Towards communication-efficient quantum oblivious key distribution

Abstract

Oblivious Transfer, a fundamental problem in the field of secure multi-party computation is defined as follows: A database DB of N bits held by Bob is queried by a user Alice who is interested in the bit DB b in such a way that (1) Alice learns DB b and only DB b and (2) Bob does not learn anything about Alice's choice b. While solutions to this problem in the classical domain rely largely on unproven computational complexity theoretic assumptions, it is also known that perfect solutions that guarantee both database and user privacy are impossible in the quantum domain. Jakobi et al. [Phys. Rev. A, 83(2), 022301, Feb 2011] proposed a protocol for Oblivious Transfer using well known QKD techniques to establish an Oblivious Key to solve this problem. Their solution provided a good degree of database and user privacy (using physical principles like impossibility of perfectly distinguishing non-orthogonal quantum states and the impossibility of superluminal communication) while being loss-resistant and implementable with commercial QKD devices (due to the use of SARG04). However, their Quantum Oblivious Key Distribution (QOKD) protocol requires a communication complexity of O(N log N). Since modern databases can be extremely large, it is important to reduce this communication as much as possible. In this paper, we first suggest a modification of their protocol wherein the number of qubits that need to be exchanged is reduced to O(N). A subsequent generalization reduces the quantum communication complexity even further in such a way that only a few hundred qubits are needed to be transferred even for very large databases.

Quantum and classical oblivious transfer: A comparative analysis

“…They avoid the assumptions of the no-go theorems [33,35] because their protocol is not perfectly concealing; that is, the sender may obtain some (limited) information about the receiver's choice. This protocol inspired several works that tried to improve on Jakobi's initial proposal [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59]. Moreover, this concept was introduced earlier under a different name (weak string erasure) and with its security based on the noisy-storage model [60].…”

“…It is important to note that these oblivious keys are primarily generated through quantum processes [11,[45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60], and to the best of our knowledge, there are no classical protocols to generate them. For this reason, we may also call them QOKs.…”

Improved and formal proposal for device-independent quantum private query *

“…Several modifications and advancements have been made towards the proposal of the first implementable QPQ scheme by Jakobi et al [16], which was based on a Quantum key distribution (QKD) protocol [17]. This was followed by a flexible generalization by Gao et al [18] and further efficiency improvements suggested by Rao and Jakobi [19]. Zhang et al [20] proposed a QPQ protocol based on the counterfactual QKD scheme [21] and Yang et al developed a flexible QPQ protocol [22] based on the B92 QKD scheme [23].…”

Provably Secure Symmetric Private Information Retrieval with Quantum Cryptography

“…In light of these negative results, protocols for SPIR have largely evolved to cheat-sensitive protocols, also known as quantum private query [ 11 ]. Examples of these protocols include those based on quantum oblivious key distribution [ 12 , 13 , 14 , 15 , 16 ], those based on sending states to a database oracle [ 17 , 18 ], and those based on round-robin QKD protocol [ 19 ]. In these protocols, the parties are averse to being caught cheating, so cheat-detection strategies allows one to construct protocols with more relaxed conditions as compared to those of SPIR [ 20 ].…”