2024/05/28 by Okko Makkonen, Makkonen, Okko, David Karpuk +3 · 1 citation
Computer Science · #Cooperative Communication and Network Coding #Cryptography and Data Security #FOS: Computer and information sciences #Information Theory (cs.IT) #Privacy-Preserving Technologies in Data
paper · pdf · doi:10.48550/arxiv.2405.18052
openalex publication_date 2024/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A new framework for interference alignment in secure and private information retrieval (PIR) from colluding servers is proposed, generalizing the original cross-subspace alignment (CSA) codes proposed by Jia, Sun, and Jafar. The general scheme is built on algebraic geometry codes and explicit constructions with replicated storage are given over curves of genus zero and one. It is shown that the proposed scheme offers interesting tradeoffs between the field size, file size, number of colluding servers, and the total number of servers. When the field size is fixed, this translates in some cases to higher retrieval rates than those of the original scheme. In addition, the new schemes exist also in cases where the original ones do not.