An anonymous voting method based on one-way quantum walk on a circle

Abstract

The present application belongs to the technical field of quantum communication, and discloses an anonymous voting method based on one-way quantum walk on a circle, which comprises the following steps: 1, according to the Chinese remainder theorem, a voting center prepares a plurality of different voting parameters, and sends a unique voting parameter to each voter; the voting center TP prepares a plurality of quantum walk states required for quantum voting, and sends them to legal voters for sequential use; 2, after the i-th voter receives the quantum walk states, the voter detects the security of the quantum channel together with the corresponding particle sequence sender; 3, the legal voter completes voting on the voting object by performing a one-way evolution operator operation on all quantum walk states; 4, the voting center TP performs an inverse one-way evolution operator and quantum measurement operation on the quantum walk states after completing all the voting, and completes the vote counting on the voting object. The present application can effectively resist multiple voting attacks by dishonest voters, and simultaneously realize voting verifiability and anonymity.

Description

Technical Field

[0001] This invention belongs to the field of quantum communication technology, specifically relating to an anonymous voting method based on one-way quantum walking on a circle. Background Technology

[0002] With the rapid development of communication and digital technologies, electronic voting, as a form of collective voting, has profoundly impacted people's work and lives, from its application in class committee elections to the formulation and implementation of major corporate decisions. However, traditional electronic voting schemes are mainly based on classical cryptography, and their security relies on the computational complexity of cracking the key. This not only fails to meet unconditional security requirements but also cannot resist attacks from future quantum computers. To overcome the many problems of existing voting methods, it is necessary to apply more efficient and secure communication technologies to the field of electronic voting. Quantum cryptography applies quantum technology to the field of classical cryptography. Its security is guaranteed by the quantum no-cloning theorem and the Heisenberg uncertainty principle, and it is of great significance to the development of encryption technology. In 1984, researchers proposed the first quantum key distribution protocol, BB84, using the polarization state of a single photon, achieving unconditionally secure communication. Since then, quantum encryption protocols applied to different scenarios have attracted increasing attention, such as quantum summation, quantum secret sharing, quantum secret comparison, quantum voting, and quantum auctions.

[0003] Quantum mobile voting requires only one entangled state to complete the voting for all voters, conserving quantum resources. Existing technologies, such as the "shadowing" technique, have proposed a highly universal and practical group voting scheme based on the characteristics of d-dimensional three-particle entangled states. However, this voting function is binary voting, allowing only "yes" or "no" votes. Further technological solutions have emerged, such as anonymous quantum voting protocols based on the Chinese Remainder Theorem. This protocol stores voting information in a quantum phase, improving security, but voter privacy cannot be effectively protected. Another approach is a secure multi-party quantum voting protocol designed to reduce the overhead of quantum communication and computation, requiring each voter to prepare an auxiliary particle, but this protocol cannot prevent malicious voting by dishonest individuals. Existing technologies also include a multi-center, efficient, quantum-safe voting scheme combining quantum walking and semi-quantum techniques, suitable for scenarios with large numbers of voters. However, this scheme cannot resist multiple voting attacks by dishonest voters, and voters cannot verify whether their votes have been correctly counted.

[0004] In the aforementioned quantum voting method, all legitimate voters must cast their votes for publicly available candidates, and the voting results are tallied and published by the voting center. However, in the real world, it is difficult to guarantee that the voting center is completely trustworthy, meaning that it is impossible to effectively protect the correct counting of voters' votes. Furthermore, some existing quantum voting methods often sacrifice voting functionality to improve security, i.e., limiting the number of candidates, which is unsuitable for voting scenarios involving multiple candidates. Summary of the Invention

[0005] The purpose of this invention is to provide an anonymous voting method based on one-way quantum walks on a circle, in order to solve the technical problems of existing technologies being unable to resist multiple voting attacks by dishonest voters and being difficult to achieve vote verifiability while protecting voter privacy.

