Multi-party semi-quantum synchronous price increasing auction method based on single particle state

Abstract

The invention discloses a multi-party semi-quantum synchronous price increasing auction method based on a single particle state, and the method comprises the steps: generating particles through an honest quantum user HTP, generating different quantum sequences for different participants, and distributing different key sequences; performing eavesdropping detection on a quantum channel between the quantum user HTP and each participant Pi; and each participant determines whether to bid, performs corresponding unitary operation in the corresponding quantum sequence, completes bid intention identification and identity code verification, generates a private bid sequence to perform unitary operation on the corresponding particle, completes bid, and sends the bid to the quantum user. And the quantum user HTP publishes the highest bid of each item, a new round of auction quantum sequence is generated, and the auction is finished until no new highest bid appears on all items. According to the invention, synchronous price increasing auction of multiple items can be realized among users with different quantum operation capabilities.

Description

Technical Field

[0001] The present invention belongs to the field of quantum communication, and specifically relates to a multi-party semi-quantum synchronous ascending price auction method based on single-particle states. Background Art

[0002] Quantum cryptography is an important research direction in the field of quantum information. Combining the advantages of quantum physics and traditional cryptography, it has become a current research hotspot. After years of development, quantum cryptography has achieved remarkable results in aspects such as Quantum Key Distribution (QKD), Quantum Secure Direct Communication (QSDC), and Quantum Secret Sharing (QSS). These technologies have been widely applied in the field of e-commerce, such as quantum voting and quantum transactions, promoting the innovation and development of related industries.

[0003] As a special trading method, auctions play an important role in social life. Common auction types include English auctions, Dutch auctions, and sealed-bid auctions. Auctions can be divided into open auctions and sealed-price auctions. Traditional English auctions and Dutch auctions belong to open auctions, with the whole process being transparent, and bidders can understand price changes in real time. In contrast, sealed-bid auctions allow bidders to submit prices secretly, protecting the privacy of bidders. This method is particularly suitable for auction scenarios that require confidentiality, ensuring that the private information of each participant is not leaked.

[0004] However, the security of traditional sealed-auction schemes often relies on classical cryptography, and its encryption mechanism is based on mathematical complexity. However, with the rapid development of quantum technology, the computational advantages brought by quantum mechanics pose a serious threat to classical cryptographic systems. For example, the Shor quantum algorithm can solve the factorization problem in polynomial time. The Grover algorithm can accelerate the search efficiency to the square root level in the search of an unordered database, which means that sealed-auction schemes assisted by classical cryptographic techniques are vulnerable to attacks by quantum adversaries.

[0005] In this context, the research and development of the Quantum Sealed-bid Auction (QSA) protocol has become the focus of the academic community. However, the existing quantum sealed-bid auction protocols have some limitations, especially in the case of difficult quantum resource preparation. These protocols mainly focus on single-item auctions, while the research and application of multi-item auctions are relatively less. Under the current quantum technology conditions, the preparation of quantum resources is still relatively difficult, and not all bidders can afford complex quantum operations. To solve this problem, researchers have proposed the concept of Semi Quantum Secure Multiparty Summation (SQSMS), which has received extensive attention. The semi-quantum secure multiparty summation protocol is different from the traditional Quantum Secure Multiparty Summation (QSMS) protocol in that it allows users to have different levels of quantum capabilities.

[0006] In summary, it is of great practical significance to research and develop a quantum synchronous ascending-price auction scheme that can be implemented among users with different quantum operation capabilities. The design of this scheme can not only solve the difficulties of existing protocols in quantum resource preparation, but also expand the application scope of quantum auctions, making it applicable to multi-item auction scenarios. By allowing users to have different levels of quantum capabilities, the scheme reduces the participation threshold, enables more users to participate, and improves the fairness and efficiency of the auction. At the same time, this innovation also provides a new idea for solving the complexity problems existing in traditional auctions, and promotes the application and development of quantum technology in actual economic activities. With the continuous progress of technology, this scheme is expected to play a greater role in the commercial and social fields. Summary of the Invention

[0007] The purpose of the present invention is to provide a multi-party semi-quantum synchronous ascending-price auction method based on single-particle states, through which multi-item synchronous ascending-price auctions can be realized among users with different quantum operation capabilities.

[0008] The purpose of the present invention is achieved through the following technical solutions:

[0009] A multi-party semi-quantum synchronous ascending-price auction method based on single-particle states, which is divided into four stages:

[0010] 1) First, an honest quantum user HTP generates particles, generates different quantum sequences for different participants, and at the same time assigns different key sequences to different participants. It should be noted that the particles generated by the quantum user HTP for participants in the same group are the same, and the particles generated by the quantum user HTP for participants in different groups are different.

[0011] 2) Perform eavesdropping detection on the quantum channel between the quantum user HTP and each participant Pi according to the following specific scheme.

[0012] 3) Again, each participant determines whether to bid, performs the corresponding unitary operation on the corresponding quantum sequence, completes the bidding intention identification and identity coding verification, and at the same time, each participant generates a private bidding sequence to perform unitary operations on the corresponding particles, completes the bid, and sends it to the quantum user.

[0013] 4) Finally, the quantum user HTP announces the highest bid for each item according to the following specific plan and generates a new round of auction quantum sequence until there is no new highest bid for all items and the auction ends.

[0014] The specific method workflow is as follows:

[0015] Step 1: Initialization phase. First, the honest quantum user Honest Third Party (HTP) randomly generates rotating state particles and decoy particles, and uses the key placement between the quantum user HTP and the semi-quantum participant Pi (i = 1, 2, 3, ..., n) to form different quantum sequences Seq for different participants. i .

[0016] Step 2: Eavesdropping detection phase. Semi-quantum participant Pi determines the quantum sequence Seq according to the key K'i sequence" i After receiving the particles directly reflected back by the semi-quantum participant Pi in sequence, the quantum user HTP uses the corresponding measurement basis to measure and calculates the error rate of the measurement result with reference to the initially prepared quantum state. If the error rate exceeds a certain threshold, it terminates; otherwise, it proceeds to the next step.

