Quantum anonymous multi-party ranking method based on quantum merge ranking algorithm and application thereof

Abstract

The invention discloses a quantum anonymous multi-party ranking method based on a quantum merge ranking algorithm and application thereof, and belongs to the technical field of quantum security multi-party computing. The method aims at solving the technical problems that an existing quantum anonymous multi-party ranking scheme depends on a semi-honest third party, quantum resource consumption is large, transportability is poor, and the anti-attack ability is insufficient. According to the method, a non-collusion node constraint + modular quantum operation framework is constructed, two non-collusion participants are used for guaranteeing safety, and privacy protection coding is achieved in combination with d-dimensional single particle state, quantum Fourier transform and permutation / shift operation. According to the method, under the condition that no third party participates, distributed data anonymous ranking is dynamically completed on the premise that data privacy and identity association are not leaked by a plurality of participants. Meanwhile, the method is compatible with mainstream quantum sorting algorithms such as quantum merge sorting through modular design, quantum resource consumption is only bound with the size of a data set (independent of the upper limit of a data value), and the resource efficiency is remarkably improved when facing a large-range data set.

Description

Technical Field

[0001] This invention belongs to the field of quantum secure multi-party computation (QSMC) technology, specifically involving a quantum anonymous multi-party ranking method based on the quantum merge sort algorithm, the framework for implementing the method, and its applications. Background Technology

[0002] With the rapid development of multi-party collaboration technologies and large language models, data privacy and security issues are becoming increasingly prominent. To address the risk of sensitive information leakage during collaborative computation by distributed participants, secure multi-party computation (SMC) technology has emerged—allowing distributed nodes to complete collaborative computation without sharing the original data, ensuring that sensitive information is only visible to the data owner. However, the security of traditional SMC technology relies on complex mathematical problems such as large number factorization and discrete logarithms, while breakthroughs in quantum computing technology (such as Shor's algorithm and Grover's algorithm) have posed a potential threat to these classical cryptographic foundations. Therefore, there is an urgent need to reconstruct the secure multi-party computation framework based on fundamental principles of quantum mechanics (such as the uncertainty principle and the quantum no-cloning theorem), making quantum secure multi-party computation (QSMC) a research hotspot.

[0003] Quantum Anonymous Multi-Party Ranking (QAMR), a key subfield of QSMC, aims to achieve the dual goals of "multi-party data ranking" and "participant anonymity"—it needs to output accurate dataset ranking results while hiding the relationship between participants and private data, avoiding identity privacy risks caused by data leakage (such as the leakage of personal preferences in anonymous voting or the exposure of bidding strategies in corporate auctions). Traditional QAMR schemes typically rely on classical cryptographic components (such as public key infrastructure, digital signatures, and commitment schemes) to achieve anonymity, but these components are vulnerable to quantum attacks and cannot meet the privacy protection needs of the quantum era.

[0004] To address the threat of quantum attacks, Huang et al. first proposed the concept of QAMR in 2014, constructing a framework that satisfies four constraints: correct ordering, anonymity, data-identity non-traceability, and resistance to quantum attacks. They designed three specific schemes based on d-dimensional Bell states, GHZ states, and single-particle systems. While the single-particle system-based scheme reduced quantum resource requirements, it still had limitations: it relied on a semi-honest third party for key distribution, and the quantum state dimension was strongly tied to the amount of ordered data, requiring a large number of high-dimensional quantum particles when the total data volume was large, thus limiting its practicality. In the same year, Luo et al. proposed an improved QAMR scheme, optimizing efficiency by reducing the number of key distributions, but it still relied on a semi-honest third party and did not solve the problem of "a surge in quantum resource consumption due to increased data volume."

[0005] To reduce the quantum state dimensionality requirement, in 2016, Lin et al. designed a d-dimensional single-particle QAMR method based on the Chinese Remainder Theorem, improving the practicality of the scheme through data dimensionality compression. However, this scheme did not consider the problem of data tampering by malicious participants, posing a risk of manipulation of the sorting results. In 2020, Wang et al. proposed a verifiable QAMR scheme, allowing participants to verify data integrity through an index, but requiring the user's data volume to be less than the quantum state dimension d, and the quantum sequence length to be greater than the range of the sorted dataset, still resulting in resource waste. In 2021, Li et al. further proposed an index-based QAMR scheme for low-dimensional quantum systems, but this required the introduction of an additional index distribution scheme, increasing the scheme overhead. In 2024, Wang et al. designed a verifiable QAMR scheme combining the law of large numbers and multi-particle entangled states. Although this strengthened the authentication capability, it still relied on a semi-honest third party, and the preparation and manipulation of multi-particle entangled states were difficult, hindering hardware implementation.

[0006] In addition, existing QAMR schemes have two major problems: First, quantum resource consumption is strongly correlated with the upper limit of data value - most schemes need to determine the quantum state dimension based on the upper limit of data value. When the upper limit of data value is much larger than the size of the dataset (e.g., the data value range is 1 to 1000 but only 10 data points need to be sorted), the consumption of quantum particles will increase dramatically with the upper limit of data value, resulting in resource waste. Second, poor portability - existing schemes often tightly couple the sorting logic with the anonymity mechanism, making it difficult to flexibly integrate mainstream quantum sorting algorithms such as quantum merge sort and quantum quick sort, and making it difficult to adapt to sorting needs in different scenarios.

[0007] In summary, the current QAMR field urgently needs a technical solution that is "free from third-party dependencies, consumes low quantum resources, and is highly portable" to address the shortcomings of existing solutions in terms of practicality, efficiency, and flexibility, and to promote the application of QAMR technology in real-world scenarios such as quantum voting and distributed privacy statistics.

[0008] This invention focuses on Quantum Anonymous Multi-party Ranking (QAMR), a core sub-direction of QSMC. By integrating quantum technologies such as d-dimensional single-particle state manipulation, quantum Fourier transform (QFT), and modular quantum merge sorting (QMS), it solves the problem of anonymously ranking private data of multiple participants in distributed scenarios. It can be widely applied to quantum network scenarios with high requirements for both "data privacy protection" and "identity anonymity," such as quantum voting, quantum auctions, and distributed privacy data statistics. It provides secure and efficient technical support for multi-party collaborative data processing in the era of quantum computing. Summary of the Invention

[0009] The purpose of this invention is to address the technical pain points of existing quantum anonymous multi-party ranking (QAMR) schemes, which are characterized by "reliance on semi-honest third parties, strong binding of quantum resource consumption to the upper limit of data value, and poor portability." This invention provides a quantum anonymous multi-party ranking method and system based on the quantum merge sort algorithm, which features no third-party dependency, low quantum resource consumption, high portability, and strong security protection.