[0006] The anonymous voting method based on one-way quantum walks on a circle includes the following steps: Step 1: According to the Chinese Remainder Theorem, the voting center prepares several different voting parameters and sends a unique voting parameter to each voter; the voting center prepares the quantum walk states required for quantum voting, forming... A sequence of quantum states, then inserted The first particle sequence is obtained from the decoy particles. And sent to the first voter ; in, Indicates the first Each voter , Indicates the first Each voting object, The voting center is a semi-trusted third-party voting center, TP. Step 2, the i-th voter Received the i-th particle sequence Then, together with the corresponding particle sequence sender, they will test the security of the quantum channel; Step 3, A legitimate voter Through the Quantum state sequence Perform one-way evolution operator operations to complete the process. Each voting object The vote; The expression is ,in Indicates the first A quantum walking state; after the last voter has cast their vote, this needs to be... Quantum state sequence Send to the voting center TP; Step 4, the voting center (TP) processes all completed votes. Quantum state sequence Perform inverse one-way evolution operator operations to complete the vote counting operation for each voting object.

[0007] Preferred, Indicates the first Each voter Indicates the first There are 10 voting targets, and the first voter is... The voting center is a semi-trusted third-party voting center TP. Step 1 includes the following sub-steps: Step 1.1, Preparation of Voting Center TP coprime positive integers ,in Indicates the first A positive integer, ;calculate The product of positive integers and except the Beyond positive integers The product of positive integers ; Step 1.2, the voting center TP will... Product The corresponding number theory reciprocal and positive integers Components of voting parameters And send it to the first via the classic channel. One legitimate voter This continues until each voter receives a unique voting parameter; Step 1.3, Preparation of Voting Center TP share Each is in the initial quantum walk state. quantum state sequence ; The sequence of quantum states is shown below: , Indicates the first A quantum walking state; Step 1.4, the voting center TP randomly selects from the measurement base. One particle is used as a decoy particle and inserted. Quantum state sequence In the process, the first particle sequence was obtained. Send to the first voter .

[0008] Preferably, in step 1.1, this is calculated. The product of positive integers and except the Beyond positive integers The product of positive integers The formula for calculation is:

[0009] Based on the above formula, the product can be calculated. With the positive integers The reciprocal of the modulus of number theory Then there is ;mod represents the modulo operation.

[0010] Preferably, the method for adding decoy particles in step 1.4 includes: randomly selecting from the measurement base. One particle was inserted as a decoy particle into the corresponding... From a sequence of quantum states, a corresponding sequence of particles is formed, with the measurement basis serving as the computational basis. or Fourier Where QFT stands for Quantum Fourier Transform. The Hilbert space dimension represents the quantum walk state.

[0011] Preferably, step 2 includes the following sub-steps: Step 2.1, the particle sequence sender publishes the i-th particle sequence. The specific location of the decoy particles and their corresponding measurement basis; Step 2.2, the i-th voter The decoy particles were measured according to the published measurement standards, and the measurement results were published. In step 2.3, the particle sequence sender determines whether the quantum channel is secure by statistically analyzing the error rate of the decoy particles. If the error rate exceeds a predetermined threshold, the subsequent operation will be terminated, and the process will return to step 1.3 to be re-executed; otherwise, the operation in step 3 will be executed.

[0012] Preferably, step 3 includes the following sub-steps: Step 3.1, the i-th voter Particle sequence removal The decoy particle in the middle, when i=1, is the first voter. get All are in the initial quantum walking state quantum state sequence , ;when From 2 voters Starting with the i-th voter After receiving the votes of the previous voter Quantum state sequence , Then, when Combined with the i-th voter Voting parameters And their own voting intentions, the i-th voter Prepare the corresponding voting content ; Step 3.2, the i-th voter Through the Quantum state sequence The first in A quantum wandering state Apply Sub-unidirectional evolution operator The result is obtained from the i-th voter. After voting Quantum state sequence The first of them The expression for each quantum walk state is as follows: ,in, Indicates the i-th voter For the first Each voting object A randomly generated positive integer; Step 3.3, the i-th voter Using the decoy particle addition method described in step 1.4, after voting... Quantum state sequence Add decoy particles and send them to the next voter. ; Step 3.4, starting from the second voter Then, each voter repeats steps 2, 3.1, 3.2, and 3.3 to complete the voting process and submit their vote. A sequence of quantum states is sent to the next voter until all voters have completed their votes, then step 3.5 is executed; Step 3.5, the last one individual voters After voting on its own, the decoy particle addition method in step 1.4 is used. Quantum state sequence Add decoy particles and send them to the voting center TP.