[0017] Step 3: Bidding intention identification and identity coding stage. The semi-quantum participant Pi performs the corresponding unitary operation at the first position of the rotating particle sequence to complete the bidding intention identification; according to the value of the private vector vi, the identity is encoded in the corresponding grouped particle sequence, and σ is encoded in the non-corresponding grouped sequence. I Operation; perform corresponding unitary operations on the corresponding particle sequence according to the private bidding binary sequence, and make corresponding commitments for the bids of each item in each round to complete the specific bid. After all the above operations are completed, send the remaining quantum sequences in order to the quantum user HTP bit by bit.

[0018] Step 4: Highest bid announcement stage. After the quantum user HTP receives the quantum sequences returned by each participant Pi one by one in order, it first verifies the identity codes of each participant Pi, measures the quantum sequences of each participant Pi one by one using the corresponding measurement bases, generates a measurement comparison result matrix of the quantum sequences, calculates the modulo-n sum of each column of the matrix, and compares it with the identity code in Scheme 1, and announces whether the identity code is successful this time according to the rules. Secondly, using the corresponding measurement bases, it measures the bid intention particles and the specific bid particle sequences of each quantum sequence, and announces the highest bid for each item in the first round of auction according to the rules. After all participants negotiate the starting price of the next round of auction, repeat the above process until there is no new highest bid for all auction items, then the auction ends. At the same time, the quantum user HTP publicly announces the highest bid for each item according to the rules, the highest bidder for each item makes a public commitment, and other participants and the quantum user HTP conduct verification according to the rules.

[0019] Furthermore, in the initialization stage, the quantum user HTP randomly generates rotation state particles R’i (a total of (n(log2(d - 1)+n + 1)) particles) and decoy particles C’i (a total of nm particles) in groups from the particle states {|0>, |1>, |+>, |->}. It should be noted that according to the groups divided in Scheme 1, in the stage of Scheme 2, the rotation state particles and decoy particles generated in the same group (quantum user HTP) are the same, while the rotation state particles and decoy particles generated between different groups are different.

[0020] Generation of quantum sequences. The quantum user HTP places the rotation state particles and decoy particles according to the following rules.

[0021] If the key between the quantum user HTP and the participant Pi then place rotation state particles;

[0022] If the key between the quantum user HTP and the participant Pi then place decoy particles.

[0023] After placement, the rotation state particles and decoy state particles together form the quantum sequence Seq”. i , after placement, divide the quantum sequence Seq” according to the groups in Scheme 1 i and send it to each participant Pi. It should be noted that the rotation state particles and decoy particles generated in the same group are the same, but due to the different keys between each participant and the quantum user, the generated quantum sequence Seq” i is different.

[0024] In the wiretap detection stage, after each participant Pi generates the received quantum sequence Seq” i , according to the value of the key , determine the destination of the particles. If Then the participant Pi directly reflects the particles to the HTP in sequence. If then the participant Pi temporarily retains the particles in hand and waits for the operations in the bid intention identification and identity encoding stage.

[0025] After the quantum user HTP receives the particles directly reflected by each participant Pi, it combines the key value and the prepared measurement basis information to detect eavesdroppers. Calculate the error rate of the measurement results using the initial state. If the error rate exceeds a certain threshold, this scheme is aborted; otherwise, this scheme proceeds to the next step.

[0026] In the bid intention identification and identity encoding stage, after each participant Pi directly reflects the decoy particles to the HTP according to the key Ki sequence, only the rotated particles remain in hand. The quantum user HTP and each participant Pi have pre-negotiated and default that the first bit of the rotated particle sequence (quantum sequence Seq” i (removing the decoy particles without changing the positions of the rotated particles) is the bid intention particle, and the n bits of particles following the first bit together constitute the identity encoding sequence of each participant Pi. After identity encoding, it is the specific bid particle sequence (a total of log2(d - 1)). The first-round bid range is [0, d - 1]. Each participant Pi converts his bid (p is the p-th auction item, p = 1, 2, 3,..., q) into the corresponding private bid binary sequence. The encoding rules for each participant are as follows:

[0027] (1) First, each participant encodes his identity code (only encodes the serial number, not the group number) in the identity encoding sequence according to the group divided by Scheme 1. If the private vector vi = 0, then the participant Pi performs the σ I operation on the particles in hand; if the private vector vi = 1, then the participant performs the σ Y operation on the particles in hand.

[0028] Y operation (identity encoding) I operation (identity encoding) |0> Y|0> = i|1> I|0>＝|0> |1> Y|1> = -i|0> I|1>＝|1> |+> Y|+> = i|-> I|+>＝|+> |-> Y|-> = i|+> I|->＝|->

[0029] (2) If each participant Pi has a bid intention for the item in this auction, then perform the H gate operation on the bid intention particle, and encode it one by one from right to left in the specific bid particle sequence according to the private bid binary sequence of each participant. If the private bid binary sequence v’i = 0, then the participant performs the σ I operation on the particles in hand; if the private bid binary sequence v’i = 1, then the participant performs the σ Y operation on the particles in hand. Otherwise, perform the σ I operation on the bid intention particle, and the specific bid particle sequence performs the σ I operation accordingly.

[0030]

[0031] (3) While performing quantum operations, each participant Pi uses a hash function to commit to the bid for each item in each round. The honest quantum user HTP records the commitment values of each participant's bids for each item in each round. The rules are as follows:

[0032] Each participant Pi randomly selects an integer (where i = 1, 2, ……, n; p =), and calculates where is the decimal bid of each participant for each item in each round. Each participant can update the bid for each item in each round, but the update must be made at the quantum user HTP to commit to the updated bid.

[0033] (4) Each participant returns the encoded (unitary operation) particle sequence Seq”’ i to HTP bit by bit in order.

[0034] In the highest bid announcement stage, after the quantum user HTP receives the quantum sequences Seq”’ i from each participant, it operates according to the following scheme:

[0035] (1) First, verify the identity coding sequences of each quantum sequence. In Scheme 1, the quantum user HTP records the identity coding (including group number and serial number) of each participant. According to the secret key between the quantum user and each participant, combined with the initial state of the particle at this position, use the corresponding measurement basis to measure the identity coding quantum sequences of each user in groups.