[0010] Technical Solution: A quantum anonymous multi-party ranking method based on the quantum merge sort algorithm, wherein the m participants in the ranking are represented as P1, P2, ..., P m Let the participants P1 and P2 be set. m As non-collusive nodes, each participant P i Holding private datasets n i The private dataset contains the number of elements, and the total dataset consisting of all participants is represented as X = X 1 ||X 2 ||...||X m Where || denotes concatenation, and the total data volume The upper limit of the data value is d, where d > max{X};

[0011] Based on the above settings, the following stages will be executed:

[0012] Initial phase: Participant P m Prepare d-dimensional single-particle sequences Φ of length L=N1+(m-1)ξ+δ m ', where N1 represents participants P1 to P m-1 The total amount of data, ξ is the number of randomly retained particles, δ is the number of decoy particles, and Φ is the single-particle sequence. m 'Association measurement basis set A = {a i ∈{0,1}|i=1,2,...,L} and random number sequence Participant P m Single-particle sequence Φ m 'Transmitted to participant P1, participant P1 randomly selects δ decoy particles to verify P' m Honesty check: If all measurement bases are of a single type, most quantum states are the same, or the measurement error exceeds the threshold, the process terminates; otherwise, it continues.

[0013] Execution phase: Participant P1 removes the decoy particles to obtain the particle sequence Φ. m The substitution operation U is executed sequentially. σ The permutation operation includes shuffling the correspondence between particle positions and measurement basis, and then based on the random sequence R 1 shift operation U xA particle sequence Φ1 is generated and a decoy particle is inserted to obtain a single particle sequence Φ1', which is then transmitted to participant P2; participant P2 to participant P m-1 The eavesdropping detection is performed sequentially, following the same logic as the initial decoy particle verification, removing the decoy particles and randomly retaining ξ particles, and then performing the detection based on its own random sequence R. k The shift operation generates a single-particle sequence Φ. k 'and transmit to the next participant P' k+1 Or P1;

[0014] Testing phase: Participant P1 removes single-particle sequence Φ m-1 The decoy particles yield the particle sequence Φ m-1 After randomly retaining ξ particles, a sequence Φ is formed. (m-1)* ;According to participants P2→P3→...→P m-1 →P1 sequentially verifies the security of the transmission path: each participant P k The sample particle position H is disclosed, and the preceding participant discloses the corresponding random sequence RC. j Participant P1 disclosed the reverse permutation position. Participant P m Disclosure of measurement basis AC and random number RC m Participant P k Measure the sample particles using the measurement basis AC, if the following conditions are met: If the measurement results are satisfactory, the path is safe; otherwise, the method is terminated.

[0015] Aggregation phase: Participant P1 removes each participant's random sequence R. i The values ​​used for path detection are used to obtain R. i ';Participants P1, P2, ..., P m Disclose respectively based on R i 'with X i Constructed RS i RS i Only the private data is embedded in the corresponding position of its own data; the rest are R. i The inverse of '; Participant P1 to RS m Perform a substitution operation Combined with Φ (m-1)* With all RS i Build Reverse displacement After inserting decoy particles, Transmit to P m ;

[0016] Ranking Phase: Participant P m Remove The decoy particles were obtained Based on the measurement basis set A * Convert it into a particle sequence This includes direct deentanglement under computational basis and QFT under Fourier basis. -1 Transformation to untangle;

[0017] Participant P m Prepare particle sequences corresponding to your own dataset Will Inputting the quantum merge sort oracle yields the sorting result O = {o} k |k=1,2,...,N} and index, matching each participant X through the index. i The ranking is invalid if there are missing data.

[0018] Furthermore, in the initial phase, participant P m Prepared single-particle sequence Φ m 'The number of 0s and 1s in the measurement basis set A is approximately equal, and the random number sequence R...' m Each r i m Independently and uniformly distributed in P1 verifies P m In terms of honesty, the error threshold is determined jointly by the characteristics of the transmission channel and the accuracy of the measuring instrument;

[0019] During the execution phase, participant P k (2≤k≤m-1) ξ particles are reserved for path safety verification in subsequent testing phases, and the value of ξ satisfies ξ≥log d N ensures that the validation sample size is sufficient to cover the data distribution characteristics;

[0020] In the testing and aggregation phases, the insertion positions and measurement basis selections of all decoy particles are randomly generated, and the quantum state distribution of the decoy particles is consistent with that of the normal data particles, thus avoiding being identified and circumvented by attackers.

[0021] Furthermore, to address the practical need for "dynamic data changes (additions / deletions)" in quantum anonymity multi-party ranking scenarios, this method adds a separate quantum data addition / deletion processing stage, the specific process of which is as follows:

[0022] When any participant needs to add or delete private data, the non-colluding node P should be the first to do so. m Increase the dimension of the system's current quantum state from d to 2d. Then, sort the data from the first round O = {o} k |k=1,2,...,N} and P m Private data is merged into P m This round features a new private dataset.

[0023] Participants simultaneously define a unified encoding rule: newly added private data x to be sorted is encoded as a "new tag (x)" that can be recognized by the quantum state, and private data x to be deleted is encoded as a "deletion tag (denoted as 2d-x)", ensuring that data change operations can be accurately recognized by subsequent quantum operation modules.

[0024] After dimensionality adaptation and encoding are completed, the system does not need to reconstruct the core process of "initial stage - execution stage - testing stage - aggregation stage - ranking stage". It can directly reuse the original solution logic to execute the initial stage, execution stage, testing stage, aggregation stage and ranking stage in the method.

[0025] In P m Before publishing the new sorted data, check the data in the sorted set whose values ​​are in the range [d, 2d-1]. Let this set be DE = {de}. i |i=1,…k}, remove 2d-de from the sorting. i For the part, remove Nk zeros from the data, output the remaining data in the range [0, d-1], and publish the index in the order of this data.

[0026] Furthermore, the privacy and security protection mechanism established based on this method includes detection and protection mechanisms against the following attacks:

[0027] Entanglement measurement attack: If an attacker intercepts a particle sequence and performs an entanglement operation... |e> represents the attacker's auxiliary system, which must satisfy a jk =δ jk δ jk Let a be the Kronecker function, and when j = k, a jk =1, when j≠k, a jk =0 is required to avoid decoy particle detection; at this time, U E By degenerating into unit operations, attackers cannot obtain any valid data, thus ensuring the security of the solution.

[0028] Collusion Attack: When t (t≤m-2) participants collude, the probability of successfully obtaining the private data of the other participants is: n i Let p be the amount of data for the target participants, and N be the total amount of data. As N increases, p approaches 0, and the non-colluding nodes P1 and P2... m The constraints further reduce the success rate of collusion and ensure the scheme's anti-collusion capability;

[0029] Intercepting Retransmission Attacks: After an attacker intercepts and tampers with the particle sequence, the measurement results during the testing phase cannot meet the requirements. Tampering will cause the XOR result to mismatch, and the scheme will terminate; at the same time, the random distribution of decoy particles makes it impossible for attackers to distinguish between decoy and normal particles, and thus they cannot tamper with them in a targeted manner, further strengthening the protection.

[0030] Furthermore, the operations on the d-dimensional single-particle state include quantum Fourier transform and inverse Fourier transform, where the quantum Fourier transform is represented as QFT and defined as:

[0031]

[0032] The quantum inverse Fourier transform is represented as QFT. -1 Defined as:

[0033]

[0034] When i = 0, |j> i For the computation basis; when i = 1, |j> i For Fourier.