[0013] Preferably, in step 3, the one-way evolution operator The formula is:

[0014] in, The coin flipper operator is calculated as follows:

[0015] For the unit operator in location space, For a one-way movement operator, the formula is: ) in, and They are all translation operators, with the current index being... ,exist : .

[0016] Preferably, step 4 includes the following sub-steps: Step 4.1, the voting center (TP) notifies each voter via broadcast technology. Begin counting votes, each voter The random numbers during the voting process are published. ; Step 4.2, the voting center (TP) processes all completed votes. Quantum state sequence The first in A quantum wandering state implement Secondary inverse unidirectional evolution operator The operation yields a new quantum walking state. ; Step 4.3, the voting center TP uses a measurement basis to compare the votes after counting. Quantum state sequence Measurements were taken one by one; then, the voter turntable (TP) at the polling center tallied the results. The first quantum state sequence A quantum wandering state The measurement results yielded the first Number of votes for each voting candidate ; Step 4.4, the voting center TP shuffles the positive integer sequence. The order of positive integers is then used to obtain a new sequence of positive integers. And through a classical channel, the new positive integer sequence and the positive integer product are... Announcement; simultaneously, TP will announce the sum of the votes cast by each voting entity. ; Step 4.5, the voting center TP, based on the published new positive integer sequence... Product of positive integers The sum of the votes cast by each voting candidate Count the number of voters for the i-th vote. For the first Each voting object Voting results ; Step 4.6: The voting center (TP) counts the number of votes for each candidate and publishes the results through the classic channel.

[0017] Preferably, in step 4, the inverse one-way evolution operator The specific expression is as follows:

[0018] in, For reverse coin flipping operators, The reverse one-way shift operator has the following formula:

[0019] Preferably, in step 4.3, for the first Number of votes for each voting candidate That is, the maximum value in the corresponding measurement results. In step 4.5, the i-th voter is counted. For the first Each voting object Voting results The formula is:

[0020] In the above formula, if A value of 1 indicates a "yes" vote; if A value of 0 indicates a "no" vote; if If the value is neither 0 nor 1, then the ticket is invalid.

[0021] This invention offers the following advantages: It utilizes quantum walking states as quantum voting resources, which are easier to prepare compared to quantum entangled states. The voting parameters are generated using the Chinese Remainder Theorem, effectively resisting multiple voting attacks by dishonest voters and protecting voter privacy while ensuring vote verifiability. Voters in this scheme only need to execute a one-way evolution operator on the quantum walking state to complete the voting operation, effectively reducing the complexity of the voting operation and the requirements for voters' quantum capabilities. In practical applications, the algorithm of this invention can adjust the number of voting objects according to the voting scenario, exhibiting good versatility and scalability. Attached Figure Description

[0022] Figure 1 This is a flowchart of the anonymous voting method based on one-way quantum walks on a circle in this invention.

[0023] Figure 2 This is a simulated quantum roadmap of the entire voting process in this invention. Detailed Implementation

[0024] The following detailed description of the embodiments, with reference to the accompanying drawings, will further illustrate the specific implementation of the present invention, in order to help those skilled in the art to have a more complete, accurate, and in-depth understanding of the inventive concept and technical solution of the present invention.

[0025] like Figures 1-2 As shown, the present invention provides an anonymous voting method based on one-way quantum walks on a circle, comprising the following steps.

[0026] Step 1: According to the Chinese Remainder Theorem, the voting center prepares several different voting parameters and sends a unique voting parameter to each voter; the voting center prepares the quantum walk states required for quantum voting, forming... A sequence of quantum states, then inserted The first particle sequence is obtained from the decoy particles. And sent to the first voter .

[0027] In this voting method, the voting entities include the voting center, A legitimate voter and Each voting object ,in Indicates the first Each voter Indicates the first There are 10 voting targets, and the first voter is... The voting center is a semi-trusted third-party voting center, TP.

[0028] Step 1 includes the following sub-steps: Step 1.1, Preparation of Voting Center TP coprime positive integers ,in Indicates the first A positive integer, The following formula is used to calculate this. The product of positive integers and except the Beyond positive integers The product of positive integers : (1) Based on the above formula, the product can be calculated. With the positive integers The reciprocal of the modulus of number theory Then there is ;mod represents the modulo operation.