[0036] If the measurement basis is the computational basis and the measurement result is opposite to the initial state of the particle at this position, then (where i is a participant in the same group; j = 1, 2, 3, ……, n) Otherwise,

[0037] If the measurement basis is the Fourier basis and the measurement result is opposite to the initial state of the particle at this position, then (where i is a participant in the same group; j = 1, 2, 3, ……, n) Otherwise,

[0038]

[0039] The quantum user HTP forms the measurement comparison results into a matrix, and performs modulo-n addition on each column. The rules are as follows: If each column of the matrix is (Note that if all participants do not perform identity coding at a certain position, then this column ) and the measurement comparison result here should be consistent with the summation result in Scheme 1, indicating that the identity code distribution is successful and there is no duplicate identity code; otherwise, it indicates that the identity code distribution fails and the protocol is aborted.

[0040] (3) Secondly, if each participant has an intention to bid on the item in the auction, perform an H gate operation on the bid intention particle. If the initial preparation basis is the computational basis, the measurement basis is the Fourier basis.

[0041] If the initial state of the particle at this position is |0> and the measurement result is |+>, it indicates that the participant has an intention to bid.

[0042] If the initial state of the particle at this position is |1> and the measurement result is |->, it indicates that the participant has an intention to bid.

[0043] If the initial preparation basis is the Fourier basis, the measurement basis is the computational basis.

[0044] If the initial state of the particle at this position is |+> and the measurement result is |0>, it indicates that the participant has an intention to bid.

[0045] If the initial state of the particle at this position is |-> and the measurement result is |1>, it indicates that the participant has an intention to bid.

[0046] If the participant has no intention to bid on the item in the auction, perform a σ I operation. Regardless of the measurement result, it indicates that the participant has no intention to bid on the item in the auction.

[0047] Result of H gate operation Measurement result of quantum user HTP Bid intention |0> |+> |+> Bid |0> |+> |-> Reject bid |1> |-> |-> Bid |1> |-> |+> Reject bid |+> |0> |0> Bid |+> |0> |0> Reject bid |-> |1> |1> Bid |-> |1> |0> Reject bid

[0048] (3) Thirdly, the quantum user HTP measures the specific bid particle sequence sequentially from right to left bit by bit:

[0049] If the measurement basis is the computational basis and the measurement result is opposite to the initial state of the particle at this position, then Otherwise,

[0050] If the measurement basis is the Fourier basis and the measurement result is opposite to the initial state of the particle at this position, then Otherwise,

[0051]

[0052]

[0053] It should be noted that if the measurement comparison result of a specific bid particle sequence If they are all 0, regardless of the measurement result of the bid-intention particles, it means that the participant has no bid intention for the auction item. The quantum user HTP measures the specific bid sequence (bid private binary sequence) of the participant for the auction item Arrange them bit by bit in order. After the arrangement is completed, convert them into the corresponding decimal data, and select the highest first-round bid for the item and announce it on the bulletin board (or broadcast it through the classical channel).

[0054] Repeat the above process for the first-round bids of multiple items.

[0055] When the first-round bids for all auction items are completed, the participants negotiate the price increase range for each round, that is, the starting price for the next round of auction. For example, the participants negotiate that the starting price for each round of auction except the first round is increased by 10% based on the highest bid in the previous round of the item. The starting price for the next round becomes (1 + 10%) × [the highest bid in the previous round], and repeat the above process.

[0056] After the quantum user HTP receives the quantum sequences of all participants, perform the operation in Step4. If the decimal data converted from the measurement result is not higher than the highest bid for the item in the previous round, the highest bid on the bulletin board is not updated. The sign of the end of the auction is: if the highest bids for all items are not updated, announce the highest bids for all items on the bulletin board (or through classical communication).

[0057] The highest bidder for each item announces the random number in the commitment stage, and other participants calculate until there is no complaint from the complainant, and the auction is completed. The complaint rules are as follows:

[0058] 1. Assume that participant Pj is the highest bidder for an item. He will publicly disclose his bid for the item and the random number Other participants calculate and verify his

[0059] 2. If participant Pj passes the verification of all other participants and the quantum user HTP, then he will be the highest bidder for the item; otherwise, the verification fails.

[0060] 3. If a participant Po (o ≠ j, o = 0, 1, 2,..., n) claims that his bid for the item is higher than the highest bid for the item announced by the quantum user HTP, then participant Po will initiate a complaint. At this time, participant Po will publicly disclose his bid for the item and the random number Other participants and the quantum user HTP verify whether the bid of Po is higher. If the verification is successful, the quantum user HTP will update the highest bid and the highest bidder of the item. If the verification fails, indicating that the complaint fails, the quantum user HTP will maintain the highest bid and the highest bidder of the item.

[0061] 4. If no participant complains about the final result, then participant Pj will be the highest bidder of the item.

[0062] In the present invention, the multi-party semi-quantum identity encoding distribution method based on single-particle states is divided into four stages:

[0063] First, the honest quantum user HTP generates particles, generates different quantum sequences for different participants, and at the same time assigns different key sequences to different participants. Secondly, the quantum channels between the quantum user and each participant are detected for eavesdropping according to the following specific scheme. Thirdly, different participants determine their respective groups and generate private vectors to perform unitary operations on the corresponding particles to complete identity encoding and send it to the quantum user. Finally, the quantum user announces whether the identity encoding is successfully distributed according to the following specific scheme.

[0064] The working process of the method is as follows:

[0065] 1) Initialization stage. The method proposed in the present invention first has the honest quantum user Honest Third Party (HTP)

[0066] randomly generate rotated state particles and decoy particles, and use the key placement between the quantum user HTP and the semi-quantum participant Pi (i = 1, 2, 3,..., n) to form different quantum sequences Seq i .

[0067] 2) Eavesdropping detection stage. The semi-quantum participant Pi decides the destination of the particles in the quantum sequence Seq according to the key Ki sequence. After the quantum user HTP receives the particles directly reflected bit by bit in sequence by the semi-quantum participant Pi, it performs measurements using the corresponding measurement bases, calculates the error rate of the measurement results with reference to the initially prepared quantum state. If the error rate exceeds a certain threshold, it terminates; otherwise, it proceeds to the next step. i 3) Identity encoding stage. The semi-quantum participant Pi measures the first grouped particles using the corresponding measurement bases according to the pre-negotiated rules and the measurement bases of the quantum user HTP on the bulletin board, determines their respective groups, and at the same time generates a private vector vi. According to the value of the private vector vi, identity encoding is performed on the corresponding grouped particle sequence, and σ

[0068] operations are performed on the non-corresponding grouped sequences. After the operation is completed, the remaining quantum sequence Seq' in hand is sent bit by bit in sequence I in order.i Sent to quantum user HTP.

