Abstract
The traditional quantum secret sharing does not succeed in the presence of rational participants. A rational participant’s motivation is to maximize his utility, and will try to get the secret alone. Therefore, in the reconstruction, no rational participant will send his share to others. To tackle with this problem, we propose a rational quantum secret sharing scheme in this paper. We adopt the game theory to analyze the behavior of rational participants and design a protocol to prevent them from deviating from the protocol. As proved, the rational participants can gain their maximal utilities when they perform the protocol faithfully, and the Nash equilibrium of the protocol is achieved. Compared to the traditional quantum secret sharing schemes, our scheme is fairer and more robust in practice.
Highlights
The traditional quantum secret sharing does not succeed in the presence of rational participants
We have proposed a rational quantum secret sharing (RQSS) scheme to manage rational participants who try to maximize their utilities
The dealer encodes the secret state into an entangled state and distributes to the participants, while participants can use reverse operations to recover the secret state
Summary
The traditional quantum secret sharing does not succeed in the presence of rational participants. This implies the Nash equilibrium corresponds to the case that nobody sends his share to others, resulting in a failure of Shamir’s scheme in the presence of rational participants To mitigate this problem, Halpern et al.[2] introduced the concept of “rational secret sharing” (RSS), and it has become an active area of research in recent years[3,4,5]. The achieved Nash equilibrium corresponds to the case when all the rational participants perform the protocol faithfully, and eventually, the shared quantum state can be recovered with the involvement of all participants. The preliminaries of underlying QSS have been introduced adequately in other existing schemes, and only the preliminaries of rational part are focused They are formalized in terms of rationality, fairness and Nash equilibrium, while quantum operations to be used in this work are introduced. Where |j1〉 and |j2〉 are referred as the control particle and target particle, respectively; and “+” is defined as the adder modulo d hereinafter
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