Quantum secure two-party computation for set intersection with rational players

Abstract

Recently, Shi et al. (Phys. Rev. A, 2015) proposed Quantum Oblivious Set Member Decision Protocol (QOSMDP) where two legitimate parties, namely Alice and Bob, play a game. Alice has a secret k and Bob has a set {k1, k2, · · · kn}. The game is designed towards testing if the secret k is a member of the set possessed by Bob without revealing the identity of k. The output of the game will be either "Yes" (bit 1) or "No" (bit 0) and is generated at Bob's place. Bob does not know the identity of k and Alice does not know any element of the set. In a subsequent work (Quant. Inf. Process., 2016), the authors proposed a quantum scheme for Private Set Intersection (PSI) where the client (Alice) gets the intersected elements with the help of a server (Bob) and the server knows nothing. In the present draft, we extended the game to compute the intersection of two computationally indistinguishable sets X and Y possessed by Alice and Bob respectively. We consider Alice and Bob as rational players, i.e., they are neither "good" nor "bad". They participate in the game towards maximizing their utilities. We prove that in this rational setting, the strategy profile ((cooperate, abort), (cooperate, abort)) is a strict Nash equilibrium. If ((cooperate, abort), (cooperate, abort)) is strict Nash, then fairness as well as correctness of the protocol are guaranteed.

A New Quantum Private Protocol for Set Intersection Cardinality Based on a Quantum Homomorphic Encryption Scheme for Toffoli Gate

“…Each of them chooses a sequence, , where are randomly chosen from . Then, she(he) uses the Quantum One-time Pad algorithm (QOTP) [ 25 ] to encrypt the k th particle of and get . The new particles sequence is denoted by .…”

“…Then they presented a quantum scheme for PSI based on n encoded states, n quantum operators, and n von Neumann measurements. In [ 25 ], Arpita gave a two-party protocol for computing set intersection securely in the quantum domain in a rational setting, where the players are trying to maximize their utilities. However, PSI reveals too much private personal information in some scenarios.…”

Private Set Intersection with Delegated Blind Quantum Computing

“…In the quantum setting, previous work considered the two-party and multi-party PSI scenario [9][10][11][12][13]. Instead, to the best of our knowledge, the server-aided one has not been considered so far.…”

SEPSI: A Secure and Efficient Privacy-Preserving Set Intersection with Identity Authentication in IoT

“…Cheng's protocol shows that the protocol [18] is not as efficient as claimed because the communication complexity should be O(nlogN) instead of O(n). Later, Maitra [20] presented a fair quantum PSI protocol based on a set membership decision protocol [21]. However, these protocols need complicated oracle operators and multi-particle entangled states.…”