[0029] Step 1.2, the voting center TP will... Product The corresponding number theory reciprocal and positive integers Components of voting parameters And send it to the first via the classic channel. One legitimate voter This continues until each voter receives a unique voting parameter.

[0030] Step 1.3, Preparation of Voting Center TP share Each is in the initial quantum walk state. quantum state sequence (Contains two particles), the expression is: ,in Indicates the first A quantum walk state, the entire The sequence of quantum states is shown below: (2) Step 1.4, the voting center TP randomly selects from the measurement base. One particle is used as the decoy particle, and the measurement basis is the computational basis. or Fourier Where QFT stands for Quantum Fourier Transform. The Hilbert space dimension represents the quantum walk state. The voting center TP will use this... Insert a decoy particle Quantum state sequence In the middle, the length is then obtained as The first particle sequence Then, the voting center TP transmits the first particle sequence via a quantum channel. Send to the first voter .

[0031] Step 2, the i-th voter Received the i-th particle sequence Then, together with the corresponding particle sequence sender, they test the security of the quantum channel.

[0032] In this step, the first voter Received the first particle sequence Then, together with the voting center TP, it checks the i-th voter starting from the second voter. Received the i-th particle sequence Then, and the (i-1)th voter Tested together, at this time .

[0033] Step 2 includes the following sub-steps: Step 2.1, the particle sequence sender publishes the i-th particle sequence. The specific location of the decoy particles and their corresponding measurement basis.

[0034] Step 2.2, the i-th voter The decoy particles were measured based on the published measurement standards, and the results were published.

[0035] Step 2.3: The particle sequence sender determines whether the quantum channel is secure by statistically analyzing the error rate of the decoy particles. If the error rate exceeds a certain predetermined threshold (e.g., 0.05), the quantum channel is considered insecure, and subsequent operations are terminated, returning to step 1.3 for re-execution; otherwise, step 3 is executed.

[0036] Step 3, A legitimate voter Through the Quantum state sequence Perform one-way evolution operator operations to complete the process. Each voting object Voting. One-way evolution operator. The formula is: (3) in, The coin flipper operator is calculated as follows: (4) For the unit operator in location space, For a one-way movement operator, the formula is: (5) in, and They are all translation operators, with the current index being... ,exist : (6) Step 3 includes the following sub-steps in the voting process: Step 3.1, the i-th voter Particle sequence removal After the decoy particle, when i=1, the first voter get All are in the initial quantum walking state quantum state sequence , ;when From 2 voters Starting with the i-th voter After receiving the votes of the previous voter Quantum state sequence , Then, combine the votes of the i-th voter. Voting parameters And their own voting intentions, the i-th voter Prepare the corresponding voting content The expression is ,in , Indicates voting indicators, and They represent the i-th voter, respectively. voted for Each voting object The votes were "against" and "in favor".

[0037] Step 3.2, the i-th voter The voting begins; specifically: the i-th voter Through the Quantum state sequence The first in A quantum wandering state Apply Sub-unidirectional evolution operator The result is obtained from the i-th voter. After voting Quantum state sequence , No. The expression for each quantum walk state is as follows: ,in, Indicates the i-th voter For the first Each voting object Randomly generated positive integers. Quantum state sequence. Become the i-th voter Quantum state sequence after voting The expression is as follows: .

[0038] Step 3.3, the i-th voter Using the decoy particle addition method described in step 1.4, after voting... Quantum state sequence Add decoy particles and send them to the next voter. .

[0039] Specifically, it is the i-th voter Randomly selected from the measurement base One particle is used as a decoy particle, and the measurement basis is a computational basis or a Fourier basis. The voting center TP will use this... A decoy particle was inserted after the vote. Quantum state sequence In the middle, the length is then obtained as The i-th particle sequence Then, the voting center TP transmits the i-th particle sequence via a quantum channel. Send to the next voter .

[0040] Step 3.4, starting from the second voter Then, each voter repeats steps 2, 3.1, 3.2, and 3.3 to complete the voting process and insert... After each decoy particle votes for itself A sequence of quantum states is sent to the next voter until all voters have completed their votes, and then step 3.5 is executed.

