Quantum voting method based on quantum detectable Byzantine protocol

Abstract

The invention belongs to the technical field of quantum communication, and particularly relates to a quantum voting method based on a quantum detectable Byzantine protocol. Comprising the steps of initializing a system and performing consistency negotiation; the voters generate local masks and fuse the votes to obtain phase parameters; constructing a time slot sequence, segmenting the time slot sequence and distributing the segmented time slot sequence to voters; voters select data, reference and trap slots from corresponding time periods and prepare quantum states of the corresponding slots; the time slot sequence is transmitted along a loop, each voter executes phase loading according to the phase parameter in the own time period, and an output time coding quantum state is obtained after transmission for one week; calculating the detection probability according to the trap slot position, if the detection probability exceeds a preset threshold value, stopping, otherwise, continuing; each voter carries out accumulative phase estimation on the output time coding quantum state according to the data slot position and recovers the final total vote number; verifying the final total number of votes to ensure that honest nodes obtain consistent numbers of votes; according to the method, the defects that a traditional protocol depends on a trusted center and lacks fault-tolerant capability are overcome, and the security and practicability of the quantum voting protocol are improved.

Description

Technical Field

[0001] This invention belongs to the field of quantum communication technology, specifically relating to a quantum voting method based on the quantum detectable Byzantine protocol. Background Technology

[0002] With the rapid development of quantum communication technology, cryptographic protocols based on quantum mechanics principles can theoretically provide unconditional security. However, existing electronic voting protocols still face several challenges in practical applications. Traditional electronic voting schemes rely heavily on computational complexity assumptions, and with the improvement of quantum computing power, their security faces serious threats. On the other hand, existing quantum voting protocols typically assume the existence of a completely trusted third-party vote counting center or require all participating nodes to be honest. However, in real-world distributed network environments, nodes may exhibit Byzantine behavior (i.e., sending incorrect or inconsistent information) due to attacks or internal malice, allowing attackers to threaten the fairness of the protocol by disrupting the consensus process or tampering with ballots. Furthermore, ensuring the verifiability of vote counting results and network-wide consistency while guaranteeing absolute anonymity of voters (i.e., votes cannot be traced back to individuals) is a critical issue that urgently needs to be addressed in the field of quantum voting.

[0003] Currently, while some research has attempted to address these issues using entanglement swapping or multi-party computation techniques, a comprehensive solution that simultaneously combines dynamic invisible mask generation, anti-interference trap detection, and Byzantine fault tolerance mechanisms is lacking. In practical applications, such as large-scale elections or board voting, fault tolerance for malicious nodes is often required, and existing solutions struggle to effectively meet this need.

[0004] In summary, designing a quantum voting method that supports Byzantine fault tolerance, has dynamic mask generation capabilities, and does not require a fully trusted center, while ensuring system security and anonymity, and balancing result consistency and protocol robustness, has become a key issue that urgently needs to be addressed in the field of quantum information security. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a quantum voting method based on the quantum detectable Byzantine protocol, which includes:

[0006] S1: Initialize the system, randomly select a leader from the voters and confirm the order of the circular voters, and the leader performs consensus negotiation;

[0007] S2: Voters generate local masks;

[0008] S3: Voters merge the ballot with the local mask to obtain the phase parameters;

[0009] S4: Construct a time slot sequence, divide the time slot sequence into segments according to the number of voters, and assign each time segment to a voter one-to-one; voters select data slots, reference slots, and trap slots from the corresponding time segments and prepare time-encoded quantum states for the corresponding slots;

[0010] S5: The time slot sequence is transmitted along the loop. Each voter performs phase loading on the time-coded quantum state according to the phase parameter during their own time period, so that the late time slot component of the time-coded quantum state produces a phase shift corresponding to the phase parameter. After the time slot sequence is transmitted for one cycle, an output time-coded quantum state carrying the accumulated phase information is obtained.

[0011] S6: Identify the abnormal trap slots and calculate the detection probability. If the detection probability exceeds the preset threshold, stop the voting process for this round and discard the measurement results of the time slot sequence for this round; otherwise, execute steps S7~S8 to complete the vote counting and consistency verification for this round.

