Intercept-Resend Attacks on Semi-quantum Secret Sharing and the Improvements
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Intercept-Resend Attacks on Semi-quantum Secret Sharing and the Improvements Jason Lin · Chun-Wei Yang · Chia-Wei Tsai · Tzonelih Hwang
Received: 5 February 2012 / Accepted: 14 August 2012 / Published online: 6 September 2012 © Springer Science+Business Media, LLC 2012
Abstract Recently, Li et al. [Phys. Rev. A 82(2):022303, 2010] presented two semiquantum secret sharing (SQSS) protocols using Greenberger-Horne-Zeilinger-like states. The proposed schemes are quite practical because only the secret dealer needs to be equipped with advanced quantum devices such as quantum memory, whereas the other agents can merely perform classical operations to complete the secret sharing. However, the present study demonstrates the existence of a security pitfall in the eavesdropping check phase of both the schemes, which can lead to an intercept-resend attack and a Trojan horse attack on the two schemes by a dishonest agent, to determine the other agent’s shadow and consequently derive the master key of the SQSS. This contradicts the security requirement of QSS. Fortunately, two possible solutions are proposed herein to eliminate this security pitfall. Keywords GHZ-like state · Intercept-resend attack · Quantum cryptography · Quantum secret sharing · Trojan horse attack 1 Introduction Since the proposal of the first quantum secret sharing (QSS) protocol via a triplet Greenberger-Horne-Zeilinger (GHZ) state by Mark et al. in 1999 [1], several QSS schemes J. Lin · C.-W. Yang · T. Hwang () Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Rd., Tainan City, 70101, Taiwan, ROC e-mail: [email protected] J. Lin e-mail: [email protected] C.-W. Yang e-mail: [email protected] C.-W. Tsai Smart Network System Institute, Institute for Information Industry, 7F., No. 133, Sec. 4, Minsheng E. Rd., Taipei City 105, Taiwan, ROC e-mail: [email protected]
Int J Theor Phys (2013) 52:156–162
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have been proposed [2–13]. The main goal of QSS scheme is to distribute a secret among several agents using techniques based on quantum mechanics. Only when a sufficient number of subsets of legitimate agents cooperate can the secret be recovered. On the other hand, no agent is able to solely acquire the dealer’s secret using his/her own shadow. A secure QSS scheme should be able to avoid an attack from both an outside eavesdropper and an inside malicious user. Recently, Li et al. proposed two novel semi-quantum secret sharing (SQSS) protocols via a triplet GHZ-like state [13]. According to their definition, the term “semi-quantum” implies that the secret dealer is a powerful quantum server, whereas the other agents are all classical clients. More precisely, the secret dealer has the ability to perform the following operations: (1) preparing a GHZ-like state, (2) performing the Bell measurement and the three-qubit joint measurement, and (3) storing photons in a short-term quantum memory. Meanwhile, the classical agents are restricted to performing the following operations over t
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