[0035] The displacement operation U σ With shift operation U x The mathematical definition of is:

[0036]

[0037] In the formula, σ∈S d For a d-ary symmetric group (k∈{0,1}), the operation has the effect U. σ |j> k =|σ(j)> k ;

[0038]

[0039] The effect of operations on the computational basis is The effect of the operation on Fourier bases is

[0040]

[0041] During the aggregation phase, RS i The construction rules are as follows:

[0042] For participant P1,

[0043] in

[0044] For participant P k (2≤k≤m-1),

[0045] in

[0046] For participant P m ,

[0047] in C1 and C2 are P m Preset constants.

[0048] The quantum merge sort oracle in the ranking phase includes the operations Sorter(n) and Merge(n):

[0049]

[0050] Where C[i,j] is the quantum comparator gate and I is the unit operation;

[0051]

[0052] The quantum merge sort oracle recursively executes Sorter(n) and Merge(n) to sort the oracle. Convert to a monotonically ordered sequence.

[0053] Furthermore, the method includes data privacy protection in scenarios such as auction price ranking and medical data classification and anonymization, as well as applications in edge computing scenarios;

[0054] The edge computing scenario refers to the allocation and sorting of computing tasks offloading to edge computing nodes using the method described above. The application process includes mapping participant P1 to an edge computing node, responsible for anonymizing the edge node's identity; and mapping participant P... m Mapped to a cloud management platform, which serves as a scheduling platform for allocating and offloading computing tasks, adaptable to large-scale data sorting needs; other ordinary participants P i The mapping is to an edge computing node, which directly encodes the business data it generates, including resource utilization or computing task processing status; in cases where edge nodes are occupied or offline, the method involves adding or deleting nodes.

[0055] Participant P i Resource data is encoded as d-dimensional single-particle states (d = 100 to accommodate 0-99% utilization), P m Preparation of particle sequence Φ m ', P1 removes the decoy particles and then executes U σ The system uses the QMS oracle to sort edge nodes in ascending order of energy consumption and outputs the resource optimization ranking of each node. It supports dynamic adjustment of the d value of edge computing nodes (e.g., d is adjusted from 100 to 200 when energy consumption increases suddenly). When the number of devices exceeds 1000, the quantum merge sort oracle is replaced with the quantum fast sort oracle.

[0056] The application of the quantum anonymity multi-party ranking method described in this invention in the edge computing network scenario combines the acceleration capability and data privacy protection capability of quantum computing with the edge computing network. Quantum encryption technology uses quantum features to enhance security, and the edge computing network can deploy relevant encryption protocols to improve the security of data transmission.

[0057] This invention also provides a quantum voting system based on a quantum anonymous multi-party ranking method. The system is implemented based on the above-mentioned quantum anonymous multi-party ranking method, including configuring the system according to the non-collusion node constraint and modular quantum operations according to the method, ensuring security with two non-collusion participants, and combining d-dimensional single-particle states, quantum Fourier transform, and permutation / shift operations to achieve privacy protection coding.

[0058] The system includes:

[0059] Participant layer: Consists of m local participant nodes, represented as participants P1, P2, ..., P... m Each node is equipped with a quantum state preparation module, a quantum manipulation module, and a local data storage module, where P1 and P... m As non-colluding nodes, they cannot collude directly or indirectly. Therefore, participant node P1 is additionally equipped with a sequence aggregation module. m An additional quantum sorting module is provided, including an integrated quantum merge sorting oracle; wherein the quantum operation module combines d-dimensional single-particle states, quantum Fourier transform, and permutation / shift operations to achieve privacy-preserving coding;

[0060] Communication layer: It adopts a point-to-point encrypted transmission mechanism, embedding decoy particles when transmitting particle sequences between participants, supports the synchronous transmission of quantum state and classical control information, and the classical information is encrypted end-to-end using AES-CCM; including the use of LoRaWAN low-power solution to transmit classical control information, the use of fiber optic channel for quantum state transmission, and the support for dynamic adjustment of d value for each voter's quantum device;

[0061] Security verification layer: Deployed in each participant node, including an eavesdropping detection module and a path security verification module, which monitor abnormal operations during the execution of the scheme in real time; the eavesdropping detection module performs decoy particle verification, and the path security verification module is used to perform sequence alignment during the testing phase;

[0062] The quantum state preparation module is used to perform the initial stage operation of the method; the quantum operation module is configured to perform the execution stage of the method; the sequence aggregation module is configured to perform the aggregation stage of the method; and the quantum sorting module is configured to perform the ranking stage of the method.

[0063] According to the implementation scheme of this invention, a modular design of "decoupling the anonymity mechanism and sorting logic" is adopted, which supports flexible replacement of sorting algorithms and has portability, as detailed below:

[0064] The "Initialization-Execution-Testing-Aggregation" phase of the scheme uses a general anonymity mechanism, which is independent of the sorting logic. The QMS oracle in the ranking phase is an independent module that can be replaced with mainstream quantum sorting algorithms such as quantum quicksort and quantum bubble sort. The addition and deletion phases are independent of the above five phases and can be combined according to actual needs. When replacing, only the operation logic of Sorter(n) and Merge(n) needs to be adjusted (e.g., quantum quicksort needs to be replaced with "partition operation (Partition(n))" and "recursive sorting operation"), without modifying the anonymity mechanism and quantum operations (QFT, permutation, shift), adapting to sorting requirements in different scenarios (e.g., quantum auction requires quicksort, quantum voting requires stable sorting).

[0065] The system described in this invention adopts a core architecture of "non-collusion node constraints + modular quantum operations," which has strong versatility across various scenarios. Addressing diverse needs in the field of quantum anonymity ranking (such as privacy protection in auction bidding, hierarchical anonymity of medical data, and identity isolation in campus performance evaluations), it does not require restructuring the core process of the solution. Cross-domain adaptation can be achieved simply through "three scenario-specific configuration adjustments," and all adjustments are based on the quantum operation logic and security constraints of the preceding technical solutions, ensuring technical consistency and reproducibility. The specific adaptation logic is as follows:

[0066] (1) Dynamic mapping of participant roles: Non-collusion node constraints remain unchanged, while roles are adjusted according to scenario functions.

[0067] In this architecture, there are two non-collusive nodes (P1 and P2). m )+m-2 ordinary participants (P i The core role framework of ")" is fixed, but the functional positioning of each role can be mapped to specific business roles according to the needs of the scenario, and the constraint that "non-collusion nodes cannot directly / indirectly exchange data or collude" always applies:

[0068] For commercial scenarios (such as quantum anonymous auctions and credit scoring): P1 is mapped to a "supervisory / regulatory role" (auction supervision node, financial regulatory node), responsible for data compliance verification and sequence aggregation; P m Mapped as "statistical / execution roles" (auction statistics nodes, third-party statistics nodes), responsible for initial particle preparation and quantum sorting; ordinary participant P i Mapped to "data holder roles" (bidders, financial institutions), who only hold and encode private business data (bids, credit scores);

[0069] For public service scenarios (such as medical data grading and campus awards): P1 is mapped to a "compliance / management role" (health supervision node, moral education department node), focusing on privacy compliance verification and data integration; P m Mapped to "professional statistical roles" (medical statistics node, academic affairs office node), focusing on ranking execution and result output; ordinary participants P i The data is mapped to "data proxy roles" (hospitals, homeroom teachers) to hold sensitive private data (patient conditions, student scores) on their behalf, thus preventing sensitive entities from directly participating in quantum operations.

