Quantum secure non-malleable-extractors
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866910602702618624 |
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| author | Boddu, Naresh Goud Jain, Rahul Kapshikar, Upendra |
| author_facet | Boddu, Naresh Goud Jain, Rahul Kapshikar, Upendra |
| contents | We construct several explicit quantum secure non-malleable-extractors. All the quantum secure non-malleable-extractors we construct are based on the constructions by Chattopadhyay, Goyal and Li [2015] and Cohen [2015].
1) We construct the first explicit quantum secure non-malleable-extractor for (source) min-entropy $k \geq \textsf{poly}\left(\log \left( \frac{n}ε \right)\right)$ ($n$ is the length of the source and $ε$ is the error parameter). Previously Aggarwal, Chung, Lin, and Vidick [2019] have shown that the inner-product based non-malleable-extractor proposed by Li [2012] is quantum secure, however it required linear (in $n$) min-entropy and seed length.
Using the connection between non-malleable-extractors and privacy amplification (established first in the quantum setting by Cohen and Vidick [2017]), we get a $2$-round privacy amplification protocol that is secure against active quantum adversaries with communication $\textsf{poly}\left(\log \left( \frac{n}ε \right)\right)$, exponentially improving upon the linear communication required by the protocol due to [2019].
2) We construct an explicit quantum secure $2$-source non-malleable-extractor for min-entropy $k \geq n- n^{Ω(1)}$, with an output of size $n^{Ω(1)}$ and error $2^{- n^{Ω(1)}}$.
3) We also study their natural extensions when the tampering of the inputs is performed $t$-times. We construct explicit quantum secure $t$-non-malleable-extractors for both seeded ($t=d^{Ω(1)}$) as well as $2$-source case ($t=n^{Ω(1)}$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_03097 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Quantum secure non-malleable-extractors Boddu, Naresh Goud Jain, Rahul Kapshikar, Upendra Cryptography and Security Quantum Physics We construct several explicit quantum secure non-malleable-extractors. All the quantum secure non-malleable-extractors we construct are based on the constructions by Chattopadhyay, Goyal and Li [2015] and Cohen [2015]. 1) We construct the first explicit quantum secure non-malleable-extractor for (source) min-entropy $k \geq \textsf{poly}\left(\log \left( \frac{n}ε \right)\right)$ ($n$ is the length of the source and $ε$ is the error parameter). Previously Aggarwal, Chung, Lin, and Vidick [2019] have shown that the inner-product based non-malleable-extractor proposed by Li [2012] is quantum secure, however it required linear (in $n$) min-entropy and seed length. Using the connection between non-malleable-extractors and privacy amplification (established first in the quantum setting by Cohen and Vidick [2017]), we get a $2$-round privacy amplification protocol that is secure against active quantum adversaries with communication $\textsf{poly}\left(\log \left( \frac{n}ε \right)\right)$, exponentially improving upon the linear communication required by the protocol due to [2019]. 2) We construct an explicit quantum secure $2$-source non-malleable-extractor for min-entropy $k \geq n- n^{Ω(1)}$, with an output of size $n^{Ω(1)}$ and error $2^{- n^{Ω(1)}}$. 3) We also study their natural extensions when the tampering of the inputs is performed $t$-times. We construct explicit quantum secure $t$-non-malleable-extractors for both seeded ($t=d^{Ω(1)}$) as well as $2$-source case ($t=n^{Ω(1)}$). |
| title | Quantum secure non-malleable-extractors |
| topic | Cryptography and Security Quantum Physics |
| url | https://arxiv.org/abs/2109.03097 |