[0041] When all voters have finished casting their votes, the last voter... individual voters Voting Quantum state sequence The expression is In each quantum state sequence, the quantum walk state becomes The expression is as follows: (8) In the formula For all voters on the Each voting object The sum of the votes. The entire quantum state sequence becomes as follows: (9) Step 3.5, the last one individual voters After voting on its own, the decoy particle addition method in step 1.4 is used. Quantum state sequence Add decoy particles and send them to the voting center TP.

[0042] Step 4, the voting center (TP) processes all completed votes. Quantum state sequence Perform inverse one-way evolution operator operations This is to complete the vote counting operation for each voting object.

[0043] Inverse one-way evolution operator The specific expression is as follows: (10) in, For reverse coin flipping operators, The reverse one-way shift operator has the following formula: (11) in, and As a translation operator, the formula (6) is the same.

[0044] Step 4 specifically includes the following sub-steps: Step 4.1, the voting center (TP) notifies each voter via broadcast technology. Begin counting votes, each voter The random numbers during the voting process are published. .

[0045] Step 4.2, the voting center (TP) processes all completed votes. Quantum state sequence The first in A quantum wandering state implement Secondary inverse unidirectional evolution operator The operation yields a new quantum walking state. The expression is as follows: (12) Afterwards, the entire quantum state sequence after the vote count becomes as follows: (13) Step 4.3, the voting center TP adopts a measurement basis (e.g., a calculation basis). After the vote count Quantum state sequence The measurements were taken one by one. Then, the voter turnout (TP) at the polling center tallied the results. The first quantum state sequence A quantum wandering state The measurement result, the maximum value in the corresponding measurement result is... As a response to the first The number of votes cast for each voting subject.

[0046] Step 4.4, the voting center TP shuffles the positive integer sequence. The order of positive integers is then used to obtain a new sequence of positive integers. And multiply the sequence by a positive integer through a classical channel. Announcement; simultaneously, TP will announce the sum of the votes cast by each voting entity. .

[0047] Step 4.5, the voting center TP, based on the published positive integer sequence... Product of positive integers The sum of the votes cast by each voting candidate The i-th voter is counted using the following formula. For the first Each voting object Voting results : (14) In the above formula, if If it is 1, it means the first... individual voters To the Each voting object The vote was "yes"; if If it is 0, it means the first... individual voters To the Each voting object The vote was "against"; if If the value is neither 0 nor 1, then the ticket is invalid.

[0048] Step 4.6: The voting center (TP) counts the number of votes for each candidate and publishes the results through the classic channel.

[0049] The security analysis of the above anonymous voting method is as follows.

[0050] I. External attacks.

[0051] (1) Intercept-retransmit attack.

[0052] In the quantum voting method provided by this invention, the particle sequences transmitted between each voting node all contain randomly inserted decoy particles, and the position, number, and corresponding measurement basis of the decoy particles are determined by the sender voter. Voters in advance with the receiver via a classic secure channel It was agreed that Eve, the external eavesdropper, would not be able to obtain the above parameters.

[0053] When Eve attempts to execute an intercept-retransmission attack, it first intercepts... Send to The complete particle sequence, and in the case of unknown decoy particle distribution, randomly selected from the measurement base. or Select a measurement base, measure the intercepted particles, and then prepare the same number of fake particles based on the measurement results, and send them to... .

[0054] Because Eve cannot distinguish between real information particles and decoy particles, and for each fake particle located at the decoy particle's position, the probability that its measurement basis selection matches the correct measurement basis is only [missing information]. Accordingly, the probability of the decoy particle being detected as abnormal is When the total number of decoy particles is If Eve employs the intercept-retransmission attack described above on all decoy particles, the probability that her attack will go completely undetected during the entire decoy particle detection process is: Therefore, the probability that Eve's attack behavior will be successfully detected by the voting method security detection mechanism is... This indicates that when the number of decoy particles... When the value is large enough, the probability of intercept-retransmission attacks being detected is close to 1, thus ensuring the security of the quantum channel.

[0055] (2) Entanglement-measurement attack.