[0070] For IoT / scientific research scenarios (such as device resource prioritization and scientific data collaboration): P1 is mapped to a "gateway / management role" (IoT gateway, project management node), responsible for device anonymization or data authenticity verification; P m Mapped to "cloud / platform roles" (cloud management platform, scientific research statistics node) to adapt to large-scale data sorting needs; ordinary participant P i Mapped to "terminal / team roles" (IoT devices, research teams), directly encoding the business data (resource utilization, experimental parameters) generated by themselves.

[0071] (2) Flexible adaptation of quantum parameters: The core operation logic remains unchanged, while the parameters are adjusted according to the data characteristics.

[0072] In the preceding technical solution, core quantum parameters such as the d-dimensional single-particle state, the number of decoy particles δ, and the number of verification particles ξ can be dynamically adjusted according to the "range, sensitivity, and scale" of the scenario data. Furthermore, the parameter calculation logic is consistent with the definition of quantum operations (such as QFT, UTF-8). σ U x To maintain consistency and ensure the correctness of quantum operations:

[0073] Quantum state dimension d adaptation: The value of d always follows "d > max{X}" (X is the scenario's private dataset). For example, in a credit scoring scenario, the data range is 0-999 points, so d = 1000; in a charitable donation scenario, the data range is 0-10 million yuan, so d = 10. 6 In IoT resource occupancy scenarios, the data range is 0-99%, therefore d = 100; the basis set definition (calculating basis i = 0, Fourier basis i = 1) and QFT transform formula for d-dimensional single-particle states in all scenarios. Completely unified;

[0074] Verification and decoy particle number adaptation: The verification particle number ξ always satisfies "ξ≥log d N (where N is the total amount of data) is used to ensure that the validation sample covers the data distribution characteristics, such as N=100 and d=10 in a scientific research data collaboration scenario. 4 Therefore Take ξ = 2 > 1; the number of decoy particles δ is always calculated according to "δ ​​= NL" (L is the code length of a single data point). For example, in the campus evaluation scenario, N = 50 (50 students) and L = 1 (single score data), so δ = 50 × 1 = 50; the characteristics of "random insertion and consistent with normal particle state distribution" of decoy particles remain unchanged in all scenarios to ensure the effectiveness of eavesdropping detection;

[0075] Sorting algorithm adaptation: All scenarios use the Quantum Merge Sort (QMS) oracle by default (recursively executed by Sorter(n) and Merge(n)). When the amount of data in the scenario exceeds the threshold (e.g., N>1000), it can be replaced with Quantum Quick Sort by pre-order modular design (adjusting QMS(n) to “Partition(n)”). There is no need to modify the non-collusion node constraints and data encoding process. For example, in the IoT device sorting scenario, when the number of devices exceeds 1000, the sorting efficiency is improved by more than 30% after replacing the algorithm.

[0076] (3) Precise calibration of anonymous targets: The core of data-identity decoupling remains unchanged, while the anonymity granularity is adjusted according to the needs of the scenario.

[0077] The core anonymity objective of this architecture, "data ranking results are not related to participant identities," remains consistent across all scenarios. However, the anonymity granularity (i.e., "the degree of correlation between hidden data and identity") can be precisely calibrated according to the sensitivity requirements of each scenario, and is achieved through quantum operations of the preceding technical solutions.

[0078] Coarse-grained anonymization (e.g., research data collaboration, equipment resource ranking): only hides the "direct association between data and participant identity," and the ranking results can retain the original data values ​​(e.g., experimental parameters, resource utilization). This can be achieved through permutation operations. σ Disrupt the correspondence between particle positions and participants to ensure that data ownership cannot be determined by location;

[0079] Medium-granularity anonymization (e.g., auction bids, credit scores): hides the "correlation between raw data values ​​and identity," and the sorting results can retain the relative size of the data (e.g., bid ranking, credit rating ranking), through RS. i The original data value is obscured by constructing rules (embedding private data only at the corresponding data location, and the rest being random sequence inverses), while preventing data derivation through non-colluding node constraints.

[0080] Fine-grained anonymization (e.g., medical data classification, campus awards): This method completely hides the "original data value, participant identity, and data ownership". The sorting results only output "statistical distribution ranking" (e.g., ranking of the number of disease classifications, ranking of the number of award levels). After untangling through QFT inverse transformation, only statistical features are retained, ensuring that the identity of sensitive subjects (patients, students) is completely isolated from the data.

[0081] The technical solution of this invention, through the three-dimensional adaptation logic of "role dynamic mapping, parameter flexible adaptation, and anonymity target calibration", can quickly adapt to various scenarios in the field of quantum anonymity ranking without changing the core architecture and quantum operation definition, significantly reducing the cost of scenario-based development, while ensuring that all scenarios inherit the security (anti-collusion, anti-entanglement measurement, and anti-interception retransmission) and correctness of the previous solution, providing efficient support for the cross-domain application of quantum anonymity technology.

[0082] Beneficial Effects: This invention, through its innovative design of "non-collusion node constraints + modular quantum operations + end-to-end security protection," addresses the core pain points of existing quantum anonymity multi-party ranking (QAMR) schemes regarding third-party dependence, quantum resource consumption, portability, and security. Furthermore, it offers the following multi-dimensional beneficial effects:

[0083] (1) Eliminate reliance on third parties and reduce trust costs and deployment thresholds.

[0084] Existing QAMR schemes generally rely on semi-honest third parties to assist in key distribution or data aggregation. However, the trustworthiness and availability of these third parties directly limit the practical application scenarios of the schemes (e.g., it is difficult to find a universally recognized trusted third party in scenarios such as quantum voting and corporate auctions). This invention innovatively employs "two non-colluding nodes (P1 and P2)..." m The "sequence verification-preparation" approach replaces the traditional semi-honest third party, ensuring the security of the solution without the need for additional trusted entities through the division of roles between the two parties in "sequence verification-preparation" and the constraint of non-collusion.

[0085] Practical value: No need to build a third-party trust architecture, reducing the hardware and manpower costs of solution deployment; avoids global security risks caused by third-party attacks or collusion, making the solution adaptable to distributed scenarios lacking trusted third parties (such as cross-institutional privacy data sorting, decentralized quantum voting).

[0086] (2) Optimize quantum resource consumption and improve the practicality of the solution.