[0069] 4) Result announcement stage. Quantum user HTP first calculates the grouping of each participant Pi. Using the corresponding measurement bases, it measures the quantum sequence Seq' of each participant Pi bit by bit in sequence i , generating the measurement comparison result matrix of the quantum sequence Seq' i , calculates the modulo-n sum of each column of the matrix, and announces whether the identity coding is successfully distributed this time according to the rules.

[0070] The multi-party semi-quantum identity coding distribution method based on single-particle states proposed by the present invention uses the Pre-grouping and Main-computing ideas proposed by Shi in "Quantum Secret Permutating Protocol" to distribute the identity coding of each participant Pi.

[0071] Before the technical solution starts, the present invention assumes that the communication model has 1 honest third party as the quantum user HTP, with complete quantum operation capabilities; n participants Pi are semi-quantum users, with the quantum operation capabilities of computational basis and Fourier basis measurements, unitary operations, and directly reflecting quantum states. The quantum user HTP assigns different key Ki sequences to different participants Pi, where

[0072] Step1: Initialization stage. The quantum user HTP randomly generates rotation state particles Ri (a total of 4n 2 +n) and decoy particles Ci (a total of nm) from the particle states {|0>, |1>, |+>, |->}.

[0073] Step2: Generation of quantum sequence. The quantum user places the rotation state particles and decoy particles according to the following rules.

[0074] If the key between the quantum user and the participant Pi then place rotation state particles;

[0075] If the key between the quantum user and the participant Pi then place decoy particles.

[0076] After the placement is completed, the rotation state particles and decoy state particles together form the quantum sequence Seq i , after the placement is completed, the quantum sequence Seq i (each quantum sequence has (4n + 1 + m)) is sent to each participant Pi.

[0077] Step3: Eve detection stage. After each participant Pi generates the received quantum sequence Seq i , according to the key The value determines the direction of the particle. If then each participant Pi directly reflects the particle bit by bit in sequence to the HTP. If then the participant temporarily retains the particle in hand and waits for the operation in Step 5.

[0078] Step 4: After the quantum user HTP receives the particles directly reflected by each participant Pi, it performs eavesdropper detection by combining the value of the key and the prepared measurement basis information. Calculate the error rate of the measurement results using the initial state. If the error rate exceeds a certain threshold, this scheme terminates; otherwise, this scheme proceeds to the next step.

[0079] Step 5: Identity encoding stage. After each participant Pi directly reflects the decoy particles to the HTP according to the key Ki, only the rotated particles remain in hand. The quantum user HTP and each participant Pi have pre-negotiated and default that the first bit of the rotated particle sequence (quantum sequence Seq i with the decoy particles removed and the positions of the rotated particles unchanged) is the grouped particle. The quantum user HTP announces (or broadcasts through the classical channel) the measurement basis of the first rotated particle on the bulletin board. The grouping rules are as follows:

[0080] If the measurement result of participant Pi is |0>, it means that this participant is assigned to group 1;

[0081] If the measurement result of participant Pi is |1>, it means that this participant is assigned to group 2;

[0082] If the measurement result of participant Pi is |+>, it means that this participant is assigned to group 3;

[0083] If the measurement result of participant Pi is |->, it means that this participant is assigned to group 4;

[0084] Step 6: After each participant Pi measures the grouped particles, a private vector vi (n bits) is randomly generated, where only 1 component in the corresponding group is 1 and the remaining components are 0. Each participant performs a unitary transformation on the remaining particles in hand according to the private vector vi. The rules are as follows:

[0085] If the private vector vi = 0, the participant performs a σ I operation on the particles in hand;

[0086] If the private vector vi = 1, the participant performs a σ Y operation on the particles in hand;

[0087] After the unitary transformation operation, each participant Pi sends the remaining quantum sequence Seq' i in hand bit by bit in sequence to the quantum user HTP.

[0088] For example, assume that the result of participant P1 measuring the first grouped particle is |0>. Then participant P1 is assigned to group 1, and P1 has the remaining particles in group 1 (the first to nth positions, a total of n particles), the particles in group 2 (the (n + 1)th to 2nth positions, a total of n particles), the particles in group 3 (the (2n + 1)th to 3nth positions, a total of n particles), the particles in group 4 (the (3n + 1)th to 4nth positions, a total of n particles), and the randomly generated private vector is v1 = (0, 1, 0, 0,..., 0). Then P1 performs a σ Y operation on the second position of the particles in group 1, and a σ I operation on the other particles. After the operation is completed, the remaining quantum sequence Seq’ i is sent to the quantum user HTP.

[0089] Step7: Result announcement stage. After the quantum user HTP receives the quantum sequences Seq’ i from each participant Pi, it first verifies the first grouped particles of each quantum sequence. According to the secret keys between the quantum user HTP and each participant and combined with the initial state of the particles at this position, the quantum user HTP deduces the grouping of each participant Pi. The quantum sequences Seq’ i of each participant Pi are measured bit by bit in order using the corresponding measurement bases. The rules are as follows (as shown in the table):

[0090] If the prepared measurement basis is the computational basis and the measurement result is opposite to the initial state of the particle at this position, then (where i = 1, 2, 3,..., n; j = 1, 2, 3,..., 4n) Otherwise,

[0091] If the measurement basis is the Fourier basis and the measurement result is opposite to the initial state of the particle at this position, then (where i = 1, 2, 3,..., n; j = 1, 2, 3,..., 4n) Otherwise,

[0092]

[0093] It should be noted that the global phase does not affect the measurement result. In the computational basis, the measurement results of i|1> and -i|0> are |1> and |0> respectively, and the global phase does not affect the measurement result. In the Fourier basis, the measurement results of i|-> and i|+> are |-> and |+> respectively, and the global phase does not affect the measurement result.

