Classical versus Quantum Graph-based Secret Sharing

TL;DR

This paper compares classical and quantum graph-based secret sharing schemes, providing characterizations of authorized sets and showing their equivalence in the classical case, with insights into quantum state sharing.

Contribution

It introduces a classical graph-based secret sharing scheme and establishes its equivalence to quantum schemes for classical secrets, with new characterizations of authorized sets.

Findings

Classical scheme characterized by neighbor-encrypted shares.

Equivalence shown between classical and quantum schemes for classical secrets.

Authorization criteria extended to quantum states with complement set conditions.

Abstract

We study a simple graph-based classical secret sharing scheme: every player's share consists of a random key together with the encryption of the secret with the keys of his neighbours. A characterisation of the authorised and forbidden sets of players is given. Moreover, we show that this protocol is equivalent to the graph state quantum secret sharing (GS-QSS) schemes when the secret is classical. When the secret is an arbitrary quantum state, a set of players is authorised for a GS-QSS scheme if and only if, for the corresponding simple classical graph-based protocol, the set is authorised and its complement set is not.