[0012] S7: For the time slot sequence after one cycle of transmission along the loop in step S5, perform interferometry on the output time-coded quantum state in the data slot to obtain the estimated value of the cumulative phase and convert it into the final total number of votes;

[0013] S8: Each voter uses the QDBA protocol to verify the final total number of votes to ensure that honest nodes receive a consistent number of votes.

[0014] Preferably, step S1 includes:

[0015] Construct a ring-shaped topology network, including N voters, a quantum state distributor Bob, and a vote counter Charlie;

[0016] A leader is randomly selected from the voters, and the order of the circular voters is determined.

[0017] The leader generates consensus parameters and uses the QDBA protocol to reach consensus parameters with all voters.

[0018] Furthermore, step S2 includes:

[0019] Bob prepares N pairs of M-dimensional generalized Bell states;

[0020] For each pair of adjacent voters Bob will put a pair of entangled particles In Distributed to ,Will Distribute to ;

[0021] Each voter Generate a private key locally; determine the node type of the voter based on the private key and calculate the local mask.

[0022] Furthermore, the process of calculating the local mask includes:

[0023] When voters Generate private key According to the local mask calculation formula Calculate the local mask;

[0024] When voters Generate private key According to the local mask calculation formula Calculate the local mask;

[0025] All local masks satisfy the constraints. ;

[0026] Where M represents the modulus to prevent overflow. This represents the first entangled particle measurement value for voter i. This represents the second entangled particle measurement value for voter i.

[0027] Preferably, the formula for calculating the phase parameter is:

[0028]

[0029] in, This represents the phase parameter of voter i. This represents the modulus used to prevent overflow. This represents the ballot information of voter i. This represents the local mask of voter i.

[0030] Preferably, the formula for calculating the detection probability is:

[0031]

[0032] in, This indicates the probability that the system successfully detected an active attack. This indicates the proportion of anomaly trap slots in the time slot sequence. This indicates the number of time slots the attacker attempted to tamper with.

[0033] Preferably, the formula for obtaining the estimated value of the cumulative phase is expressed as:

[0034]

[0035] in, This represents the estimated value of the cumulative phase. This represents the modulus used to prevent overflow. Indicates the number of voters. This represents the ballot information of voter i.

[0036] The preferred formula for converting the final total number of votes is:

[0037]

[0038] in, This represents the final total number of votes obtained by the i-th voter after decoding. This represents the modulus used to prevent overflow. This represents the estimated cumulative phase of the i-th voter, and the round function represents the rounding operation.

[0039] The beneficial effects of this invention are as follows: This invention achieves unconditional anonymity of voting content by using dynamic invisible masking technology, effectively defends against external eavesdropping and internal tampering attacks through time slot coding and trap detection mechanisms, and ensures the consistency of network parameters and results in the presence of malicious nodes by using quantum detectable Byzantine protocol. It solves the defects of traditional protocols that rely on trusted centers and lack fault tolerance, improves the security and practicality of quantum voting protocol, and has good application prospects. Attached Figure Description

[0040] Figure 1 This is a flowchart of the quantum voting method based on the quantum detectable Byzantine protocol in this invention. Detailed Implementation

[0041] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] This invention proposes a quantum voting method based on the quantum detectable Byzantine protocol, such as... Figure 1 As shown, the method includes the following:

[0043] S1: Initialize the system, randomly select a leader from the voters and confirm the order of the circular voters, and the leader performs consensus negotiation.

[0044] The initialization system based on the quantum detectable Byzantine protocol specifically involves: constructing a ring topology network, and building within the ring topology network, such as... Figure 1 As shown, including voters , , ···, And Bob, the entangled state distributor, and Charlie, the vote counter. Bob, the entangled state distributor, is responsible for preparing Bell pairs; Charlie is responsible for receiving the time slot sequence after the loop transmission ends and organizing its publication and verification; Leader is responsible for parameter negotiation; and the vote counters are responsible for mask generation, phase encoding, and result verification.