[0087] Existing solutions strongly bind quantum particle consumption to the upper limit of data value (e.g., 1000 particles need to be prepared when the data value range is 1 to 1000). When the upper limit of data value is much larger than the data set size, quantum particle consumption increases dramatically with the upper limit of data value, resulting in resource waste. This invention, through the design of "d-dimensional single-particle state + shift / permutation encoding", makes quantum resource consumption only bound to the total amount of data (unrelated to the upper limit of data value).

[0088] (3) Modular design improves portability and adapts to multiple scenario requirements.

[0089] Existing QAMR schemes often tightly couple the anonymity mechanism with the sorting logic (e.g., hardcoding a specific quantum sorting algorithm into the scheme), making it difficult to flexibly replace the sorting algorithm and adapt to the sorting requirements of different scenarios (e.g., quantum auctions require fast sorting, quantum voting requires stable sorting). This invention adopts a modular architecture that decouples the anonymity mechanism from the sorting logic:

[0090] The general anonymity module: The "initialization-execution-testing-aggregation" phase is a general process independent of the sorting algorithm. It is responsible for data privacy encoding and transmission security verification, and does not need to be modified due to changes in the sorting algorithm.

[0091] Replaceable sorting module: The quantum merge sort (QMS) oracle in the ranking stage is an independent component that can be directly replaced by mainstream quantum sorting algorithms such as quantum quicksort and quantum bubble sort. Only the operation logic of Sorter(n) and Merge(n) needs to be adjusted.

[0092] Scenario adaptability: For example, in quantum voting scenarios, it can be replaced with a stable sorting algorithm to ensure that those with the same vote have the same ranking priority; in distributed big data sorting scenarios, it can be replaced with quantum fast sorting to improve efficiency, greatly expanding the application scope of the solution.

[0093] (4) Full-process security protection to resist multiple types of attacks.

[0094] This invention designs a special protection mechanism against typical attacks in quantum scenarios (entanglement measurement, collusion, interception and retransmission) to ensure the security of the solution throughout the entire process.

[0095] (5) The sorting results are accurate and verifiable, ensuring the reliability of the scheme.

[0096] This invention provides triple assurance of the sorting correctness through "theoretical derivation + instance verification + quantum simulation" and supports participants in verifying the integrity of the results.

[0097] (6) The addition and deletion computation phase effectively fills the technical gap of existing QAMR solutions that "can only process static data" by supporting real-time addition and deletion operations of quantum data. It successfully adapts to real dynamic scenarios such as quantum auctions (temporary addition and reduction of bids), IoT device sorting (data changes caused by device offline / online), and medical data classification (adding patient cases / deleting invalid medical records). There is no need to change the solution framework due to data changes, which upgrades the technical solution from "applicable to a single static scenario" to "compatible with multiple dynamic scenarios", significantly broadening the actual application scope of the solution and meeting the core needs of dynamic data collaboration in the field of quantum secure multi-party computation.

[0098] (7) Promote the implementation of QAMR technology and empower quantum privacy collaboration in multiple fields.

[0099] The design of this invention takes into account "security, efficiency, and practicality" and can be directly applied to quantum scenarios with high demands for "privacy protection and anonymous ranking". Specifically, these scenarios include: quantum anonymous auction system, quantum anonymous credit scoring and ranking system, quantum anonymous medical data hierarchical statistics system, quantum anonymous scientific research data collaborative ranking system, quantum anonymous IoT device resource occupancy ranking system, quantum anonymous campus merit ranking system, and quantum anonymous public welfare donation ranking system.

[0100] In summary, this invention achieves breakthroughs in eliminating third-party dependencies, optimizing quantum resources, and improving portability and security, providing efficient and reliable technical support for multi-party privacy collaboration in the quantum era, and possessing significant theoretical innovation value and practical application prospects. Attached Figure Description

[0101] Figure 1 This is the logic flowchart of the QMS algorithm;

[0102] Figure 2 This is a diagram of the initial stage of the plan;

[0103] Figure 3 This is a diagram showing the implementation phases of the plan;

[0104] Figure 4 This is a diagram of the solution testing phase;

[0105] Figure 5 This is a diagram of the solution aggregation stage;

[0106] Figure 6 This is a diagram showing the sequence of the proposed solutions.

[0107] Figure 7 It is an analog overall circuit diagram;

[0108] Figure 8 shows the participant operation circuit, where Figure 8(a) shows the structural details of the operation "P1_Adder" of P1; Figure 8(b) shows the structural details of the operation "P2_Adder" of P2; Figure 8(c) shows the structural details of the operation "P3_Adder" of P3; and Figure 8(d) shows the structural details of the operation "P1_Adder" of P1. + The structural details of "_Adder";

[0109] Figure 9 This is the circuit diagram of the QMS oracle;

[0110] Figure 10 This is a circuit diagram for a shift operation;

[0111] Figure 11 This is a quantum comparison switching circuit diagram;

[0112] Figure 12 This is a graph showing the experimental results. Detailed Implementation

[0113] To illustrate the technical solution provided by this invention in detail, the following description is provided in conjunction with the accompanying drawings.

[0114] To make the technical solution of this invention clearer and easier to understand, this embodiment takes a quantum anonymity ranking scenario with four participants as an example, and, in conjunction with the IBM Qiskit quantum simulation platform, elaborates in detail the complete execution flow, parameter settings, simulation verification, and result analysis of the quantum anonymity multi-party ranking method based on the quantum merge sort algorithm described in this invention. In this embodiment, the participants exist as "players to be ranked," and their private data is "data to be ranked." The final data ranking is output through the scheme, and the association between the participants' identities and the data is completely hidden. Through IBM Qiskit simulation verification, the ranking accuracy is 100% in 10 rounds of testing. Figure 1 The operational logic of the QMS oracle is demonstrated.

[0115] 1. Basic settings of the implementation example

[0116] 1.1 Participants and Data Parameters

[0117] Number of participants: There are 4 participants in total, denoted as P1, P2, P3, and P4. Among them, P1 and P4 are non-collusion nodes (by default, they cannot directly / indirectly exchange data or collude), while P2 and P3 are ordinary nodes.

[0118] Private dataset: Each participant holds one dataset, specifically:

[0119] X 1 ={6},X 2 ={5},X 3 ={4},X 4 ={3};

[0120] Key parameter: Total data volume The total data volume from P1 to P3 is N1 = 3; the upper limit of data values ​​is d = 8 (d > max{X} = 6, ensuring that all sorted data can be encoded by d-dimensional quantum states); the number of verification particles is ξ = log d N = log84 ≈ 0.667, ξ = 1 (to ensure the validation sample covers the data distribution); number of decoy particles δ = NL = 4 × 1 = 4 (L = 1 is the data length, no multi-dimensional encoding is needed for a single data point); initial particle sequence length

[0121] L=N1+(m-1)ξ+δ=3+(4-1)×1+4=10.

