A symmetric extensible protocol for quantum secret sharing

TL;DR

The paper tackles secure, scalable secret sharing in the quantum regime by introducing SEQSS_n, an entanglement-based protocol that uses GHZ_n states distributed among $n$ players. The core idea is a two-phase process: a quantum phase that distributes GHZ entanglement and generates correlated measurement data, followed by a public broadcast from the spymaster to enable the agents to recover the secret, with the reveal timing controlled by the spymaster. The authors present concrete constructions for the 3-player SEQSS$_3$ and extend the framework to the general SEQSS$_n$, highlighting the fundamental correlations $ oldsymbol{a} ots ot oldsymbol{s} $ (and its generalization) that bind the agents' data to the secret $oldsymbol{s}$. They argue that security arises from the monogamy of entanglement and that the public broadcast of a single piece of information by the spymaster does not compromise security, while enabling controlled reveal of the secret. The work offers a symmetric, extensible approach to quantum secret sharing with potential practical benefits, and calls for further security and performance analyses to validate and optimize its implementation.

Abstract

This paper introduces the Symmetric Extensible Quantum Secret Sharing protocol, which is a novel quantum protocol for secret sharing. At its heart, it is an entanglement based protocol that relies on the use of maximally entangled GHZ tuples, evenly distributed among the players, endowing the spymaster with the ability to securely share a secret message with her agents. It offers uncompromising security, making virtually impossible for a malicious eavesdropper or a rogue double agent to disrupt its successful execution. It is characterized by symmetry, since all agents are treated indiscriminately, utilizing identical quantum circuits. Furthermore, it can be seamlessly extended to an arbitrary number of agents. After the completion of the quantum part of the protocol, the spymaster will have to publicly transmit some information, in order to enable the agents to discover the secret message. Finally, it has the additional advantage that the spymaster has the privilege to decide when it is the right time for the agents to discover the secret message.

Figures (6)

• Figure 1: This quantum circuit can be used in Qiskit to entangle 3 qubits in the $\ket{ GHZ_3 } = \frac{ \ket{0} \ket{0} \ket{0} + \ket{1} \ket{1} \ket{1} }{\sqrt{2}}$ state.
• Figure 2: The state vector description of 3 qubits entangled in the $\ket{ GHZ_3 }$ state.
• Figure 3: This figure visualizes the quantum circuit implementing the SEQSS$_3$ protocol.
• Figure 4: Alice is spatially separated from her agents Bob and Charlie, who are in the same region. A third party, the source, creates $m$ triplets of $GHZ_3$ entangled photons and sends one qubit from every triplet to Alice and the remaining two to Bob and Charlie.
• Figure 5: A schematic representation of the quantum circuit implementing the SEQSS$_n$ protocol.