A simple participant attack on the Bradler-Dusek protocol

TLDR

The paper discusses the ring‑arrangement quantum secret‑sharing protocol introduced by Brádler and Dušek. The authors aim to describe a participant attack strategy and propose a protocol improvement. They detail the attack strategy and outline a countermeasure to prevent it. The protocol is secure against eavesdroppers but a dishonest participant can steal another's share and recover the secret, as shown by Bob’s undetected attack. Referenced in Quantum Semiclassical Optics.

Abstract

The ring-arrangement quantum secret sharing protocol in the paper [K. Br\'{a}dler and M. Du\v{s}ek (2004) {\textit{J. Opt. B: Quantum Semiclass. Opt.}} {\textbf{6}} 63] is analyzed and it is shown that this protocol is secure for any eavesdropper except for a dishonest participant. For example, by a special strategy, Bob can steal Charlie's portion of information without being detected and then recover Alice's secret by himself. We give a description of this strategy and point out a possible way to improve the protocol to stand against this attack.