[0122] 1.2 Quantum Operations and Tool Setup

[0123] Quantum state preparation: d=8 dimensional single-particle states were used, with computational basis (i=0) as {|0>0,|1>0,…,|7>0} and Fourier basis (i=1) as {|0>1,|1>1,…,|7>1}, where…

[0124] Quantum operation implementation: QFT, shift operation U x Displacement operation U σ The Quantum Merge Sort (QMS) oracle is built using the `qiskit.circuit.library` module of IBM Qiskit and is implemented custom-based on the `QuantumCircuit` class.

[0125] Simulation platform: IBM Qiskit version 0.46.0, with `qasm_simulator` as the simulation backend. Each round of testing is executed 1000 times (shots=1000) to ensure statistical significance of the results.

[0126] 2. Complete Implementation Steps (Five Stages)

[0127] 2.1 Initial Stage: Particle Sequence Preparation and Honesty Verification, such as Figure 2 As shown.

[0128] Step I1: (P4 Prepares the Initial Sequence) P4 generates the measurement basis set A = {0,0,1,1,1,1,0,1,0,1} (10 elements, with approximately equal numbers of 0s and 1s), and the random number sequence R. 4 ={5,3,6,2,4,2,7,1,0,6} (each Construct the initial particle sequence in Specifically:

[0129] Φ4'={|5>0,|3>1,|6>0,|2>1,|4>0,|2>1,|7>0,|1>1,|0>0,|6>1};

[0130] P4 has preset constants C1 = 5 and C2 = 3, and transmits Φ4' to P1.

[0131] Step I2: (P1 verifies P4's honesty) P1 randomly selects δ = 4 decoy particles and discloses their positions as {7,8,9,10}; P4 discloses the measurement basis A for the corresponding positions. decoy ={0,1,0,1} and random numbers P1 press A decoy Measurement of decoy particles: Measurement results obtained {7,1,0,6} – Measurement error is 0 (not exceeding the threshold of 10). -6Furthermore, the measurement basis is not of a single type and the quantum states are not repetitive. The verification was successful, and the process entered the execution phase.

[0132] 2.2 Execution Phase: Sequence Encryption and Eavesdropping Detection, combined with Figure 3 As shown.

[0133] Step E1: P1 performs substitution and shifting. P1 removes the four decoy particles of Φ4', resulting in:

[0134] Φ4={|5>0,|3>0,|6>1,|2>1,|4>1,|2>1};

[0135] Displacement operation U σ : Select σ∈S8 as Execute U on Φ4 σ ,generate:

[0136] U σ (Φ4)={|2>1,|5>0,|4>1,|2>1,|3>0,|6>1};

[0137] Shift operation U x P1 generates a random sequence R 1 ={3,2,1,5,3,2}, according to Calculation, obtained P1 inserts four decoy particles at random positions to form Φ1', which is then transmitted to P2.

[0138] Step E2: (P2 eavesdropping detection) P2 requests P1 to disclose the measurement basis and quantum state of the decoy particle. P2 measures and compares the measurements to perform eavesdropping detection.

[0139] Step E3: (P2 operation and transfer to P3) P2 removes the decoy particle to obtain Φ1, randomly retains ξ = 1 particle (position 6), and the remaining particles form Φ. 1* ={|5>1,|7>0,|5>1,|7>1,|6>0}; P2 generates R 2 ={2,1,7,1,4}, perform a shift operation U similar to P1. x ,get After inserting four decoy particles at random positions, Φ2' is formed and transmitted to P3.

[0140] Step E4: (P3 operation and P1 final detection) P3 repeats the operation of P2 (retaining the 5th particle with ξ=1, according to R) 3 ={2,4,0,6} is shifted to generate Φ3, and 4 decoy particles are randomly inserted at the positions. Φ3' is then transmitted to P1. P1 performs an eavesdropping detection. The measurement result is consistent with the ground / quantum state disclosed by P3, and the detection passes.

[0141] 2.3 Testing Phase: Transmission Path Security Verification, combined with Figure 4 As shown.

[0142] Step T1: (P1 preprocessing sequence) P1 removes the decoy particle Φ3' to obtain Φ3, randomly retains ξ = 1 particle (position 4), and the remaining particles form Φ 3* ={|1>1,|4>0,|4>1}.

[0143] Step T2: (Verify the path node by node)

[0144] Verify the P2 path: P2 discloses sample location H = {6} (reserved |0>0); P1 discloses RC1 = {2} (R 1 r at the corresponding position i 1 =1); P1 discloses the inverse permutation position P4 discloses AC = {1} (the base of position 6 in A is 1), RC4 = {6} (R 4 r in position 6 i 4 =6); P2 measured Consistent with |0>1, the path is safe.

[0145] Verify the paths P3 and P1: Repeat the above logic, P3 measures... P1 was measured All meet All paths were verified successfully.

[0146] 2.4 Aggregation Phase: Data integration among multiple participants, combined with... Figure 5 As shown.

[0147] Step A1: (Build RS) i Sequence) P1 removes each R i The verification value is obtained as R. 1 ={3,2,1}、R 2 ={2,1,7}、R 3 ={2,4,0}、R 4 ={5,4,2}; Each participant discloses RS i :

[0148] P1's RS 1 : Therefore j = 2, 3 are non-data positions. That is, RS 1 ={3,6,7};

[0149] P2's RS 2 : Therefore j = 1, 3 are non-data positions. That is, RS 2 ={6,4,1};

[0150] P3's RS 3 : Therefore j = 1, 2 are non-data positions That is, RS 3 ={6,4,4};

[0151] P4's RS 4 :a i When = 0, a i When = 1,

[0152] That is, RS 4 ={0,7,1}.

[0153] Step A2: (P1 Aggregation and Transmission) P1 to RS 4 implement generate Combined with Φ 3* RS 1 RS 2 RS 3 ,according to Calculation yields: Perform inverse permutation have to After inserting 4 decoy particles, it forms Transmit to P4.

[0154] Step A3: P4 eavesdropping detection. The result of P4 measurement of the decoy particles is consistent with the value disclosed in P1, and the detection is passed.

[0155] 2.5 Ranking Stage: Quantum Merge Sort and Result Output, combined with Figure 6 As shown.

[0156] Step R1: Unentangle and sort P4 Remove decoy particles Based on A * ={0,1,1} converted to P4 prepares its own data sequence After series connection, we get

[0157] Then input the cascaded sequence into QMS: Execute in

[0158] QMS(2)=Sorter(2)=C[1,2].

[0159] Compare |5>0 with |4>0, swap them to get |4>0,|5>0; compare |6>0 with |3>0, swap them to get |3>0,|6>0, and the particle sequence becomes |4>0,|5>0,|3>0,|6>0.

[0160] implement Final output sorted sequence

[0161] O = {|3>0,|4>0,|5>0,|6>0}, corresponding to the sorted data result of {3,4,5,6}.

[0162] ( Compare |4>0 and |6>0, and swap them to get |4>0,|6>0; compare |5>0 and |3>0, and swap them to get |3>0,|5>0. The particle sequence then becomes |4>0,|3>0,|5>0,|6>0. Compare |4>0 and |3>0, swap them to get |3>0,|4>0; compare |5>0 and |6>0, swap them to get |5>0,|6>0, and the particle sequence becomes |3>0,|4>0,|5>0,|6>0).

