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International Journal of Quantum Information

CRYPTANALYSIS AND IMPROVEMENT OF THE SECURE QUANTUM SEALED-BID AUCTION WITH POSTCONFIRMATION

Guoai Xu, ZHI-WEN ZHAO, Xiu‐Bo Chen, Yixian Yang

Published Aug 25, 2011• 13 citations
Publisher

Abstract

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.

DOI
10.1142/s0219749911008076

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Comment on "Cryptanalysis and improvement of the secure quantum sealed-bid auction with post confirmation"

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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.
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.
The secure quantum sealed-bid auction protocol [Mosayeb Naseri, Opt. Commun.282 (2009) 1939] is revisited. It is found that, utilizing intercept-measure-resend attacks, any evil bidder can make the auction aborted without being detected by the auctioneer. Further, if the evil bidder succeeds to be the first bidder, then he/she can win conclusively in the auction. To prevent such attacks, some defence strategies are adopted in the qubit distribution stage and the channel security check stage respectively and the original protocol is therefore modified somewhat.
Sealed-bid auction is an important tool in modern economic especially concerned with networks. However, the bidders still lack the privacy protection in previously proposed sealed-bid auction schemes. In this paper, we focus on how to further protect the privacy of the bidders, especially the non-winning bidders. We first give a new privacy-preserving model of sealed-bid auction and then present a quantum sealed-bid auction scheme with stronger privacy protection. Our proposed scheme takes a general state in N-dimensional Hilbert space as the message carrier, in which each bidder privately marks his bid in an anonymous way, and further utilizes Grover's search algorithm to find the current highest bid. By O(lnn) iterations, it can get the highest bid finally. Compared with any classical scheme in theory, our proposed quantum scheme gets the lower communication complexity.
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.
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.