A Proposal for Rational Quantum Multi‐Secret Sharing

ABSTRACT Quantum secret sharing (QSS) holds a significant place in quantum cryptography. Unlike traditional QSS schemes, which often simplistically model participants as either completely honest or fully malicious, rational QSS introduces a more realistic framework by modeling participants as rational entities who strategically act to maximize their own utility. In this paper, for the first time, a rational quantum multi‐secret sharing scheme designed to share a classical bit string by configuring multiple effective reconstruction rounds is proposed. Further, a novel method is proposed to facilitate equilibrium achievement—deception deterrence. In terms of efficiency, the scheme achieves, for the first time, an effective reconstruction round ratio and a communication efficiency are independent of the total number of reconstruction rounds configured in the scheme, overcoming the communication efficiency limitation inherent in existing schemes. In terms of equilibrium achievement, the proposed new method not only returns to the essence of strategic interaction among rational participants themselves but also avoids the substantial verification cost.