
| contents | We prove that the permutation computed by a reversible circuit with $\tilde{O}(nk\cdot \log(1/\varepsilon))$ random $3$-bit gates is $\varepsilon$-approximately $k$-wise independent. Our bound improves on currently known bounds in the regime when the approximation error $\varepsilon$ is not too small. We obtain our results by analyzing the log-Sobolev constants of appropriate Markov chains rather than their spectral gaps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08499 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | More Efficient $k$-wise Independent Permutations from Random Reversible Circuits via log-Sobolev Inequalities Gretta, Lucas He, William Pelecanos, Angelos Computational Complexity Cryptography and Security We prove that the permutation computed by a reversible circuit with $\tilde{O}(nk\cdot \log(1/\varepsilon))$ random $3$-bit gates is $\varepsilon$-approximately $k$-wise independent. Our bound improves on currently known bounds in the regime when the approximation error $\varepsilon$ is not too small. We obtain our results by analyzing the log-Sobolev constants of appropriate Markov chains rather than their spectral gaps. |
| title | More Efficient $k$-wise Independent Permutations from Random Reversible Circuits via log-Sobolev Inequalities |
| topic | Computational Complexity Cryptography and Security |
| url | https://arxiv.org/abs/2406.08499 |