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arXiv 2408.00542cs.ITmath.IT
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用于安全且私有信息检索的秘密共享:一种基于代数几何码的构造

Secret Sharing for Secure and Private Information Retrieval: A Construction Using Algebraic Geometry Codes

Okko Makkonen, David Karpuk, Camilla Hollanti

AI总结:

本文提出一种基于代数几何码的同态秘密共享框架,推广了交叉子空间对齐码,用于合谋服务器下的安全私有信息检索,并在场大小固定时取得更高检索率。

摘要:

私有信息检索(PIR)考虑的是在不泄露所检索数据项任何信息的情况下,从数据库或分布式存储系统中检索数据项的问题。安全PIR通过进一步要求数据内容保持安全来补充这一问题。隐私和安全性可以通过使用秘密共享方法向查询和数据中添加合适的噪声来实现。本文针对来自合谋服务器的安全且私有信息检索,提出了一种新的同态秘密共享框架,推广了Jia、Sun和Jafar最初提出的交叉子空间对齐(CSA)码。我们利用该框架给出了一种基于任意亏格超椭圆曲线上代数几何码的安全PIR构造。结果表明,所提方案在场大小、文件大小、合谋服务器数量与服务器总数之间提供了有趣的权衡。当场大小固定时,在某些情况下这转化为比原始方案更高的检索率。此外,新方案在一些原始方案不存在的参数下也能存在。

英文摘要:

Private information retrieval (PIR) considers the problem of retrieving a data item from a database or distributed storage system without disclosing any information about which data item was retrieved. Secure PIR complements this problem by further requiring the contents of the data to be kept secure. Privacy and security can be achieved by adding suitable noise to the queries and data using methods from secret sharing. In this paper, a new framework for homomorphic secret sharing in secure and private information retrieval from colluding servers is proposed, generalizing the original cross-subspace alignment (CSA) codes proposed by Jia, Sun, and Jafar. We utilize this framework to give a secure PIR construction using algebraic geometry codes over hyperelliptic curves of arbitrary genus. 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 for some parameters where the original ones do not.

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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