[0056] In an entanglement-measurement attack, the eavesdropper Eve attempts to generate an auxiliary particle and entangle it with a quantum wandering state, then measures this auxiliary particle to try and obtain the voters' votes. ① Assume Eve intercepts the voters' votes. Send to voters particle sequence And it is known that it is located at the measurement base. Subsequently, Eve prepares a quantum state. As a probe particle, and and Perform the operation together Entangled state is obtained ,in Let be the coefficients of this entangled state. Then, Eve will... Send to The system retains the probe particle in its entangled state and performs quantum measurements on it to obtain the voters' voting information. To counter this attack, the probe particle... It became And since it is controlled by Eve, then it exists. In order to make voters and This attack will not be detected in quantum-secure channel testing. Should be targeted This is true; at this point, the entangled state is... .

[0057] ②Another scenario is that the choice of decoy particles may be based on the measurement base. or Assuming voters Send to voters The particles are in the measurement base The decoy particle can be written as , Eve detects particles and Perform the operation Afterwards, an entangled state will be formed. At this point, the quantum state Depend on Formed by quantum Fourier inverse transform , and the entangled state becomes To ensure that this attack will not be detected during quantum channel detection, for and Must be satisfied And there are It holds true. If both of these conditions occur simultaneously, then... Established.

[0058] Combining ① and ②, we can conclude that and Therefore, if Eve wants to use an entanglement-measurement attack method to obtain voters... The voting information, and not allow and To detect this attack behavior during quantum channel detection, the probe particle must be... Independent of the particle sequence used for voting. In this case, Eve's probe particles are also independent of the particle sequence. This means that no useful information about the voting results can be obtained.

[0059] (3) Participant attack.

[0060] In the method of this invention, different voters They perform similar voting operations, and the votes are independent and do not interfere with each other. Here, we need to discuss two attack examples by dishonest voters.

[0061] Assuming there are dishonest voters In conversation with voters After completing the quantum channel security test, I want to measure the quantum state sequence. ( ), in an attempt to find out the voters The voting content for each voting object. In the method of this invention, the random number is only published after all quantum walk states have been sent to TP, therefore, the voters... I have no idea about random numbers The value cannot be obtained from the voters. Any useful voting information.

[0062] Furthermore, the method of this invention only allows each voter to cast one vote for each voting object. This assumes dishonest voters... Attempting to maliciously influence the voting results, i.e., casting two or more votes for a specific candidate. In this case, since all voting parameters are published by TP, each voter can exploit a sequence of positive integers. To count all the votes, after calculation, the voters If a voter casts ≥2 votes for a particular candidate instead of the correct 1 or 0, other voters and the voting team (TP) will detect the voter's malicious voting behavior.

[0063] The embodiments of the present invention are as follows: In an embodiment of the method of the present invention, there are 3 voters. , and For example, if the voting intentions for the same candidate are "oppose", "oppose", and "yes", the anonymous voting method based on single-vector quantum walks on a circle proposed in this application is illustrated in the following steps: Based on steps 1.1 and 1.2, TP prepares three coprime positive integers. The voting parameters for the three voters can be calculated as follows: , and And sent to voters in turn. , and TP preparation is performed according to steps 1.3 and 1.4. All are in the initial quantum walking state The quantum state sequence is obtained, and in step 2, the security of the quantum transmission channel is detected by adding decoy particles. According to steps 3.1 and 3.2, voters... Voting content If the random number is used ,So Need to Quantum walking state Apply two one-way evolution operators Then the wandering state becomes Then in step 3.3, quantum walking state Send to the next voter .

[0064] In steps 3.4 and 3.5, if the voters and The random numbers are respectively and And their voting content is respectively and At this point, the two voters need to determine the quantum walk state. Applying a one-way evolution operator The number of times were 3 and 7 respectively. After execution, the quantum walk state became... : (16) Finally, in steps 4.1, 4.2, and 4.3, each of the three voters will submit their random numbers. , and The results will be published. TP performs six reverse-direction unidirectional evolution operators on the quantum walk state based on these three random numbers. Finally, in order to obtain the voting results, TP needs to measure the quantum walk states. The maximum value measured at each position is the sum of the votes. The simulated quantum circuit for the entire voting process is as follows: Figure 2 As shown. Here, coin is the qubit of the coin system, with a quantity of 1, responsible for determining the direction of the quantum walk; pos0-pos3 are the four qubits of the walk system respectively; c is a classical register; It is a one-way evolution operator; It is a one-way evolution operator in the opposite direction; symbol This refers to quantum measurement.