[0094] The quantum user HTP compares the measurement results i of the quantum sequences Seq’ Construct an \(n\times4n\) matrix, and perform modulo \(n\) addition on each column. The rules are as follows: If each column of the matrix is (Note that if all participants do not encode their identities at a certain position, then this column ), it indicates that the identity encoding is successfully distributed and there are no duplicate identity encodings; otherwise, it indicates that the identity encoding distribution fails, and the above process of Step 1 - Step 7 is repeated. During the repeated process, each participant regenerates its private vector.

[0095] Note that if the quantum user HTP deduces the grouping, but the encoded values of the participants' private vectors are not encoded into the specified grouped quantum sequences, then the identity encoding fails, and the above process of Step 1 - Step 7 is repeated. The sign of successful identity encoding distribution is that the private vectors \(v_i\) of all participants \(P_i\) are encoded into the correct groups and there are no duplicate identity encodings among the groups.

[0096] The beneficial effects of the present invention are as follows:

[0097] The present invention can not only solve the difficulties in quantum resource preparation of existing protocols, but also expand the application scope of quantum auctions, making it applicable to the auction scenarios of multiple items. By allowing users to have different degrees of quantum capabilities, the scheme reduces the participation threshold, enabling more users to participate, and improving the fairness and efficiency of the auction. At the same time, it also provides a new idea for solving the complexity problems existing in traditional auctions, promoting the application and development of quantum technology in actual economic activities. With the continuous progress of technology, this scheme is expected to play a greater role in the commercial and social fields.

[0098] Through this method, it is possible to realize the synchronous ascending-price auction of multiple items among users with different quantum operation capabilities. Brief Description of the Drawings

[0099] Figure 1 Flowchart of multi-party semi-quantum synchronous ascending-price auction based on single-particle states.

[0100] Figure 2 Flowchart of multi-party semi-quantum identity encoding distribution based on single-particle states. Detailed Embodiments

[0101] The present invention will be specifically introduced below in conjunction with the accompanying drawings and specific examples.

[0102] Synchronous price-increasing auction is a mechanism applicable to the simultaneous auction of multiple items. Its core feature is that bidders submit sealed bids for items in each round, ensuring the privacy of the bids. The auction starts from the first round without a starting price, and bidders can freely bid within a certain range. After each round, the auctioneer announces the highest bid for each item and uses it as the starting price for the next round (raising it by 5%-10% based on the highest bids of each item in the previous round). This process continues until there are no new highest bids for all items in a certain round, at which point the auction ends.

[0103] In the present invention, quantum users have complete quantum operation capabilities, including preparing and measuring any quantum state. Semi-quantum users have limited quantum operation capabilities, usually limited to performing limited measurements on quantum states, unitary operations, and directly reflecting quantum states. The computational basis is the most commonly used basis in quantum computing, consisting of |0> and |1>. The Fourier basis is obtained through the quantum Fourier transform (QFT). For a single qubit, its Fourier basis consists of |+> and |->, expressed as:

[0104]

[0105] Unitary operation: An operation is unitary if its matrix satisfies where is the conjugate transpose of U, and I is the identity matrix. Several simple unitary operations are introduced below.

[0106] The matrix of the I operation is:

[0107]

[0108] The actions of the I operation on a single qubit are respectively:

[0109] I operation |0> I|0>＝|0> |1> I|1>＝|1> |+> I|+>＝|+> - I-＝-

[0110] The matrix of the Y operation is:

[0111]

[0112] The actions of the Y operation on a single qubit are respectively:

[0113] Y operation |0> Y|0> = i|1> |1> Y|1> = -i|0> |+> Y|+> = i-0> |-> Y|-> = i|+>

[0114] The matrix of the H gate (Hadamard gate) operation is:

[0115]

[0116] The actions of the Z operation on a single qubit are respectively:

[0117] H gate operation |0> H|0>＝|+> |1> H|1>＝|-> |+> H|+>＝|0> |-> H|->＝|1>

[0118] A multi-party semi-quantum synchronous ascending auction method based on single-particle states, which is divided into the following four stages:

[0119] 1) The honest quantum user HTP generates particles, generates different quantum sequences for different participants, and at the same time assigns different key sequences to different participants. The particles generated by the quantum user HTP for participants in the same group are the same, and the particles generated by the quantum user HTP for participants in different groups are different;

[0120] 2) Detect eavesdropping on the quantum channels between the quantum user HTP and each participant Pi;

[0121] 3) Each participant determines whether to bid, performs corresponding unitary operations on the corresponding quantum sequence, completes the bid intention identification and identity coding verification. At the same time, each participant generates a private bid sequence to perform unitary operations on the corresponding particles, completes the bid, and sends it to the quantum user;

[0122] 4) The quantum user HTP announces the highest bid for each item, generates a new round of auction quantum sequences until there are no new highest bids for all items, and the auction ends.

[0123] Specifically as follows:

[0124] Suppose there is 1 honest third party as the quantum user HTP, with complete quantum operation capabilities; 3 participants P1, P2, P3 are semi-quantum users, with unitary operation and quantum operation capabilities of directly reflecting quantum states. Suppose participants P1, P2, P3 both bid on two auction items A and B (in fact, participants P1, P2, P3 choose one or both of the two auction items A and B to bid). For the convenience of demonstration, this example assumes that the auction is completed with only one round of bidding. The quantum user HTP assigns different key sequences K’1, K’2, K’3 to different participants, where:

[0125] K’1 = {0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0},

[0126] K’2 = {1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1},

[0127] K’3 = {1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1}.