[0045] A leader is randomly selected from the voters to determine the order of the circular voters, specifically as follows: A leader S is randomly selected for this round, and the order of the circular participants is determined: .

[0046] The leader generates consensus parameters and uses the QDBA protocol to reach consensus parameters with all voters. Specifically, Leader S generates the following parameters: RoundID (round identifier), M (modulus), ... To prevent overflow), P (the probability of selecting a swap operation during the mask generation phase). Leader S uses the QDBA protocol (Quantum Detectable Byzantine Protocol) to communicate these parameters to all participants.

[0047] The modular mapping rules agreed upon during system initialization are as follows: Let the set of voting options be { Map it to the set of integers {0,1,…,L-1} modulo M, where When the i-th voter's option is At that time, let them know their ballot information ,in .

[0048] S2: Voters generate local masks.

[0049] By utilizing the quantum channel between the entangled source and participating nodes, a dynamic invisible mask generation process is performed, enabling all network nodes to collectively construct a global mask with an algebraic sum of zero without revealing their own mask values. Specifically:

[0050] Bob prepares N pairs of M-dimensional generalized Bell states, whose quantum state representation is as follows: An M-dimensional generalized Bell state is a maximally entangled state consisting of two particles, whose two subsystems are denoted as... and The corresponding entangled particle pairs are denoted as .

[0051] For any two adjacent voters Bob will entangle the particles Distribute to entangled particles Distribute to ,in Simultaneously receive the particles from the previous pair of entangled particles. ,therefore hold .

[0052] To ensure the generated dynamic invisible mask satisfies the global elimination property, a private key-controlled measurement basis selection strategy is used to operate on entangled particles. This strategy includes at least computational basis measurements as endpoint nodes and Bell-state generalized basis measurements as transparent relay nodes. Specifically:

[0053] Each voter Generate private key locally :

[0054] like ,but As an endpoint node;

[0055] like ,but As a transparent relay node.

[0056] Calculate the local mask based on the voter's node type determined by the private key:

[0057] When voters Generate private key Perform a base measurement calculation; the local mask calculation formula is as follows: ;

[0058] When voters Generate private key Perform Bell state generalized basis measurement, and the local mask calculation formula is as follows: .

[0059] The local subnet mask of the entire network meets the constraints. .

[0060] Where M represents the modulus to prevent overflow. This represents the first entangled particle measurement value for voter i. This represents the second entangled particle measurement value for voter i; that is, for any voter... The particles it holds and According to its private key The selected measurement method and The measurement was performed, and two measurement output values ​​were obtained, which are denoted as follows: , Used to calculate voters local mask .

[0061] S3: Voters merge the ballot with the local mask to obtain the phase parameters.

[0062] The generation of anonymous voting results relies on the encoding of phase parameters, which are transmitted through the voter's vote. The phase of the embedded ring quantum state is used to realize the fusion of the vote and the local mask, specifically:

[0063]

[0064] in, This represents the phase parameter of voter i. This represents the result of fusing voter i's vote with the local mask. This represents the modulus used to prevent overflow. This represents the ballot information of voter i. This represents the dynamic invisible mask, or local mask, for voter i. The phase parameter is used to hide the vote information within the mask.

[0065] S4: Construct a time slot sequence, divide the time slot sequence into segments according to the number of voters, and assign each time segment to a voter one-to-one; voters select data slots, reference slots, and trap slots from the corresponding time segments and prepare time-encoded quantum states for the corresponding slots.

[0066] Construct a time slot sequence, which includes at least the following slot types: data slots carrying the accumulation of voting phases, reference slots for phase reference calibration, and trap slots for detecting eavesdropping, thereby verifying the security of the channel while completing the voting statistics.

[0067] In subsequent steps (see steps S5 to S7), the data slots are used for interferometry to estimate the cumulative total phase, the reference slots are used for phase reference calibration, and the trap slots are used for security detection. The time-coded quantum states on each slot are transmitted along the loop with the time slot sequence and are sequentially superimposed by each voter in the subsequent phase loading step.

