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

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 Twiee-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.     

Twice-Hadamard-CNOT attack on Li et al.’s fault-tolerant quantum private comparison and the improved scheme

Recently, Li et al. presented a two-party quantum private comparison scheme using Greenberger–Horne–Zeilinger (GHZ) states and error-correcting code (ECC) [Int. J. Theor. Phys. 52, 2818 (2013)], claiming it is fault-tolerant and could be performed in a non-ideal scenario. However, there exists a fatal loophole in their private comparison scheme under a special attack, namely the twice-Hadamard-CNOT attack. Specifically, a malicious party may intercept the other party’s particles and execute Hadamard operations on the intercepted particles as well as on his or her own particles. Then, the malicious party could sequentially perform a controlled-NOT (CNOT) operation between intercepted particles and the auxiliary particles, as well as between his or her own particles and the auxiliary particles prepared in advance. By measuring the auxiliary particles, the secret input will be revealed to the malicious party without being detected. For resisting this special attack, a feasible improved scheme is proposed by introducing a permutation operator before the third party (TP) sends the particle sequences to each participant.