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Science in China. Series G, Physics, mechanics & astronomy/Science in China. Series G, Physics, Mechanics & Astronomy

Eavesdropping in a quantum secret sharing protocol based on Grover algorithm and its solution

Jun Li

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

A detailed analysis has showed that the quantum secret sharing protocol based on the Grover algorithm (Phys Rev A, 2003, 68: 022306) is insecure. A dishonest receiver may obtain the full information without being detected. A quantum secret-sharing protocol is presents here, which mends the security loophole of the original secret-sharing protocol, and doubles the information capacity.

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Eavesdropping in a quantum secret sharing protocol based on Grover algorithm and its solution

Liang Hao, Junlin Li, GuiLu Long

Science China Physics Mechanics and Astronomy•Mar 1, 2010•89 citations
A detailed analysis has showed that the quantum secret sharing protocol based on the Grover algorithm (Phys Rev A, 2003, 68: 022306) is insecure. A dishonest receiver may obtain the full information without being detected. A quantum secret-sharing protocol is presents here, which mends the security loophole of the original secret-sharing protocol, and doubles the information capacity.
A marked state can be found with certainty in the two-qubit case of Grover's algorithm. This property is included in the proposed quantum secret-sharing protocol. In the proposed scheme, the sender prepares some initial state in private and then performs a phase shift of the marked state as the sender's bit. Then, the sender sends these two qubits to each of the two receivers. Only when the sender broadcasts the initially prepared state and then the receivers perform the corresponding inversion operation about the average, is the sender's bit faithfully revealed. Moreover, the sender can detect deception using cheat-detecting states. The proposed quantum secret-sharing protocol is shown to be secure.
In this paper, the perfect secret sharing in quantum cryptography is investigated. On one hand, the security of a recent protocol [Adhikari et al. Quantum Inform. \& Comput. 12 (2012) 0253-0261] is re-examined. We find that it violates the requirement of information theoretic security in the secret sharing and suffers from the information leakage. The cryptanalysis including several specific attack strategies are given, which shows that a dishonest participant can steal half or all of the secrets without being detected. On the other hand, we design a new quantum secret sharing protocol. The security of protocol is rigorously proved. It meets the fundamental requirement of information theoretic security. Furthermore, the security analysis including both the outside attacks and participant attacks is given in details. It is shown that our proposed protocol can achieve perfect secret sharing.
Quantum communication protocols can be designed to detect eavesdropping attacks, something that classical technologies are unable to do since classical information can be replicated in a non-destructive manner. Eavesdropping detection is, therefore, a standard feature in all the proposed quantum secret sharing (QSS) protocols. However, detection is often done by a statistical analysis of the outcome of multiple decoy rounds, and this causes a significant communication overhead. In our quest for a QSS protocol that works even in one round, we came across a one-shot secret-sharing framework proposed by Hsu (Phys. Rev. A 2003). The scheme was designed to work over public channels without requiring multiple rounds to detect eavesdropping but it lacked a thorough security analysis. In this work we present a complete characterisation of the correctness and security properties of this framework. Our characterisation allowed us to improve the original protocol to be more resistant towards eavesdropping. However, we prove a couple of impossibility results, including one that dictates that complete security against an eavesdropper is not possible in this framework. Thus, it is not possible to design a perfect QSS using this framework.
Abstract Quantum secret sharing(QSS) is a cryptographic protocol based on the uncertainty principle and quantum no-cloning theorem and is an essential aspect in quantum computing. This paper describes the Grover search algorithm and how to improve QSS protocol by Grover Algorithm. The QSS based on the Grover algorithm is more secure and easier to operate compared to old QSS protocols. Some scientists improved the security of the first QSS protocol based on QSA by changing the check mode. After that, a protocol with quite different procedures was proposed. The improved one enhances the feasibility of the protocol and it could also make sure that the communication is secure from the attacks.