基于Kolmogorov复杂度和列表译码的存储增强
Storage Enforcement with Kolmogorov Complexity and List Decoding
摘要：
我们考虑在外包存储中出现的以下问题：用户将其数据$x$存储在远程服务器上，但希望在以后的某个时间点审计服务器，以确保它确实存储了$x$。目标是设计一个（随机化）验证协议，该协议具有以下属性：如果服务器以某种合理的高概率通过验证，则用户可以放心服务器正在存储$x$。在这项工作中，我们提出了一个最佳的解决方案（在用户的存储和通信方面），而在同一时间，确保服务器，通过验证协议与任何合理的概率将存储，在一个小的\textit{additive}因素，$C(x)$位的信息，其中$C(x)$是平原柯尔莫哥洛夫复杂性的$x$。（由于我们无法阻止服务器压缩$x$，因此$C(x)$是自然的上限。）我们的协议的安全性证明结合了Kolmogorov复杂性与列表解码，不像以前的工作，依赖于密码学的假设，我们允许服务器有无限的计算能力。据我们所知，这是第一个工作，结合柯尔莫哥洛夫复杂性和列表解码。我们的框架是通用的，足以捕捉扩展，用户分裂的$x$和存储片段跨多个服务器和我们的验证协议可以处理非响应服务器和串通服务器。作为一个副产品，我们也得到了可检索性的证明。最后，我们的研究结果也有一个应用程序中的“存储执法”计划，这反过来又有一个应用程序，试图更新一个远程服务器，这是潜在的感染病毒。
英文摘要：
We consider the following problem that arises in outsourced storage: a user stores her data $x$ on a remote server but wants to audit the server at some later point to make sure it actually did store $x$. The goal is to design a (randomized) verification protocol that has the property that if the server passes the verification with some reasonably high probability then the user can rest assured that the server is storing $x$. In this work we present an optimal solution (in terms of the user's storage and communication) while at the same time ensuring that a server that passes the verification protocol with any reasonable probability will store, to within a small \textit{additive} factor, $C(x)$ bits of information, where $C(x)$ is the plain Kolmogorov complexity of $x$. (Since we cannot prevent the server from compressing $x$, $C(x)$ is a natural upper bound.) The proof of security of our protocol combines Kolmogorov complexity with list decoding and unlike previous work that relies upon cryptographic assumptions, we allow the server to have unlimited computational power. To the best of our knowledge, this is the first work that combines Kolmogorov complexity and list decoding. Our framework is general enough to capture extensions where the user splits up $x$ and stores the fragment across multiple servers and our verification protocol can handle non-responsive servers and colluding servers. As a by-product, we also get a proof of retrievability. Finally, our results also have an application in `storage enforcement' schemes, which in turn have an application in trying to update a remote server that is potentially infected with a virus.
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。
