Quantum secure two party computation for set intersection with rational players

TL;DR

This paper extends quantum protocols for set intersection to rational players, proving that a specific strategy profile forms a strict Nash equilibrium, ensuring fairness and correctness in the quantum setting.

Contribution

It introduces a rational-player model for quantum set intersection protocols and proves the equilibrium strategy guarantees fairness and correctness.

Findings

The strategy profile ((cooperate, abort), (cooperate, abort)) is a strict Nash equilibrium.

Rational players' participation ensures protocol fairness and correctness.

The protocol extends previous quantum set intersection schemes to rational settings.

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 $\{k_1,k_2,\cdots k_n\}$. 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.