On the Information Leakage in Private Information Retrieval Systems
This work addresses privacy concerns in data retrieval systems, providing theoretical insights and optimal solutions for minimizing leakage, which is incremental to existing PIR research.
The paper tackles the problem of information leakage in private information retrieval systems by characterizing the tradeoffs between download cost and leakage (individual and total), proposing new codes to achieve optimal tradeoffs, and showing that common randomness is unnecessary under individual leakage for more than two messages.
We consider information leakage to the user in private information retrieval (PIR) systems. Information leakage can be measured in terms of individual message leakage or total leakage. Individual message leakage, or simply individual leakage, is defined as the amount of information that the user can obtain on any individual message that is not being requested, and the total leakage is defined as the amount of information that the user can obtain about all the other messages except the one being requested. In this work, we characterize the tradeoff between the minimum download cost and the individual leakage, and that for the total leakage, respectively. New codes are proposed to achieve these optimal tradeoffs, which are also shown to be optimal in terms of the message size. We further characterize the optimal tradeoff between the minimum amount of common randomness and the total leakage. Moreover, we show that under individual leakage, common randomness is in fact unnecessary when there are more than two messages.