Verifiable quantum (k, n)-threshold secret sharing

Authors:
Yu-Guang Yang;Xin Jia;Hong-Yang Wang;Hua Zhang
Affiliations:
College of Computer Science and Technology, Beijing University of Technology, Beijing, China 100124 and State Key Laboratory of Integrated Services Network, Xidian University, Xi'an, China 710071;College of Computer Science and Technology, Beijing University of Technology, Beijing, China 100124;College of Computer Science and Technology, Beijing University of Technology, Beijing, China 100124;State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, China 100876
Venue:
Quantum Information Processing
Year:
2012

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Abstract

In a conventional quantum (k, n) threshold scheme, a trusted party shares a quantum secret with n agents such that any k or more agents can cooperate to recover the original secret, while fewer than k agents obtain no information about the secret. Is the reconstructed quantum secret same with the original one? Or is the dishonest agent willing to provide a true share during the secret reconstruction? In this paper we reexamine the security of quantum (k, n) threshold schemes and show how to construct a verifiable quantum (k, n) threshold scheme by combining a qubit authentication process. The novelty of ours is that it can provide a mechanism for checking whether the reconstructed quantum secret is same with the original one. This mechanism can also attain the goal of checking whether the dishonest agent provides a false quantum share during the secret reconstruction such that the secret quantum state cannot be recovered correctly.