Security analysis with improved design of post-confirmation mechanism for quantum sealed-bid auction with single photons

Quantum and semi-quantum sealed-bid auction: Vulnerabilities and advantages

“…This renders a malicious bidder and auctioneer to collude and disclose a permutation operator to pass the verifiability. Two such collusion attacks are already mentioned in [20].…”

“…Here, we mention some additional weaknesses and inconsistencies present in The improvements proposed by Zhang et al are prone to several attacks that we list here. To begin with, a semi-quantum participant [21] is allowed to prepare and measure qubits in the computational basis only unlike "they can only control single photons" as mentioned in [20]. Thus, mere modification in the post-confirmation phase of Liu et al quantum sealed-bid auction is not expected to provide a semi-quantum scheme.…”

“…Interestingly, most of the existing protocols of quantum sealed-bid auction do not satisfy the above criteria in the strict sense. To elaborate on this point, in what follows, we will cryptanalyze a protocol of quantum sealed-bid auction proposed by Liu et al [19] and two protocols for the same task obtained by modifying the Liu et al protocol which were introduced by Zhang et al [20]. Specifically, Liu et al [19] proposed a single photon based protocol of sealed-bid auction recently.…”

“…Specifically, Liu et al [19] proposed a single photon based protocol of sealed-bid auction recently. Subsequently, the protocol was cryptanalyzed and improved by Zhang et al [20] who proposed two improved mechanisms of post-confirmation, which were claimed to be semi-quantum sealed-bid auction. The cryptanalysis performed here will establish that In fact, a classical user in semi-quantum cryptography is restricted to measure/prepare states in one basis set and reflect the qubits sent by the quantum user [21].…”

“…In fact, much progress has been made in the field of semi-quantum cryptography with some experimental realization also reported recently (see [26] for review) which has strongly established the feasibility of the implementation of the semi-quantum schemes for various cryptographic tasks. Interestingly, Zhang et al auction protocols [20] are not semi-quantum schemes, and thus this and the existing protocols of sealed-bid auction are resource demanding; in the sense that all the users (auctioneer and bidders) are required to possess quantum resources which are costly. These facts motivated us to propose a semi-quantum protocol of sealed-bid auction free from the vulnerabilities present in protocols of Liu et al and Zhang et al The rest of the letter is organized as follows.…”