arXiv 2109.030972021-09cs.CRquant-ph

量子安全的不可伪造提取器（non-malleable-extractors）

Quantum secure non-malleable-extractors

Naresh Goud Boddu, Rahul Jain, Upendra Kapshikar

AI总结：

该研究基于已有构造方案提出多种量子安全不可伪造提取器，在低最小熵、2信源及多轮篡改场景下实现突破，并据此得到通信复杂度指数级降低的2轮抗主动量子敌手隐私放大协议。

摘要：

我们构建了若干显式的量子安全不可伪造提取器（quantum secure non-malleable-extractors）。所有我们构建的量子安全不可伪造提取器均基于Chattopadhyay、Goyal与Li [2015]以及Cohen [2015]的构造方案。\n1) 我们构建了首个适用于（信源）最小熵$k \geq \textsf{poly}\left(\log \left( \frac{n}ε \right)\right)$的显式量子安全不可伪造提取器（其中$n$为信源长度，$ε$为误差参数）。此前Aggarwal、Chung、Lin与Vidick [2019]已证明Li [2012]提出的基于内积的不可伪造提取器具备量子安全性，但该方案要求最小熵与种子长度均为$n$的线性量级。\n借助不可伪造提取器与隐私放大之间的关联（该关联在量子场景下由Cohen与Vidick [2017]首次确立），我们得到了一种可抵御主动量子敌手的2轮隐私放大协议，其通信复杂度为$\textsf{poly}\left(\log \left( \frac{n}ε \right)\right)$，较[2019]方案所需的线性通信量实现了指数级提升。\n2) 我们构建了一种显式量子安全2信源不可伪造提取器，适用于最小熵$k \geq n- n^{Ω(1)}$的场景，输出大小为$n^{Ω(1)}$，误差为$2^{- n^{Ω(1)}}$。\n3) 我们还研究了当输入被篡改$t$次时这类提取器的自然扩展形式，分别为带种子场景（$t=d^{Ω(1)}$）和2信源场景（$t=n^{Ω(1)}$）构建了显式量子安全$t$-不可伪造提取器。

英文摘要：

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 ($t=n^{Ω(1)}$).

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

AI总结：

摘要：

英文摘要：

相关论文