arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1809.08263cs.ITmath.IT
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索引编码中的保密性:$k$ -有限访问方案

Privacy in Index Coding: $k$-Limited-Access Schemes

Mohammed Karmoose, Linqi Song, Martina Cardone, Christina Fragouli

摘要:

在传统的索引编码问题中,服务器采用编码将消息发送到同一广播域中的$n$客户端。每个客户端已经有一些消息作为边信息,并从服务器请求特定的未知消息。所有客户端都学习编码矩阵,以便他们可以解码和检索他们所请求的数据。我们最初的观察是,学习编码矩阵可能会带来隐私问题:它可能使客户端能够推断有关其他客户端的请求和辅助信息的信息。在本文中,我们通过允许每个客户端对编码矩阵的有限访问来减轻这种隐私问题。特别是,我们设计了编码矩阵,这样每个客户端只需要学习一些(而不是所有)行来解码她所请求的消息。通过两种不同的隐私指标,我们首先表明,这种方法确实提高了隐私的水平。基于此,我们提出了使用$k$有限访问方案:给定采用$T$传输的索引编码方案,我们创建了具有$T_k\geq T$传输的$k$有限访问方案,并且具有每个客户端最多需要$k$传输来解码她的消息的属性。我们推导出了$k$的所有值的$T_k$的上界和下界,并为这些方案开发了确定性设计,这些设计是通用的,即,与编码矩阵无关。我们证明了当$k$或$n$较大时,我们的方案是阶最优的。此外,我们提出了补充通用计划的情况下,当$n$和$k$都很小。

英文摘要:

In the traditional index coding problem, a server employs coding to send messages to $n$ clients within the same broadcast domain. Each client already has some messages as side information and requests a particular unknown message from the server. All clients learn the coding matrix so that they can decode and retrieve their requested data. Our starting observation is that, learning the coding matrix can pose privacy concerns: it may enable a client to infer information about the requests and side information of other clients. In this paper, we mitigate this privacy concern by allowing each client to have limited access to the coding matrix. In particular, we design coding matrices so that each client needs only to learn some of (and not all) the rows to decode her requested message. By means of two different privacy metrics, we first show that this approach indeed increases the level of privacy. Based on this, we propose the use of $k$-limited-access schemes: given an index coding scheme that employs $T$ transmissions, we create a $k$-limited-access scheme with $T_k\geq T$ transmissions, and with the property that each client needs at most $k$ transmissions to decode her message. We derive upper and lower bounds on $T_k$ for all values of $k$, and develop deterministic designs for these schemes, which are universal, i.e., independent of the coding matrix. We show that our schemes are order-optimal when either $k$ or $n$ is large. Moreover, we propose heuristics that complement the universal schemes for the case when both $n$ and $k$ are small.

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。

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