Abstract
Quantum private query (QPQ) requires that the database holder Bob knows nothing about his client Alice, including the index she provides and the element she obtains. However, on some occasion, Bob wants to know which element he has revealed to Alice. Therefore, we raise a symmetric quantum private query (SQPQ) problem in this paper. SQPQ can guarantee that Alice shares the real element with Bob and also partially protect the privacy of Alice's index. Some necessary conditions are need to satisfy to implement SQPQ. We prove that Alice must provide some extra information to enable Bob to know the element. Then, we define the term “absolutely secure”, which is a security notion stronger than cheat sensitive, and prove that “absolutely secure”SQPQ is impossible. In addition, we raise a cheat sensitive scheme three-databases-detection to implement SQPQ protocol. Finally, we construct a reduction from SQPQ to quantum bit commitment (QBC) to clarify that SQPQ is a problem more difficult than QBC.
Highlights
Every day, hundreds of millions of interactions between users and databases around the world are used to query data
Private information retrieval (PIR) problem [2] is an analogue of symmetrical private information retrieval (SPIR), which deals with user privacy alone
symmetric quantum private query (SQPQ) and quantum bit commitment (QBC) and we find that SQPQ can be reduced to QBC
Summary
Hundreds of millions of interactions between users and databases around the world are used to query data. Alice wants to protect the privacy of her index (she wants to keep the element in secret because the element will reveal the information of the index) and Bob wants to protect his database. Such a problem can be described as symmetrical private information retrieval (SPIR) [1]. Alice can decrypt what she is interested according to these bits in classical way This kind of protocols are named as QKD-based QPQ. We raise a symmetric quantum private query (SQPQ) based on QPQ. We present a cheat sensitive SQPQ protocol, Three-Database-Detection (TDD), and calculate the probability that dishonest Alice and Bob can escape from being detected.
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