Secure two-party quantum computation for non-rational and rational settings

TL;DR

This paper demonstrates the possibility of secure two-party quantum computation for certain functions in non-simultaneous channel models and introduces rational parties in multi-party quantum computation, achieving fairness and equilibrium.

Contribution

It shows secure quantum computation for specific functions in non-simultaneous channels and introduces rational parties, extending security and fairness concepts.

Findings

Secure quantum computation possible for functions without embedded XOR.

Quantum protocols achieve security against unbounded adversaries.

Introduction of rational parties with utility maximization in quantum setting.

Abstract

Since the negative result of Lo (Physical Review A, 1997), it has been left open whether there exist some functions that can be securely computed in two-party setting in quantum domain when one of the parties is malicious. In this paper, we for the first time, show that there are some functions for which secure two-party quantum computation is indeed possible for non-simultaneous channel model. This is in sharp contrast with the impossibility result of Ben -Or et al. (FOCS, 2006) in broadcast channel model. The functions we study are of two types - one is any function without an embedded XOR, and the other one is a particular function containing an embedded XOR. Contrary to classical solutions, security against adversaries with unbounded power of computation is achieved by the quantum protocols due to entanglement. Further, in the context of secure multi-party quantum computation, for the first time we introduce rational parties, each of whom tries to maximize its utility by obtaining the function output alone. We adapt our quantum protocols for both the above types of functions in rational setting to achieve fairness and strict Nash equilibrium.