arXiv 1802.051452018-02cs.CR

具有小块大小的次对数分布不经意RAM

Sub-logarithmic Distributed Oblivious RAM with Small Block Size

Eyal Kushilevitz, Tamer Mour

摘要：

不经意RAM（ORAM）是一种加密原语，允许客户端对存储在不受信任的服务器中的数据安全地执行RAM程序。分布式不经意RAM是ORAM的一种变体，其中数据存储在$m>1$服务器中。过去几十年的广泛研究已经成功地减少了ORAM方案的带宽开销，无论是在单服务器还是多服务器设置中，从$O(\sqrt{N})$到$O(1)$。然而，实现亚对数开销的所有已知协议要么需要繁重的服务器侧计算（例如，同态加密），要么需要至少$Ω(\log^3 N)$的大块大小。在本文中，我们提出了一个家庭的分布式ORAM结构，遵循层次的方法Goldreich和Ostrovsky [GO 96]。我们增强了已知的技术，并开发了新的技术，以更好地利用多个服务器的存在。通过在我们的构造中插入有效的已知散列方案，我们得到以下结果：1。对于任何$m\geq 2$，我们展示了一个$m$ -服务器ORAM方案，其中包含$O(\log N/\log\log N)$开销和块大小$Ω(\log^2 N)$。该方案即使在$(m-1)$ -服务器共谋的情况下也是私有的。2.具有$O(ω(1)\log N/\log\log N)$开销和块大小几乎为对数的3服务器ORAM结构，即$Ω(\log^{1+ε}N)$。我们还研究了一个模型，其中的服务器被允许执行线性量的轻本地计算，并表明，恒定的开销是可以实现的，在这个模型中，通过一个简单的四服务器ORAM协议。

英文摘要：

Oblivious RAM (ORAM) is a cryptographic primitive that allows a client to securely execute RAM programs over data that is stored in an untrusted server. Distributed Oblivious RAM is a variant of ORAM, where the data is stored in $m>1$ servers. Extensive research over the last few decades have succeeded to reduce the bandwidth overhead of ORAM schemes, both in the single-server and the multi-server setting, from $O(\sqrt{N})$ to $O(1)$. However, all known protocols that achieve a sub-logarithmic overhead either require heavy server-side computation (e.g. homomorphic encryption), or a large block size of at least $Ω(\log^3 N)$. In this paper, we present a family of distributed ORAM constructions that follow the hierarchical approach of Goldreich and Ostrovsky [GO96]. We enhance known techniques, and develop new ones, to take better advantage of the existence of multiple servers. By plugging efficient known hashing schemes in our constructions, we get the following results: 1. For any $m\geq 2$, we show an $m$-server ORAM scheme with $O(\log N/\log\log N)$ overhead, and block size $Ω(\log^2 N)$. This scheme is private even against an $(m-1)$-server collusion. 2. A 3-server ORAM construction with $O(ω(1)\log N/\log\log N)$ overhead and a block size almost logarithmic, i.e. $Ω(\log^{1+ε}N)$. We also investigate a model where the servers are allowed to perform a linear amount of light local computations, and show that constant overhead is achievable in this model, through a simple four-server ORAM protocol.

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。

摘要：

英文摘要：

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