Fully device independent quantum private query

Abstract

Quantum Private Query (QPQ) is an unconditional secure mistrustful cryptographic primitive which is assumed to be a probabilistic version of the Oblivious Transfer (OT) schemes or an imperfect version of Symmetric Private Information Retrieval (SPIR) schemes. Recently, Maitra et al. (Phys. Rev. A, 2017) identified that the B92 QKD-based QPQ scheme proposed by Yang et al. (Quant. Inf. Process., 2014) is vulnerable whenever the devices involved in that scheme are dubious and to improve the overall security, they suggested a semi-Device Independent (DI) proposal for that QPQ scheme by introducing a local test at the server's end. In this work, we overcome the limitation of the Maitra et al. proposal by removing trustworthiness from all the (involved) devices, and suggest a full DI proposal for the Yang et al. scheme, exploiting a proper self-testing mechanism of observables along with the local version of the tilted CHSH game. We compare the performance of our proposal with a recent full DI-QPQ scheme (arxiv 1901.03042) and discuss their relative advantages. Additionally, we present a DI proposal for a modified version of the Yang et al. scheme, enabling the client to retrieve maximum raw key bits during the oblivious key generation phase. We evaluate the security of all our proposals with a formal analysis.