Private Information Retrieval from Coded Storage in the Presence of Omniscient and Limited-Knowledge Byzantine Adversaries

摘要

This paper investigates an adversarial model in the scenario of private information retrieval (PIR) from n coded storage servers, called Byzantine adversary. The Byzantine adversary is defined as the one altering b server responses and erasing u server responses to a user's query. In this paper, two types of Byzantine adversaries are considered; 1) the classic omniscient type that has the full knowledge on n servers as considered in existing literature, and 2) the reasonable limited-knowledge type that has information on only b+u servers, i.e., servers under the adversary's control. For these two types, this paper reveals that the resistance of a PIR scheme, i.e., the condition of b and u to correctly obtain the desired message, can be expressed in terms of a code parameter called the coset distance of linear codes employed in the scheme. For the omniscient type, the derived condition expressed by the coset distance is tighter and more precise than the estimation of the resistance by the minimum Hamming weight of the codes considered in existing researches. Furthermore, this paper also clarifies that if the adversary is limited-knowledge, the resistance of a PIR scheme could exceed that for the case of the omniscient type. Namely, PIR schemes can increase their resistance to Byzantine adversaries by allowing the limitation on adversary's knowledge.