Participant Attacks on Quantum Secret Sharing Based on Local Measurements

Abstract

Quantum secret sharing (QSS) provides an efficient way for managing keys securely. Generally, the dishonest participant is a stronger attacker than others in QSS, and then the participant attack should be particularly analyzed. In this paper, the security of two QSS protocols based on GHZ states and local measurements has been further reviewed. Using the participant attack model, Hillery et al. (Phys. Rev. A 59, 1829, 1999) and general HBB-like protocols are analyzed, and they are both insecure: the dishonest participant can restore all of the key without being detected just using local unitary operation and local measurements. Even inserting some nonorthogonal states in the phase of distributing particles, the dishonest participant can also restore all of the key without being detected just using local unitary operation and local measurements. Two key factors of insecurity are deduced: the dishonest participant and the sender have the same ability to control GHZ states, and there are no monitoring strategies in the secret recovery phase. Therefore, how to design multi-party key distribution protocols fixing the two security vulnerabilities is meaningful.