We show that the single-server computational PIR protocol proposed by Holzbaur, Hollanti and Wachter-Zeh in [6] is not private, in the sense that the server can recover in polynomial time the index of the desired file with very high probability. The attack relies on the following observation. Removing rows of the query matrix corresponding to the desired file yields a large decrease of the dimension over \(\mathbb {F}_q\) of the vector space spanned by the rows of this punctured matrix. Such a dimension loss only shows up with negligible probability when rows unrelated to the requested file are deleted.

中文翻译：

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基于代码的单服务器计算PIR方案的私密性

我们展示了Holzbaur，Hollanti和Wachter-Zeh在[6]中提出的单服务器计算PIR协议不是私有的，因为服务器可以在多项式时间内以很高的概率恢复所需文件的索引。攻击依赖于以下观察。删除与所需文件相对应的查询矩阵的行，将使该被打孔矩阵的行所跨越的向量空间的尺寸\（\ mathbb {F} _q \）大大减小。当删除与所请求文件无关的行时，这种尺寸损失仅以可忽略的概率出现。