Quantum Electronic Contract Scheme Based on Single Photon

An electronic contract is a contract signed by electronic means, which is widely used in electronic commerce activities. In recent years, with the rapid development of quantum cryptography technology, the quantum electronic contract has been widely studied by researchers. Supported by the basic principles of quantum mechanics, a quantum electronic contract scheme based on the single photon is proposed in this paper. In this scheme, two copies of the same contract are signed by both parties involved, and then a copy of each contract is sent to a trusted third party. The trusted third party verifies the signatures of both parties and compares the signed copies to determine whether the contract is valid. Compared with the previous scheme, this scheme is based on the quantum electronic contract signed by the single photon. Because the single photon is easy to prepare and operate, this scheme is simple and easy to implement. At the same time, the scheme does not need to exchange signatures between the two parties, which reduces the complexity of communication. Nevertheless, it requires both parties and the third party to be honest and trustworthy.


Introduction
Information security is a very important element in information transmission [Jonathan and Phyllis (2019)]. Currently, most of the research on information security is based on mathematical problems such as large number decomposition and discrete logarithm. However, with the rapid development of quantum technology, conventional information security protection methods have hidden dangers. As a result, many scholars study information protection technology [Wang, Gao, Liu et al. (2019)] based on quantum mechanics. Quantum key distribution (QKD) is the ability of both parties to generate and share a random, secure key to encrypt and decrypt messages. In 1984, Bennett et al. [Bennett and Brassard (1984)] proposed the first quantum key distribution protocol-BB84 protocol. In 1992, Bennett et al. [Bennett and Wiesner (1992)] designed the B92 protocol based on non-orthogonal state by using quantum entanglement. In 1995, Goldenberg et al. scholars from the University of Lisbon proposed a quantum contract signing scheme based on entangled pairs [Yadav, Mateus, Paunkovic et al. (2019)]. This paper proposes a quantum photo-based contract scheme based on the single photon. In this scheme, the signing parties sign two copies of the same contract and send copies of their respective signed contracts to a third party. The third party verifies and compares the copies of the two signatures by means of the correlation of the Bell state particles, and checks whether the signing parties signed the same contract and whether they signed the contract without the impersonation. If the verification is passed, the third party determines that the parties to the contract have reached an agreement, then the contract is valid; otherwise the contract is invalid. Since the program reduces the number of steps between signing parties to exchange signatures, both parties to the contract and the third party must be honest and reliable. In addition, the operation of the third party enables the contract signing parties to communicate securely in the presence of Eve, and can detect and terminate the communication timely when Eve intervenes in the solution.

Quantum scheme of an electronic contract
This scheme includes two contract signers Alice, Bob and a trusted third party Charlie. Alice and Bob sign two copies of the same contract, and then they send their signed copies of the contract to Charlie, who checks whether the two signed copies are the same. This scheme includes three phases: initialization phase, signing phase and verification phase.

Initialization phase
(1) Charlie and Alice share their keys through QKD, (2) Charlie prepares quantum sequences randomly as (3) Charlie performs corresponding unitary operations on A S according to A k (Tab. 1 for specific operation rules). The four unitary operations are expressed as Eqs. (1)-(4): The sequence after the pass-through operation is recorded as ' A S . In order to detect the eavesdropping, Charlie inserts a decoy photon sequence into the sequence ' A S and declines the state of particles in a photon sequence randomly from to Alice. When Alice receives the sequence ' A S , she informs Charlie that she has received the sequence. Then Charlie tells Alice the position and measurement base of the trapped photon.
Alice uses the measurement base published by Charlie to measure the trapped photon and publish the measurement results. Charlie analyzes the error rate. If the error rate is higher than the threshold, stop the process. Otherwise, proceed to the next stage. S , he informs Charlie that he has received the sequence. Then Charlie tells Bob the position and measurement base of the trapped photon. Bob uses the measurement base published by Charlie to measure the trapped photon and publish the measurement results. Charlie analyzes the error rate. If the error rate is higher than the threshold, stop the process. Otherwise, proceed to the next stage.

Signing phase
(1) Alice and Bob sign two copies of the same contract separately. (2) Alice discards the decoy photon, measures ' A S with a Z basis, and records the measurement a . Then Alice entangles A R and A P in Bell state according to priority. The steps are as follows: Step ①: A R first passes Hadamard Gate to transform into } r ,..., r ,..., . Hadamard Gate can be represented as: Step ②:   (3) Alice performs the unitary operation on the first particle of A Θ according to A k (Table 1 for

Verification phase
(1) After Charlie received the signature sent by Alice, he measures   If they are the same, the contract will take effect. Otherwise, the contract will not take effect. This scheme is illustrated in Fig. 1

.1 Non-repudiation of signature contracts
In the initial stage, Charlie randomly generates quantum sequences A S and B S , and sends them to Alice and Bob respectively through the unitary operation. Alice and Bob carry out the z-based measurement on the quantum sequences ' A S and ' B S received respectively, And then they entangle the Bell state with the particle sequence encoded by the contract copy in order, perform the unitary operation after getting A Θ and B Θ . Alice and Bob send  , which is close to 1. Hence, this quantum electronic contract has no impersonation. , which is close to 1; therefore, the program can resist interception/measurement/ retransmission attacks.

Eavesdropping detection
In the quantum channel, if there is a man-in-the-middle attack, then in the initial stage, Charlie sends a sequence S with a deceptive photon to Alice and Bob. If the channel is not safe, the eavesdropper must perform the particle before Alice and Bob receive the particle measured. At this time, Charlie does not announce the location and state of detecting the photon. The eavesdropper does not know the location and state of the photon, so he cannot choose the correct base to decoy the photon. According to the quantum immeasurable theorem, the state of the particle changes after being measured. Then, after Alice and Bob's measurement of the temptation of photons, Charlie will find that the state of the nuzzle photons inserted is different. Then, the eavesdroppers will be discovered. As a result, they will give up the newsletter.

Summary
A single photon-based quantum electron contract scheme is proposed in this paper. A trusted third party can verify and compare whether the two signing parties sign the same contract by means of the relevance of the Bell state, that is, whether the parties signing the contract have reached an agreement; at the same time, it guarantees the non-repudiation and impersonation of the signed contract. This solution reduces the steps of exchanging signatures between contract-signing parties and reduces communication complexity. At the same time, this scheme is to operate on the single photon, which is easy to operate and easy to implement. In the presence of Eve, it is possible to communicate securely, and when Eve intervenes in the solution, the scheme can detect and terminate the communication in time to ensure security.