On the privacy of a code-based single-server computational PIR scheme

April 01, 2020 Β· Declared Dead Β· πŸ› Cryptography and Communications

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Authors Sarah Bordage, Julien Lavauzelle arXiv ID 2004.00509 Category cs.CR: Cryptography & Security Cross-listed cs.IT Citations 10 Venue Cryptography and Communications Last Checked 4 months ago
Abstract
We show that the single-server computational PIR protocol proposed by Holzbaur, Hollanti and Wachter-Zeh in 2020 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.
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