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Communications in Theoretical Physics

Attacks and Improvement of Quantum Sealed-Bid Auction with EPR Pairs

Wenjie Liu, Fang Wang, Sai Ji, Zhiguo Qu, Xiaojun Wang

Published Jun 1, 2014• 43 citations
Publisher

Abstract

Recently, an experimentally feasible three-party quantum sealed-bid auction protocol based on EPR pairs [Z.Y. Wang, Commun. Theor. Phys. 54 (2010) 997 ] was proposed. However, this study points out Wang's protocol cannot resist some internal bidders' attacks, such as the Twice-CNOT attack, the collusion attack. A malicious bidder can launch the Twice-CNOT attack to obtain the other's bid, or the dishonest auctioneer may collude with one bidder and help him/her win the action by changing his/her bid. For preventing against these attacks, a simple solution by using the QKD-based message encryption and a post-confirmation mechanism by adopting the hash function are proposed.

DOI
10.1088/0253-6102/61/6/05

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Recently, an experimentally feasible three-party quantum sealed-bid auction protocol based on EPR pairs [Z.Y. Wang, Commun. Theor. Phys. 54 (2010) 997 ] was proposed. However, this study points out Wang's protocol cannot resist some internal bidders' attacks, such as the Twice-CNOT attack, the collusion attack. A malicious bidder can launch the Twice-CNOT attack to obtain the other's bid, or the dishonest auctioneer may collude with one bidder and help him/her win the action by changing his/her bid. For preventing against these attacks, a simple solution by using the QKD-based message encryption and a post-confirmation mechanism by adopting the hash function are proposed.
In this paper, the cryptanalysis about the quantum sealed-bid auction, whose feature is that by introducing a postconfirmation mechanism the malicious bidders cannot collude with auctioneers, is given. We found that a malicious bidder can obtain the other bidders' bids with a probability of 0.854. Moreover, there will be a higher probability if some bidders collude to attack the other bidders' bids. To prevent such attacks, we propose an effective improvement by means of the hash function.
I present a new protocol for three-party quantum secure direct communication (QSDC) with a set of ordered M Einstein—Podolsky—Rosen (EPR) pairs. In the scheme, by performing two unitary operations and Bell state measurements, it is shown that the three legitimate parties can exchange their respective secret message simultaneously. Then I modify it for an experimentally feasible and secure quantum sealed-bid auction (QSBD) protocol. Furthermore, I also analyze the security of the protocol, and the scheme is proven to be secure against the intercept-and-resend attack, the disturbance attack and the entangled-and-measure attack.
A sealed-bid auction is an essential tool for trading commodities in modern society. However, the non-winning bidders in previously proposed sealed-bid auction schemes lack privacy protection. In this paper, we define a sealed-bid auction with strong privacy protection, which can protect the privacy of all non-winning bidders. In order to fulfil the task, we first present a quantum secret sharing protocol and a secure quantum summation protocol and then design their corresponding quantum circuits, where the security of the latter is guaranteed by the former, while the former is information-theoretically secure. We further present a quantum seal-bid auction (QSA) scheme with strong privacy protection based on the designed quantum protocols. In our QSA scheme, each bidder first encodes a private vector by his private bid and public agreement information, and then all bidders jointly compute the summations of their respective private vectors without a trusted third party. Finally, we verify the correctness and the feasibility of the proposed QSA scheme by circuit simulations in IBM Qiskit.
Quantum sealed-bid auction (QSA) is a special form of transaction with significant applications in the economic and financial fields. Using a unique set of locally indistinguishable orthogonal product (LIOP) states, we propose a new QSA protocol in this paper. In the protocol, the bid message is encoded as a quantum sequence of LIOP states, and the different particles of LIOP states are transmitted separately. Even though an attacker obtains a portion of the particles, they cannot recover the entire bid message because of the local indistinguishability of LIOP states. Once the auctioneer announces the winner’s bid, all bidders are able to confirm the authenticity of their bid. With the help of a semi-honest third party, collusion between the auctioneer and a malicious bidder can be discovered. Finally, our protocol is capable of meeting all requirements for secure sealed-bid auctions through security and completeness analysis. Additionally, the proposed protocol does not require any entangled resources and complicated operations, so it can be easily implemented in practice.
Recently, Gao et al.'s [ Commun. Theor. Phys. 52 (2009) 421 ] multiparty quantum secret sharing (MQSS) protocol with two-photon three-dimensional Bell states was enhanced by Hwang et al. [ Commun. Theor. Phys. 56 (2011) 79 ]. The improved protocol removes some unnecessary unitary operations, devices, and transmissions by the technique of decoy single photons and careful modification. However, in this paper, we investigate the security of the improved protocol and find it is insecure. The eavesdropper can steal all Alice's secret information. Furthermore, a feasible modification to remedy the security loophole is put forward. Our improved protocol provides a basic method to modify a kind of MQSS protocols which cannot resist the collusion attack.