[0065] In the method of this invention, IBM's Qiskit quantum computing platform was used for simulation experiments. When the number of steps was set to 6 and the number of samplings to 1024, the measurement results are shown in Table 2. As can be seen from Table 2, the measurement results are basically consistent with the probability cases in Table 1, and the maximum measured position is 6, which conforms to... The voting results are then announced by TP after steps 4.4, 4.5, and 4.6, and each voter can verify the correctness of each ballot themselves.

[0066] Table 2 Measurement results and number of quantum walks

[0067] The present invention has been described above by way of example with reference to the accompanying drawings. Obviously, the specific implementation of the present invention is not limited to the above-described manner. Any non-substantial improvements made using the inventive concept and technical solution of the present invention, or the direct application of the inventive concept and technical solution of the present invention to other occasions without modification, are all within the protection scope of the present invention.

Claims

1. An anonymous voting method based on one-way quantum walks on a circle, characterized in that: Includes the following steps: Step 1: According to the Chinese Remainder Theorem, the voting center prepares several different voting parameters and sends a unique voting parameter to each voter; the voting center prepares the quantum walk state required for quantum voting, forming... A sequence of quantum states, then inserted The first particle sequence is obtained from the decoy particles. And sent to the first voter ; in, Indicates the first Each voter , Indicates the first Each voting object, The voting center is a semi-trusted third-party voting center, TP. Step 2, the i-th voter Received the i-th particle sequence Then, together with the corresponding particle sequence sender, they will test the security of the quantum channel; Step 3, A legitimate voter Through the Quantum state sequence Perform one-way evolution operator operations to complete the process. Each voting object The vote; The expression is ,in Indicates the first A quantum walking state; after the last voter has cast their vote, this needs to be... Quantum state sequence Send to the voting center TP; Step 4, the voting center (TP) processes all completed votes. Quantum state sequence Perform inverse one-way evolution operator operations to complete the vote counting operation for each voting object.

2. The anonymous voting method based on one-way quantum walks on a circle according to claim 1, characterized in that: Step 1 includes the following sub-steps: Step 1.1, Preparation of Voting Center TP coprime positive integers ,in Indicates the first A positive integer, ;calculate The product of positive integers and except the Beyond positive integers The product of positive integers ; Step 1.2, the voting center TP will... Product The corresponding number theory reciprocal and positive integers Components of voting parameters And send it to the first via the classic channel. One legitimate voter This continues until each voter receives a unique voting parameter; Step 1.3, Preparation of Voting Center TP share Each is in the initial quantum walk state. quantum state sequence ; The sequence of quantum states is shown below: ， Indicates the first A quantum walking state; Step 1.4, the voting center TP in Quantum state sequence Adding decoy particles yields the first particle sequence. Send to the first voter .

3. The anonymous voting method based on one-way quantum walks on a circle according to claim 2, characterized in that: In step 1.1, calculate this The product of positive integers and except the Beyond positive integers The product of positive integers The formula for calculation is: Based on the above formula, the product can be calculated. With the positive integers The reciprocal of the modulus of number theory Then there is ;mod represents the modulo operation.

4. An anonymous voting method based on one-way quantum walks on a circle according to claim 3, characterized in that: The method for adding decoy particles in step 1.4 includes: randomly selecting from the measurement base. One particle was inserted as a decoy particle into the corresponding... From a sequence of quantum states, a corresponding sequence of particles is formed, with the measurement basis serving as the computational basis. or Fourier Where QFT stands for Quantum Fourier Transform. The Hilbert space dimension represents the quantum walk state.