[0163] Step R2: Anonymous ranking and verification. P4 publishes the sorting results O = {3,4,5,6} and index {1,2,3,4}; each participant matches their own data ranking: P1 holds data 6 - ranking 4, P2 holds data 5 - ranking 3, P3 holds data 4 - ranking 2, P4 holds data 3 - ranking 1; all participants' data exist in O, there are no objections, and the ranking takes effect.

[0164] 3. Simulation Verification and Result Analysis

[0165] 3.1 Simulation Parameters and Circuit Implementation

[0166] Simulation settings: Noise simulation off (ideal environment), shots = 1000, measurement basis is computation basis, and the measurement probability of each quantum state is calculated.

[0167] Quantum circuit construction: using test data 1 as a typical case. Figure 7 The integrated quantum circuit structure simulated by the scheme is shown.

[0168] Figure 8 then details the structural details of the "P1_Adder", "P2_Adder", "P3_Adder", and "QMS Oracle". Based on the expansion of this circuit architecture, Figure 9 The structural details of quantum addition are shown.

[0169] Figure 10 The oracle module shown implements quantum sorting logic. Inside this oracle module, conditional comparison and swapping operations between quantum data bits are implemented using comparison-swapping gates, and its dedicated circuit architecture is as follows: Figure 11 As shown.

[0170] After completing the circuit implementation, we simulated the solution on the IBM Quantum Experience platform.

[0171] Table 1: Initial unsorted dataset

[0172]

[0173]

[0174] 3.2 Simulation Results

[0175] Specifically, the results of ten sets of experiments (each set performing 1000 measurements) are integrated and presented in [the format of the experiment]. Figure 12 Accordingly, the ranking data of participants in the ten test groups is summarized in Table 3. Figure 12 As shown, the private data of all four participants were successfully sorted in ten sets of simulation experiments. These results confirm that the scheme can correctly sort distributed quantum encoded data under different participant input conditions, and verify its practical feasibility in a quantum network environment under ideal conditions assuming no external interference.

[0176] Table 2: Sorting Results

[0177]

[0178] Results analysis: In 10 rounds of simulation, the probability of correct ranking was 100% and the ranking matching rate of participants was 100%, proving the feasibility of the scheme in an ideal quantum environment;

[0179] 4. Key Conclusions of the Examples

[0180] This embodiment verifies the effectiveness of the invention through a "quantum anonymity ranking scenario with 4 participants":

[0181] Anonymity Guarantee: The ranking results only disclose the "data ranking" and are not associated with the identity of any participant. P1 to P4 cannot deduce the identity of the holder from the ranking results;

[0182] Correctness verification: Simulation results show that the sorting accuracy is 100%, which is consistent with the theoretical derivation that "the aggregated sequence contains the original data";

[0183] Resource efficiency: Using only d=8 dimensional single-particle states, the number of quantum particles is bound to N=4 (independent of M=8), resulting in high quantum efficiency. It is significantly superior to third-party-dependent solutions (such as the Lin et al. 2016 solution). );

[0184] This invention can also be adapted to scenarios such as "multi-data-point sorting" and "cross-institutional privacy statistics," requiring only an adjustment of n. i The parameters such as d do not require modification of the core logic of the solution, further demonstrating its modularity and portability advantages.

Claims

1. A quantum anonymous multi-party ranking method based on the quantum merge sort algorithm, characterized in that, This method represents the m participants in the ranking as P1, P2, ..., Pn. m Let the participants P1 and P2 be set. m As non-collusive nodes, each participant P i Holding private datasets n i The private dataset contains the number of elements, and the total dataset consisting of all participants is represented as X = X 1 ||X 2 ||...||X m Where || denotes concatenation, and the total data volume The upper limit of the data value is d, where d > max{X}; Based on the above settings, the following stages will be executed: Initial phase: Participant P m Prepare d-dimensional single-particle sequences Φ of length L=N1+(m-1)ξ+δ m ', where N1 represents participants P1 to P m-1 The total amount of data, ξ is the number of randomly retained particles, δ is the number of decoy particles, and the particle sequence Φ m 'Association measurement basis set A = {a i ∈{0,1}|i=1,2,...,L} and random number sequence Participant P m The particle sequence Φ m 'Transmitted to participant P1, participant P1 randomly selects δ decoy particles to verify P' m Honesty: If all measurement bases are of a single type, more than half of the quantum states are the same, or the measurement error exceeds the threshold, the verification will terminate; otherwise, it will continue. Execution phase: Participant P1 removes the decoy particles to obtain the particle sequence Φ. m The substitution operation U is executed sequentially. σ The permutation operation includes shuffling the correspondence between particle positions and measurement basis, and then based on the random sequence R 1 shift operation U x A particle sequence Φ1 is generated and a decoy particle is inserted to obtain a single particle sequence Φ1', which is then transmitted to participant P2; participant P2 to participant P m-1 The eavesdropping detection is performed sequentially, following the same logic as the initial decoy particle verification, removing the decoy particles and randomly retaining ξ particles, and then performing the detection based on its own random sequence R. k The shift operation generates a single-particle sequence Φ. k 'and transmit to the next participant P' k+1 Or P1; Testing phase: Participant P1 removes single-particle sequence Φ m-1 The decoy particles yield the particle sequence Φ m-1 A sequence is formed by randomly retaining ξ particles. According to participants P2→P3→...→P m-1 →P1 sequentially verifies the security of the transmission path: each participant P k The sample particle position H is disclosed, and the preceding participant discloses the corresponding random sequence RC. j Participant P1 disclosed the reverse permutation position. Participant P m Disclosure of measurement basis AC and random number RC m Participant P k Measure the sample particles using the measurement basis AC, if the following conditions are met: For modulo d operation, q i k If the measurement results are satisfactory, the path is safe; otherwise, the process terminates. Aggregation phase: Participant P1 removes each participant's random sequence R. i The values ​​used for path detection are used to obtain R. i ';Participants P1, P2, ..., P m Disclose respectively based on R i 'with X i Constructed RS i RS i Only the private data is embedded in the corresponding position of its own data; the rest are R. i The inverse of '; Participant P1 to RS m Perform the substitution operation U σ1 , combined With all RS i Build Reverse displacement After inserting decoy particles, Transmit to P m ; Ranking Phase: Participant P m Remove The decoy particles were obtained Based on the measurement basis set A * Convert it into a particle sequence This includes direct deentanglement under computational basis and QFT under Fourier basis. -1 Transformation to untangle; Participant P m Prepare particle sequences corresponding to your own dataset Will Inputting the quantum merge sort oracle yields the sorting result O = {o} k |k=1,2,...,N} and index, matching each participant X through the index. i The ranking is invalid if there are missing data.

