arXiv 0911.46802009-11quant-ph

量子存储的近优提取器

Near-optimal extractors against quantum storage

Anindya De, Thomas Vidick

备注：: Some typos fixed.

摘要：

我们证明了Trevisan的提取器及其变体\cite{T99,RRV99}对有界量子存储对手是安全的。一个实例给出了第一个这样的提取器以实现输出长度$Θ(K-b)$，其中$K$是源的熵，而$b$是对手的存储，以及多对数种子长度。另一个实例实现了对数密钥长度，对于任何$γ>0$，输出长度$Θ((K-b)/K^γ)$都稍小。相比之下，以前最好的构造\cite{TS09}只能提取$(K/b)^{1/15}$比特。我们的一些构造具有额外的优点，即输出的每一位都是来自源的多对数位数的函数，这对于某些加密应用至关重要。我们的论点是基于量子随机存取码的推广，我们称之为\emph{quantum functional access codes}的界限。这是至关重要的，因为它使我们避免了\cite{TS09}中方法的核心局部列表解码算法，该算法是乘法开销的来源。

英文摘要：

We show that Trevisan's extractor and its variants \cite{T99,RRV99} are secure against bounded quantum storage adversaries. One instantiation gives the first such extractor to achieve an output length $Θ(K-b)$, where $K$ is the source's entropy and $b$ the adversary's storage, together with a poly-logarithmic seed length. Another instantiation achieves a logarithmic key length, with a slightly smaller output length $Θ((K-b)/K^γ)$ for any $γ>0$. In contrast, the previous best construction \cite{TS09} could only extract $(K/b)^{1/15}$ bits. Some of our constructions have the additional advantage that every bit of the output is a function of only a polylogarithmic number of bits from the source, which is crucial for some cryptographic applications. Our argument is based on bounds for a generalization of quantum random access codes, which we call \emph{quantum functional access codes}. This is crucial as it lets us avoid the local list-decoding algorithm central to the approach in \cite{TS09}, which was the source of the multiplicative overhead.

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摘要：

英文摘要：

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