5. An anonymous voting method based on one-way quantum walks on a circle according to claim 4, characterized in that: Step 2 includes the following sub-steps: Step 2.1, the particle sequence sender publishes the i-th particle sequence. The specific location of the decoy particles and their corresponding measurement basis; Step 2.2, the i-th voter The decoy particles were measured according to the published measurement standards, and the measurement results were published. In step 2.3, the particle sequence sender determines whether the quantum channel is secure by statistically analyzing the error rate of the decoy particles. If the error rate exceeds a predetermined threshold, the subsequent operation will be terminated, and the process will return to step 1.3 to be re-executed; otherwise, the operation in step 3 will be executed.

6. An anonymous voting method based on one-way quantum walks on a circle according to claim 5, characterized in that: Step 3 includes the following sub-steps: Step 3.1, the i-th voter Particle sequence removal The decoy particle in the middle, when i=1, is the first voter. get All are in the initial quantum walking state quantum state sequence , ;when From 2 voters Starting with the i-th voter After receiving the votes of the previous voter Quantum state sequence , Then, when Combined with the i-th voter Voting parameters And their own voting intentions, the i-th voter Prepare the corresponding voting content ; Step 3.2, the i-th voter Through the Quantum state sequence The first in A quantum wandering state Apply Sub-unidirectional evolution operator The result is obtained from the i-th voter. After voting Quantum state sequence , No. The expression for each quantum walk state is as follows: ,in, Indicates the i-th voter For the first Each voting object A randomly generated positive integer; Step 3.3, the i-th voter Using the decoy particle addition method described in step 1.4, after voting... Quantum state sequence Add decoy particles and send them to the next voter. ; Step 3.4, starting from the second voter Then, each voter repeats steps 2, 3.1, 3.2, and 3.3 to complete the voting process and submit their vote. A sequence of quantum states is sent to the next voter until all voters have completed their votes, then step 3.5 is executed; Step 3.5, the last one individual voters After voting on its own, the decoy particle addition method in step 1.4 is used. Quantum state sequence Add decoy particles and send them to the voting center TP.

7. An anonymous voting method based on one-way quantum walks on a circle according to claim 6, characterized in that: In step 3, the one-way evolution operator The formula is: in, The coin flipper operator is calculated as follows: For the unit operator in location space, For a one-way movement operator, the formula is: in, and Both are translation operators. When the subscript of the translation operator is... And this value is a positive integer, therefore it exists. The formula is as follows: 。 8. An anonymous voting method based on one-way quantum walks on a circle according to claim 7, characterized in that: Step 4 includes the following sub-steps: Step 4.1, the voting center (TP) notifies each voter via broadcast technology. Begin counting votes, each voter The random numbers during the voting process are published. ; Step 4.2, the voting center (TP) processes all completed votes. Quantum state sequence The first in A quantum wandering state implement Secondary inverse unidirectional evolution operator The operation yields a new quantum walking state. ; Step 4.3, the voting center TP uses a measurement basis to compare the votes after counting. Quantum state sequence Measurements were taken one by one; then, the voter turntable (TP) at the polling center tallied the results. The first quantum state sequence A quantum wandering state The measurement results yielded the first Number of votes for each voting candidate ; Step 4.4, the voting center TP shuffles the positive integer sequence. The order of positive integers is then used to obtain a new sequence of positive integers. And through a classical channel, the new positive integer sequence and the positive integer product are processed. Announcement; simultaneously, TP will announce the sum of the votes cast by each voting candidate. ; Step 4.5, the voting center TP, based on the published new positive integer sequence... Product of positive integers The sum of the votes cast by each voting candidate Count the number of voters for the i-th vote. For the first Each voting object Voting results ; Step 4.6: The voting center (TP) counts the number of votes for each candidate and publishes the results through the classic channel.

9. An anonymous voting method based on one-way quantum walks on a circle according to claim 8, characterized in that: In step 4, the inverse one-way evolution operator The specific expression is as follows: in, For reverse coin flipping operators, The reverse one-way shift operator has the following formula: 。 10. An anonymous voting method based on one-way quantum walks on a circle according to claim 8, characterized in that: In step 4.3, for the first Number of votes for each voting candidate That is, the maximum value in the corresponding measurement results, and the sum of the votes of each voting object is. In step 4.5, the i-th voter is counted. For the first Each voting object Voting results The formula is: In the above formula, if A value of 1 indicates a "yes" vote; if A value of 0 indicates a "no" vote; if If the value is neither 0 nor 1, then the ticket is invalid.

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