Quantum multi-secret sharing scheme with access structures and cheat identification

TL;DR

This paper introduces a quantum multi-secret sharing scheme with cheat detection, leveraging a black box mechanism to identify deceitful participants and ensure secure, reliable secret reconstruction in noisy quantum environments.

Contribution

It presents a novel $d$-dimensional quantum multi-secret sharing protocol with integrated cheat detection using a black box and monotone span program, enhancing security and practicality.

Findings

Effective cheat detection in quantum secret sharing

Robustness under various noise models

Enhanced security against eavesdroppers and dishonest participants

Abstract

This work proposes a $d$-dimensional quantum multi-secret sharing scheme with a cheat detection mechanism. The dealer creates multiple secrets and distributes the shares of these secrets using multi-access structures and a monotone span program. The dealer detects the cheating of each participant using the Black box's cheat detection mechanism. To detect the participants' deceit, the dealer distributes secret shares' shadows derived from a randomly invertible matrix $X$ to the participants, stored in the black box. The Black box identifies the participant's deceitful behavior during the secret recovery phase. Only honest participants authenticated by the Black box acquire their secret shares to recover the multiple secrets. After the Black box cheating verification, the participants reconstruct the secrets by utilizing the unitary operations and quantum Fourier transform. The proposed protocol is reliable in preventing attacks from eavesdroppers and participants. The scheme's efficiency is demonstrated in different noise environments: dit-flip noise, $d$-phase-flip noise, and amplitude-damping noise, indicating its robustness in practical scenarios. The proposed protocol provides greater versatility, security, and practicality.