Asymmetric Leaky Private Information Retrieval

Information-theoretic formulations of the private information retrieval (PIR) problem have been investigated under a variety scenarios. Symmetric (SPIR) is variant where user able to privately retrieve one out K messages from N non-colluding replicated databases without learning anything about remaining K-1 messages. However, goal perfect privacy can be too taxing for certain applications. In this paper, we investigate if information-theoretic capacity SPIR (equivalently, inverse minimum download cost) increased by relaxing both and DB definitions. Such relaxation relevant in applications traded communication efficiency. We introduce Asymmetric Leaky PIR (AL-PIR) model with different leakage budgets each direction. For leakage, bound probability ratios between all possible realizations queries function non-negative constant ?. privacy, mutual undesired messages, queries, answers, ?. propose general AL-PIR scheme that achieves an upper on optimal cost arbitrary ? show upper-bounded as D * (?,?) ? 1+\frac 1N-1-\frac ?e xmlns:xlink="http://www.w3.org/1999/xlink">? xmlns:xlink="http://www.w3.org/1999/xlink">K-1 -1. Second, obtain lower ? 1Ne -1-\frac ?(Ne ) The gap analysis two bounds shows our when = 0, i.e., it within maximum multiplicative \frac N-e xmlns:xlink="http://www.w3.org/1999/xlink">-? N-1 any > 0 ? 0.