[0128] Initialization stage. The quantum user HTP randomly generates rotation state particles R’1, R’2, R’3 and decoy particles C’1, C’2, C’3 from the particle states {|0>, |1>, |+>, |->}, where the rotation state particle sequence:

[0129] R’1 = {|0>, |1>, |+>, |1>, |1>, |0>, |0>, |0>, |->, |->, |+>, |1>, |+>, |1>, |->}

[0130] R’2 = {|+>, |1>, |->, |0>, |0>, |->, |+>, |1>, |+>, |1>, |0>, |+>, |1>, |->, |->}

[0131] R’3 = {|->, |->, |+>, |0>, |1>, |->, |0>, |+>, |->, |1>, |0>, |1>, |+>, |1>, |->}

[0132] Decoy particle sequence:

[0133] C’1 = {|0>, |->, |->, |0>, |+>, |+>, |->, |0>, |+>, |->, |->, |0>, |+>, |1>, |1>}

[0134] C’2 = {|->, |+>, |1>, |->, |+>, |+>, |->, |1>, |1>, |0>, |0>, |1>, |->, |1>, |+>}

[0135] C’3 = {|->, |0>, |1>, |+>, |->, |->, |0>, |0>, |->, |+>, |->, |0>, |+>, |->, |->}

[0136] Generation of quantum sequences Seq”1, Seq”2, Seq”3:

[0137] Seq”1 = {|0>, |->, |+>, |0>, |1>, |+>, |0>, |0>, |+>, |->, |+>, |0>, |+>, |1>, |->}

[0138] Seq”2 = {|->, |1>, |->, |->, |+>, |+>, |+>, |1>, |+>, |1>, |0>, |+>, |->, |->, |+>}

[0139] Seq”3 = {|->, |0>, |+>, |+>, |1>, |->, |0>, |+>, |->, |1>, |->, |0>, |+>, |1>, |->}

[0140] Eavesdropping detection stage. Participants P1, P2, and P3 respectively reflect the highlighted parts in the quantum sequences Seq”1, Seq”2, and Seq”3 bit by bit in order directly to the quantum user HTP. The quantum user uses the prepared measurement basis to detect eavesdroppers and calculate the error rate of the measurement results. If the error rate exceeds a certain threshold, this scheme terminates; otherwise, this scheme proceeds to the next step.

[0141] Bid intention identification and identity coding stage. Participants P1, P2, and P3 respectively make bids on two auction items A and B. The range of their first-round bids is [0, 16], and the price increase interval for each round of auction except the first round is 10%. Participants P1, P2, and P3 respectively perform H-gate operations on the first particles of the remaining particle sequences in the quantum sequences Seq”1, Seq”2, and Seq”3, perform identity coding on the 2nd - 4th bits, and perform specific bid particle coding on the 5th - 8th bits at the same time.

[0142] Suppose the bids of participants P1, P2, and P3 for auction item A are 5, 7, and 8 respectively; and the bids for auction item B are 4, 3, and 9 respectively. Taking the quantum sequence of participant P1 as an example, the first particle of its remaining particle sequence is |0>. Perform an H-gate operation on |0>, and perform corresponding identity coding on the 2nd - 4th bits (in Scheme 1, the identity coding assigned to participant P1 is Group 1, No. 2, and the private vector is (0, 1, 0)). Therefore, participant P1 performs a σ Y operation on the 3rd bit. Since the bid of participant P1 for the auction of item A is 5, which is converted into the corresponding binary sequence (0, 1, 0, 1), therefore participant P1 performs a σ Y operation on the 6th and 8th bits of the remaining quantum sequence, and performs a σ I operation on other bits. After participant P1 completes the corresponding unitary operation on the remaining quantum sequence and makes a commitment to the bid for item A in this round, participant P1 returns the quantum sequence Seq”’1 bit by bit in order to the quantum user HTP. Similarly, participants P2 and P3 also perform corresponding operations and return Seq”’2 and Seq”’3 bit by bit in order to the quantum user HTP.

[0143] The multi-party semi-quantum identity coding method based on single-particle states is as follows:

[0144] The quantum user HTP publishes (or broadcasts through a classical channel) the measurement basis of the first rotating particle on the bulletin board. Participants P1, P2, and P3 respectively measure the first particles of the remaining particle sequences in the quantum sequences Seq1, Seq2, and Seq3. Taking the quantum sequence of participant P1 as an example, the first particle of its remaining particle sequence is |0>. Using the computational basis, the measurement result is |0>, then participant P1 is assigned to Group 1. Similarly, participant P2 is assigned to Group 2, and participant P3 is assigned to Group 3.

[0145] Taking participant P1 as an example, participant P1 randomly generates a private vector v1 = (0, 1, 0), participant P2 randomly generates a private vector v2 = (0, 1, 1), and participant combination P3 randomly generates a private vector v3 = (1, 0, 1). Then participant P1 performs a unitary operation on the 2nd - 4th positions of the remaining particle sequence. Specifically, participant P1 performs a σ Y operation on the 3rd position of the remaining particle sequence, and performs a σ I operation on the 2nd and 4th positions. The particles in other positions do not perform unitary operations, and the quantum sequence Seq’1 after the unitary operation is sent to the quantum user HTP. Similarly, participants P2 and P3 also perform corresponding unitary operations.

[0146] After receiving the quantum sequences Seq’1, Seq’2, and Seq’3 from participants P1, P2, and P3, the quantum user HTP first calculates the groupings of participants P1, P2, and P3. Using the corresponding measurement bases, it measures the quantum sequences Seq’ i of participants P1, P2, and P3 bit by bit in sequence, forming a 3×12 matrix as follows:

[0147]

[0148] The sum of the modulo 3 of each column is: (010011101000), which meets the conditions. Therefore, the identity code distribution is successful and there are no duplicate identity codes.

[0149] Stage of announcing the highest bid. After receiving the quantum sequence HTP, first verify the identity codes according to the groupings (the groupings of participants P1, P2, and P3 in Scheme 1 are all different). Taking participant P1 as an example, the quantum user measures the 2nd - 4th positions of participant P1 using the corresponding measurement basis, and the measurement comparison results form a 1×3 matrix, specifically: (0 1 0). The sum of the modulo 3 of each column meets the conditions. Therefore, the identity verification of participant P1 passes. Similarly, participants P2 and P3 also perform corresponding identity code verifications in groups.

[0150] Secondly, the quantum user HTP measures the first bid-intention particle of participant P1 using the Fourier basis, and the measurement result is |+>, indicating that participant P1 has a bid intention. Then, it measures the specific bid particle sequence (the 5th - 8th bits) using the corresponding measurement basis, and the measurement comparison result forms a 1×4 matrix, specifically: (0, 1, 0, 1), which is converted to the corresponding decimal number 5. Similarly, the quantum user HTP performs corresponding operations on the quantum sequences returned by participant P2 and participant P3, and obtains that the bids of participant P2 and participant P3 for item A are 7 and 8 respectively. Therefore, the quantum user HTP announces on the bulletin board that the highest bid for item A in the auction is 8. At the same time, repeating the above operations, the quantum user HTP obtains that the bids of participant P1, P2, and P3 for item B in the auction are 4, 3, and 9 respectively, and announces on the bulletin board that the highest bid for item B in the auction is 9.

