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On the Security of Index Coding With Side Information

机译：附带信息索引编码的安全性

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Security aspects of the index coding with side information (ICSI) problem are investigated. Building on the results of Bar-Yossef (2006), the properties of linear index codes are further explored. The notion of weak security, considered by Bhattad and Narayanan (2005) in the context of network coding, is generalized to block security. It is shown that the linear index code based on a matrix ${bm L}$, whose column space code ${{cal C}(bm{L})}$ has length $n$, minimum distance $d$ , and dual distance $d^{perp}$ , is $(d-1-t)$ -block secure (and hence also weakly secure) if the adversary knows in advance $tleq d-2$ messages, and is completely insecure if the adversary knows in advance more than $n - d^{perp}$ messages. Strong security is examined under the conditions that the adversary: 1) possesses $t$ messages in advance; 2) eavesdrops at most $mu$ transmissions; 3) corrupts at most $delta$ transmissions. We prove that for sufficiently large $q$ , an optimal linear index code which is strongly secure against such an adversary has length $kappa_{q}+mu+2delta$ . Here, $kappa_{q}$ is a generalization of the min-rank over $BBF_{q}$ of the side information graph for the ICSI problem in its original formulation in the work of Bar-Yossef
机译：研究了带有辅助信息的索引编码（ICSI）问题的安全性。在Bar-Yossef（2006）的结果基础上，进一步探索了线性索引代码的特性。 Bhattad和Narayanan（2005）在网络编码的上下文中考虑了弱安全性的概念，该概念被普遍用来阻止安全性。示出了基于矩阵$ {bm L} $的线性索引代码，其列空间代码$ {{cal C}（bm {L}）} $的长度为$ n $，最小距离为$ d $，并且如果对手事先知道$ tleq d-2 $消息，则双距离$ d ^ {perp} $是$（d-1-t）$-块安全（因此也是弱安全），并且如果对手事先知道的信息超过$ n-d ^ {perp} $条。在以下条件下检查强大的安全性：1）预先拥有$ t $消息； 2）最多监听$ mu $传输； 3）最多破坏$ delta $传输。我们证明，对于足够大的$ q $，可以很好地抵抗此类对手的最佳线性索引代码的长度为$ kappa_ {q} + mu + 2delta $。在此，$ kappa_ {q} $是Bar-Yossef工作中最初形式的ICSI问题的边信息图的$ BBF_ {q} $的最小秩的概括

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