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arXiv:1207.6739 · International Journal of Quantum Information

SIMPLE QUANTUM PROTOCOLS FOR THE MILLIONAIRE PROBLEM WITH A SEMI-HONEST THIRD PARTY

Guang Ping He

Published Mar 1, 2013• 15 citations
arXivHTMLPDF

Abstract

Recently there were many quantum protocols devoted to solve the millionaire problem and private comparison problem by adding a semi-honest third party. They all require complicated quantum methods, while still leak a non-trivial amount of information to at least one of the parties. But it will be shown here that once the third party is introduced, there can be protocols which is very simple in the sense that they require quantum key distribution as the only quantum resource. Meanwhile, the amount of information leaked can be made arbitrarily small. Furthermore, in most previous protocols the third party can spoil the protocols without being detected. In our protocol such cheating can also be avoided, so that the only constraint left is that the third party should not conspire with another participant. Thus our solutions surpass all existing protocols on both feasibility and security.

DOI
10.1142/s0219749913500251

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Recently there were many quantum protocols devoted to solve the millionaire problem and private comparison problem by adding a semi-honest third party. They all require complicated quantum methods, while still leak a non-trivial amount of information to at least one of the parties. But it will be shown here that once the third party is introduced, there can be protocols which is very simple in the sense that they require quantum key distribution as the only quantum resource. Meanwhile, the amount of information leaked can be made arbitrarily small. Furthermore, in most previous protocols the third party can spoil the protocols without being detected. In our protocol such cheating can also be avoided, so that the only constraint left is that the third party should not conspire with another participant. Thus our solutions surpass all existing protocols on both feasibility and security.
Abstract Based on Bell states, a new semi-quantum private comparison protocol is proposed that enables two classical users to securely compare the equality of their private information with the aid of a semi-honest third party. Different from the existing semi-quantum private comparison protocols, the two classical participants in the presented protocol do not need to measure and prepare any quantum state, which not only reduces the consumption of quantum devices, but also greatly improves the feasibility of the protocol. Performing different unitary operations on the received particles, classical users can securely compare their secret information. Besides, the devised protocol has higher qubit efficiency than the other similar counterparts, since participants can compare a two-bit privacy each time with one qubit. Meanwhile, after completing the comparison process, all Bell states could be reused since they still retain the corresponding entanglement property, which greatly facilitates the recycle of quantum resources. Security analyses indicate that the designed scheme is secure against external attack and internal attack. Moreover, the operations involved in our scheme are simulated on the IBM Quantum Experience to demonstrate the effectiveness and security of our scheme.
Abstract Semi-quantum private comparison is a method for private comparison with fewer quantum resources, enabling classical participants to collaborate with a semi-honest third party possessing complete quantum capabilities. A one-way quantum private comparison protocol is devised only by unitary operations. The protocol facilitates one-way transmission between third party (TP) and classical participants in quantum communication, where the classical participants only need to perform unitary operations and measurement operations on the transmitted qubits. In addition, classical participants do not require pre-shared keys. It is shown that the qubit efficiency of this protocol is 12.5%. Finally, security analysis and the simulation results on the IBM Quantum Experience demonstrate the security and the feasibility of this protocol.
The socialist millionaires' problem, emanating from the millionaires’ problem, allows two millionaires to determine whether they happen to be equally rich while remaining their riches undisclosed to each other. Most of the current quantum solutions to the socialist millionaires’ problem have lower efficiency and are theoretically feasible. In this paper, we introduce a practical quantum secure protocol for the socialist millionaires’ problem based on single photons, which can be easily implemented and manipulated with current technology. Our protocol necessitates the involvement of a semi-honest third party (TP) responsible for preparing the single-photon sequences and transmitting them to Alice who performs Identity or Hadamard operations on the received quantum sequences via her private inputs and the secret keys, producing new quantum sequences that are subsequently sent to Bob. Similarly, Bob encodes his private inputs into the received quantum sequences to produce new quantum sequences, which are then sent to TP. By conducting single-particle measurements on the quantum sequences received from Bob, TP can ascertain the equality of private inputs between Alice and Bob, and subsequently communicate the comparison result to them. To assess the feasibility, the proposed protocol is simulated on IBM Quantum Cloud Platform. Furthermore, security analysis demonstrates that our protocol can withstand attacks from outsiders, such as eavesdroppers, and from insider participants attempting to grab the private input of another participant.
For two participants to compare the equality of their private information without revealing them, a new quantum private protocol with the help of semi-honest third party TP is proposed. Different from previous protocols, the four particle |Wf⟩ state and the |χ+⟩ state are utilized in this protocol as the carriers of quantum information and form the entanglement swapping as basic principle. The simple measurement of quantum states and exclusive-or operation are only required to conduct in this protocol. What’s more, this protocol can compare two bits of two participants’ private information in every comparison time. Meanwhile, it needs no unitary operation to fulfill this protocol. This protocol is feasible and efficient to execute through these aspects. In the end, the security of this protocol is analyzed at great length from two kinds of attacks including the outside attack and the participant attack. And the analysis result shows that this protocol can withstand various kinds of attacks and be secure to perform efficiently.
In this paper, a protocol for quantum millionaire problem with continuous variables is proposed. In the protocol, two participants can compare the values of their fortune with the assistance of a semi-trusted third party (STTP). Only EPR states are exploited in our protocol while most other protocols exploited d-dimensional Bell states. Two participants are just required to perform single particle operations, which makes our protocol more efficiently. Our protocol can ensure fairness, correctness, security and high efficiency as well. In our protocol, only the two participants can deduce the results of comparisons, others include STTP will learn no information. Our protocol can resist various kinds of attacks from both the outside eavesdroppers and the inside participants, even the STTP.