2. The quantum anonymous multi-party ranking method based on the quantum merge sort algorithm according to claim 1, characterized in that, In the initial phase, participant P m Prepared single-particle sequence Φ m 'The random number sequence R satisfies the condition that the number of 0s and 1s in the measurement basis set A is equal.' m Each Independently and uniformly distributed in Participant P1 verifies P m In terms of honesty, the error threshold is determined jointly based on the actual application scenario and the characteristics of the transmission channel; During the execution phase, participant P k (2≤k≤m-1) ξ particles are reserved for path safety verification in subsequent testing phases, and the value of ξ satisfies ξ≥log d N ensures that the validation sample size is sufficient to cover the data distribution characteristics; In the testing and aggregation phases, the insertion positions and measurement basis selections of all decoy particles are randomly generated, and the quantum state distribution of the decoy particles is consistent with that of the normal data particles, thus avoiding being identified and circumvented by attackers.

3. The quantum anonymous multi-party ranking method based on the quantum merge sort algorithm according to claim 1, characterized in that, The steps for adding or deleting quantum data in this method are as follows: Participants first increase the quantum state dimension to 2d, encode the private data as x according to the increased data, and encode the deleted data as 2d-x, and then execute the initial phase, execution phase, testing phase, aggregation phase and ranking phase in the method; In the first round of sorting, data O = {o k |k=1,2,...,N} and P m Private data merging; concatenating with existing data strings during the sorting phase, then executing the QMS oracle for sorting; in P m Before publishing the sorted data, check the data in the sorted range that are in the range [d, 2d-1], and let it be a set DE = {de i |i=1,…k}, remove 2d-de from the sorting. i For the part, remove Nk zeros from the data, output the remaining data in the range [0, d-1], and publish the index in the order of this data.

4. The quantum anonymous multi-party ranking method based on the quantum merge sort algorithm according to claim 1, characterized in that, The privacy and security protection mechanism developed based on this method includes the detection and protection against the following attacks: Entanglement measurement attack: If an attacker intercepts a particle sequence and performs an entanglement operation... |e> represents the attacker's auxiliary system, which must satisfy a jk =δ jk δ jk Let a be the Kronecker function, and when j = k, a jk =1, when j≠k, a jk =0 is required to avoid decoy particle detection; at this time, U E By degenerating into unit operations, attackers cannot obtain any valid data, thus ensuring data security. Collusion Attack: When t (t≤m-2) participants collude, the probability of successfully obtaining the private data of the other participants is: n i Let p be the amount of data for the target participants, and N be the total amount of data. As N increases, p approaches 0, and the non-colluding nodes P1 and P2... m Constraints are implemented to reduce the success rate of collusion and ensure data's resistance to collusion. Intercepting Retransmission Attacks: After an attacker intercepts and tampers with the particle sequence, the measurement results during the testing phase cannot meet the requirements. Tampering will cause the XOR result to mismatch and terminate; at the same time, the random distribution of decoy particles makes it impossible for attackers to distinguish between decoy and normal particles, and thus prevents targeted tampering, thereby strengthening the protection.

5. The quantum anonymous multi-party ranking method based on the quantum merge sort algorithm according to claim 1, characterized in that, The operations on the d-dimensional single-particle state include quantum Fourier transform and inverse Fourier transform. The quantum Fourier transform, denoted as QFT, is defined as follows: The quantum inverse Fourier transform is represented as QFT. -1 Defined as: When i = 0, |j> i For the computation basis; when i = 1, |j> i For Fourier.

6. The quantum anonymous multi-party ranking method based on the quantum merge sort algorithm according to claim 1, characterized in that, The displacement operation U σ With shift operation U x The mathematical definition of is: In the formula, σ∈S d For a d-ary symmetric group (k∈{0,1}), the operation has the effect U. σ |j> k =|σ(j)> k ; The effect of operations on the computational basis is The effect of the operation on Fourier bases is 7. The quantum anonymous multi-party ranking method based on the quantum merge sort algorithm according to claim 1, characterized in that, During the aggregation phase, RS i The construction rules are as follows: For participant P1, in For participant P k (2≤k≤m-1), in For participant P m , in C1 and C2 are P m Preset constants.

8. The quantum anonymous multi-party ranking method based on the quantum merge sort algorithm according to claim 1, characterized in that, The quantum merge sort oracle in the ranking phase includes the operations Sorter(n) and Merge(n): Where C[i,j] is the quantum comparator gate, and I is the unit operation. is the tensor product, and ° represents the compound operation; The quantum merge sort oracle recursively executes Sorter(n) and Merge(n) to sort the oracle. Convert to a monotonically ordered sequence.

9. The quantum anonymous multi-party ranking method based on the quantum merge sort algorithm according to claim 1, characterized in that, This method includes data privacy protection in scenarios such as auction price ranking and hierarchical anonymization of medical data, as well as applications in edge computing scenarios; The edge computing scenario refers to the allocation and sorting of computing tasks offloading to edge computing nodes using the method described above. The application process includes mapping participant P1 to an edge computing node, responsible for anonymizing the edge node's identity; and mapping participant P... m The mapping is to a cloud management platform, which serves as a scheduling platform for allocating and offloading computing tasks, and is adapted to large-scale data sorting requirements. Other ordinary participants P i The mapping is to an edge computing node, which directly encodes the business data it generates, including resource utilization or computing task processing status; in cases where edge nodes are occupied or offline, the method involves adding or deleting nodes.

10. A quantum voting system based on a quantum anonymous multi-party ranking scheme, characterized in that, The system is implemented based on the quantum anonymity multi-party ranking method as described in any one of claims 1-8, including configuring the system according to the method with non-collusion node constraints and modular quantum operations, ensuring security with two non-collusion participants, and combining d-dimensional single-particle states, quantum Fourier transform, and permutation / shift operations to achieve privacy protection coding; The system includes: Participant layer: Consists of m local participant nodes, represented as participants P1, P2, ..., P... m Each node is equipped with a quantum state preparation module, a quantum manipulation module, and a local data storage module, where P1 and P... m As non-colluding nodes, they cannot collude directly or indirectly. Therefore, participant node P1 is additionally equipped with a sequence aggregation module. m An additional quantum sorting module is provided, including an integrated quantum merge sorting oracle; wherein the quantum operation module combines d-dimensional single-particle states, quantum Fourier transform, and permutation / shift operations to achieve privacy-preserving coding; Communication layer: It adopts a point-to-point encrypted transmission mechanism, embedding decoy particles when transmitting particle sequences between participants, supports the synchronous transmission of quantum state and classical control information, and the classical information is encrypted end-to-end using AES-CCM; including the use of LoRaWAN low-power solution to transmit classical control information, the use of fiber optic channel for quantum state transmission, and the support for dynamic adjustment of d value for each voter's quantum device; Security verification layer: Deployed in each participant node, including an eavesdropping detection module and a path security verification module, which monitor abnormal operations during the execution of the scheme in real time; the eavesdropping detection module performs decoy particle verification, and the path security verification module is used to perform sequence alignment during the testing phase; The quantum state preparation module is used to perform the initial stage operation of the method; the quantum operation module is configured to perform the execution stage of the method; the sequence aggregation module is configured to perform the aggregation stage of the method; and the quantum sorting module is configured to perform the ranking stage of the method.

Images