  In this paper, we propose a novel Quantum Private Query (QPQ) scheme with
full Device-Independent certification. To the best of our knowledge, this is
the first time we provide such a full DI-QPQ scheme using EPR-pairs. Our
proposed scheme exploits self-testing of shared EPR-pairs along with the
self-testing of projective measurement operators in a setting where the client
and the server do not trust each other. To certify full device independence, we
exploit a strategy to self-test a particular class of POVM elements that are
used in the protocol. Further, we provide formal security analysis and obtain
an upper bound on the maximum cheating probabilities for both the dishonest
client as well as the dishonest server.