[0151] Thirdly, participants P1, P2, and P3 negotiate that the starting bids for the second-round auctions of item A and item B are 8.8 and 9.9 respectively (i.e., the price increase interval for each round is 10%).

[0152] Finally, the quantum user HTP and participants P1, P2, and P3 repeat all the operations in the above Scheme 2. Finally, it is found that there are no new highest bids for both item A and item B in the auction, and it is verified that there are no complaints. Then it is declared that the highest bids for item A and item B in the auction are 8 and 9 respectively, and the winners are all the participants in Group 3, No. 5 (i.e., participant P3), and the auction ends.

[0153] Through this method, it is possible to realize the synchronous ascending-price auction of multiple items among users with different quantum operation capabilities.

Claims

1. A multi-party semi-quantum synchronous ascending-price auction method based on single-particle states, characterized in that, The method is divided into the following four stages: 1) The honest quantum user HTP generates particles, generates different quantum sequences for different participants, and at the same time assigns different key sequences to different participants. The particles generated by the quantum user HTP for participants in the same group are the same, and the particles generated by the quantum user HTP for participants in different groups are different; 2) Detect eavesdropping on the quantum channels between the quantum user HTP and each participant Pi; 3) Each participant determines whether to place a bid, performs corresponding unitary operations on the corresponding quantum sequences, completes the bid intention identification and identity coding verification, and at the same time each participant generates a private bid sequence, performs unitary operations on the corresponding particles, completes the bid, and sends it to the quantum user; 4) The quantum user HTP announces the highest bid for each item, generates a new round of auction quantum sequences until there are no new highest bids for all items, and the auction ends.

2. The multi-party semi-quantum synchronous ascending-price auction method based on single-particle states according to claim 1, wherein In step 1), honest quantum users randomly generate rotated state particles and decoy particles, and form different quantum sequences Seq ” i for different participants by using the key placement between the quantum user HTP and semi-quantum participants Pi (i = 1, 2, 3,..., n).

3. The multi-party semi-quantum synchronous ascending auction method based on single-particle states according to claim 2, wherein In step 2), the half-quantum participant Pi uses the key K ’ i sequence, determines the quantum sequence Seq ” i The destination of the particles in the quantum user HTP, after receiving the particles directly reflected back by the half-quantum participant Pi in sequence, uses the corresponding measurement basis for measurement, and calculates the error rate of the measurement result with reference to the initially prepared quantum state. If the error rate exceeds a certain threshold, it terminates; otherwise, it goes to step 3).

4. The multi-party semi-quantum synchronous ascending-price auction method based on single-particle states according to claim 3, wherein In step 3), the semi-quantum participant Pi performs the corresponding unitary operation at the first position of the rotating particle sequence to complete the bid intention identification; encodes the identity according to the value of the private vector vi in the corresponding grouped particle sequence, and performs the σ I operation; performs the corresponding unitary operation on the corresponding particle sequence according to the private bid binary sequence, and makes corresponding commitments to the bids for each item in each round to complete the specific bid; after all the above operations are completed, sequentially send the remaining quantum sequences in hand to the quantum user HTP bit by bit.

5. The multi-party semi-quantum synchronous ascending-price auction method based on single-particle states according to claim 4, wherein In step 4), after the quantum user HTP receives the quantum sequences returned bit by bit in order from each participant Pi, first verify the identity coding of each participant Pi, measure the quantum sequences of each participant Pi bit by bit in order using the corresponding measurement basis, generate a measurement comparison result matrix of the quantum sequences, calculate the modulo n sum of each column of the matrix, and compare it with the identity coding, and announce whether the identity coding is successful according to the rules; use the corresponding measurement basis to measure the bid intention particles and the specific bid particle sequences of each quantum sequence, and announce the highest bid for each item in the first round of auction according to the rules; after each participant negotiates the starting price for the next round of auction, repeat the above process until there are no new highest bids for all auction items, then the auction ends; the quantum user HTP publicly announces the highest bid for each item according to the rules, the highest bidder for each item makes a public commitment, and other participants and the quantum user HTP perform verification according to the rules.

6. The multi-party semi-quantum synchronous ascending price auction method based on single-particle states according to claim 2, wherein The quantum user HTP group randomly generates rotation state particles R’i (a total of (n(log2(d - 1)+n + 1)) particles) and decoy particles C ’ i (a total of nm particles) from the particle states {|0>, |1>, |+>, |->}. The rotation state particles and decoy particles generated in the same group (quantum user HTP) are the same, and the rotation state particles and decoy particles generated between different groups are different; For the generation of quantum sequences, the quantum user HTP places rotated state particles and decoy particles according to the following rules; If the key between the quantum user HTP and the participant Pi then place the rotated state particles; If the key between the quantum user HTP and the participant Pi then decoy particles are placed; After placement, the rotation-state particles and decoy-state particles together form a quantum sequence Seq ” i , after placement, the quantum sequence Seq is divided into groups according to the groups formed ” i and sent to each participant Pi; the rotation-state particles and decoy particles generated in the same group are the same. Due to the different keys between each participant and the quantum user, the generated quantum sequence Seq ” i is different.

7. The multi-party semi-quantum synchronous ascending auction method based on single-particle states according to claim 6, wherein Each participant Pi generates the received quantum sequence Seq ” i After that, according to the key value, determine the direction of the particle. If then participant Pi directly reflects the particle to the HTP in sequence. If then participant Pi temporarily retains the particle in hand and waits for the operation of the bid intention identifier and the identity code; After the quantum user HTP receives the particles directly reflected by each participant Pi, it combines the key value and the prepared measurement basis information to detect eavesdroppers; calculates the error rate of the measurement results using the initial state, and if the error rate exceeds a certain threshold, this scheme is aborted; otherwise, proceed to step 3).

8. The multi-party semi-quantum synchronous ascending-price auction method based on single-particle states according to claim 1, characterized in that In step 3), the bid intention identification and identity coding are specifically as follows: After each participant Pi directly reflects the decoy particles to the HTP according to the sequence of secret keys Ki, only the rotated particles are left in their hands. The quantum user HTP and each participant Pi have pre-negotiated and defaulted that the first bit of the rotated particle sequence is the bid intention particle. The n bits of particles following the first bit together constitute the identity coding sequence of each participant Pi. After identity coding, it is the specific bid particle sequence, with a total of log2(d - 1) particles. The first-round bid range is [0, d - 1]. Each participant Pi makes his own bid p is the p-th auction item, p = 1, 2, 3,..., q, which is converted into the corresponding private bid binary sequence. The coding rules for each participant are as follows: (1) First, each participant encodes their identity code according to the divided groups in the identity coding sequence. If the private vector vi = 0, then participant Pi performs a σ I operation on the particle in their hand; if the private vector vi = 1, then the participant performs a σ Y operation on the particle in their hand; (2) If each participant Pi has an intention to bid on the item in the auction, perform an H gate operation on the bid intention particle, and encode it one by one from right to left in the specific bid particle sequence according to the private bid binary sequence of each participant. If the private bid binary sequence v ’ i = 0, then the participant performs a σ I operation on the particle in their hand; if the private bid binary sequence v ’ i = 1, then the participant performs a σ Y operation on the particle in their hand. Otherwise, perform a σ I operation on the bid intention particle, and perform a σ I operation on the specific bid particle sequence accordingly; (3) While performing quantum operations, each participant Pi uses the hash function to commit to the bid for each item in each round. The honest quantum user HTP records the commitment values of each participant's bids for each item in each round. The rules are as follows: Each participant Pi randomly selects an integer (where i = 1, 2, ……, n; p =), and calculate where is the decimal bid of each participant for each item in each round. The bid of each participant for each item is updated in each round, and the commitment to update the bid is made here by the quantum user HTP; (4) Each participant will return the encoded particle sequence Seq ”’ i to the HTP bit by bit in sequence.

9. The multi-party semi-quantum synchronous ascending-price auction method based on single-particle states according to claim 8, characterized in that In the stage of announcing the highest bid, quantum user HTP receives the quantum sequences Seq from each participant ”’ i and then operates according to the following scheme: (1) First, verify the identity coding sequences of each quantum sequence. The quantum user HTP records the identity codes of each participant, and based on the secret keys between the quantum user and each participant Combine the initial state of the particle at this position and use the corresponding measurement basis to group and measure the identity coding quantum sequences of each user; If the measurement basis is the computational basis and the measurement result is opposite to the initial state of the particle at that position, then where i is a participant in the same group; j = 1, 2, 3, ……, n, otherwise If the measurement basis is the Fourier basis and the measurement result is opposite to the initial state of the particle at that position, then where i is a participant in the same group; j = 1, 2, 3, ……, n otherwise The quantum user HTP will measure and compare the results constitute the matrix. The modulo-n sum is performed for each column, and the rules are as follows: If each column of the matrix is If all participants do not perform identity encoding at a certain position, then this column and the measurement and comparison result here is consistent with the sum result, indicating that the identity encoding distribution is successful and there are no duplicate identity encodings; Otherwise, it indicates that the identity coding distribution fails and the protocol is aborted; (2) Secondly, if each participant has an intention to bid for the item in this auction, perform an H gate operation on the bid intention particles. If the initial preparation basis is the computational basis, the measurement basis is the Fourier basis, If the initial state of the particle at this position is |0> and the measurement result is |+>, it indicates that the participant has an intention to bid; If the initial state of the particle at this position is |1> and the measurement result is |->, it indicates that the participant has an intention to bid; If the initial preparation basis is the Fourier basis, the measurement basis is the computational basis, If the initial state of the particle at this position is |+> and the measurement result is |0>, it indicates that the participant has an intention to bid; If the initial state of the particle at this position is |-> and the measurement result is |1>, it indicates that the participant has an intention to bid; If the participant has no intention of bidding on the item in the auction, a σ I operation is performed, and regardless of the measurement result, it indicates that the participant has no intention of bidding on the item in the auction; (3) Thirdly, the quantum user HTP measures the specific bid particle sequences bit by bit in order from right to left: If the measurement basis is the computational basis and the measurement result is opposite to the initial state of the particle at that position, then (l = 1, 2, 3, ……, log2(d - 1)) Otherwise, If the measurement basis is the Fourier basis and the measurement result is opposite to the initial state of the particle at that position, then (l = 1, 2, 3, ……, log2(d - 1)) Otherwise, If the measurement comparison results of a specific sequence of bidding particles are all 0, regardless of the measurement results of the particles with the bidding intention, it means that the participant has no intention of bidding on the auction item; the quantum user HTP arranges the measurement results of the specific bidding sequence of the participant for the auction item bit by bit in order. After the arrangement is completed, it is converted into the corresponding decimal data, and the highest first-round bid for the item is announced.

10. The multi-party semi-quantum synchronous ascending-price auction method based on single-particle states according to claim 1, wherein, In step 4), the highest bidders of each item announce the random numbers in the commitment phase, and other participants perform calculations until no complainant lodges a complaint and the auction is completed. The complaint rules are as follows: (1) Suppose participant Pj is the highest bidder for an item, and his bid for the item will be made public. and a random number Other participants calculate and verify their (2) If participant Pj passes the verification of all other participants and the quantum user HTP, then he will be the highest bidder for the item; otherwise, the verification fails. (3) If a participant Po (o ≠ j, o = 0, 1, 2,..., n) claims that his bid for the item is higher than the highest bid for the item announced by the quantum user HTP, then participant Po will initiate a complaint. At this time, participant Po will disclose his bid for the item. and the random number Other participants and the quantum user HTP verify whether Po's bid is higher. If the verification is successful, the quantum user HTP will update the highest bid for the item and the highest bidder. If the verification fails, indicating that the complaint fails, the quantum user HTP will maintain the highest bid for the item and the highest bidder. (4) If no participant complains about the final result, then participant Pj will be the highest bidder for the item.

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