[0068] The time slot sequence is segmented according to the number of voters, and each time slot is assigned one-to-one to a voter. Specifically: Let the length of the time slot sequence be L, and the time number be... All time slots are divided into N non-overlapping time periods according to the number of voters N, namely: ,in Belonging to Voters During the time period in which it is assigned Select the data slot set respectively: Indicates a data slot. Indicates the reference slot. Indicates the trap slot.

[0069] The time-encoded quantum state corresponding to the slot is prepared, which is based on the early and late time slots of the time-bin qubit, as detailed below:

[0070] For any time slot t, using the early and late time slots of the time-bin qubit as the ground state, denoted as follows: ,use This indicates the arrival time of the early time slot in the t-th time slot. This indicates that the late time slot arrives at the t-th time slot.

[0071] For each Time-encoded quantum states for data slots For each Preparation of time-encoded quantum states of reference slots For each Time-encoded quantum states for preparing trap slots It is a single time slot state or .

[0072] S5: The time slot sequence is transmitted along the loop. Each voter performs phase loading on the time-coded quantum state according to the phase parameter during their own time period, so that the late time slot component of the time-coded quantum state produces a phase shift corresponding to the phase parameter. After the time slot sequence is transmitted for one cycle, an output time-coded quantum state carrying the accumulated phase information is obtained.

[0073] The time slot sequence is propagated along the loop, and the time-encoded quantum state prepared in step S4 is also propagated along the loop along the time slot sequence. Each voter performs phase loading according to the phase parameters obtained in step S3 within their allocated time period. Specifically: the time slot sequence is propagated along... , , ···, Transmission, when passing through hour, Perform a phase loading operation on all data slots in the time slot sequence: After one week of time slot sequence transmission, the time-encoded quantum state carries the cumulative phase information of all voters.

[0074] The above node-by-node phase loading process can be equivalently represented as sequentially applying the phase modulation operators of each voter to the initial time-encoded quantum state. To avoid repetition, the above phase loading process can be equivalently described in the form of operator multiplication as follows: The phase evolution process of the time-encoded quantum state in the ring topology is represented as follows:

[0075]

[0076] in This is the initial superposition state. and These represent the early and late time slot components, respectively. Let be the phase modulation operator for the i-th voter node, where With voters in step S3 The calculated phase parameters are consistent. Its function is... , The final state after one week of evolution contains information about the total number of votes across the network. After the time slot sequence is transmitted along the loop for one week, the output time-encoded quantum state carrying the cumulative phase information is obtained.

[0077] S6: Identify the abnormal trap slots and calculate the detection probability. If the detection probability exceeds the preset threshold, stop the voting process for this round and discard the measurement results of the time slot sequence for this round; otherwise, execute steps S7~S8 to complete the vote counting and consistency verification for this round.

[0078] After the sequence ends, the voters Only its trap slot set A time-resolved measurement is performed on time slot t, and compared with its locally preset trap state to determine whether the quantum state still falls within its preset trap time slot. The comparison rule is that when the voter's preset trap state in a certain trap slot t is... When the measurement result falls in the early time slot, the preset trap state should be... When the measurement results fall in the late time slot, if there is a trap slot that does not meet the above correspondence, then the trap slot is determined to be abnormal.

[0079] Furthermore, the detection probability is calculated based on the proportion of trap slots. If some slots are inconsistent, since attackers do not know the location of the trap slots, they will hit the slots with probability and expose themselves; that is, security trap detection assesses the system's attack risk in a statistical probability manner, and the formula for calculating the detection probability is:

[0080]

[0081] in, This indicates the probability that the system successfully detected an active attack. This represents the proportion of trap slots in the time slot sequence (the probability that an attacker randomly modifies a time slot and hits a trap slot when the attacker does not know the location of the trap slot). This indicates the number of time slots the attacker attempted to tamper with.

[0082] S7: For the time slot sequence after one cycle of transmission along the loop in step S5, perform interferometry on the output time-coded quantum state in the data slot to obtain the estimated value of the cumulative phase and convert it into the final total number of votes.

[0083] In step S5, after the time-coded quantum state is phase-loaded by each voter, its late-slot component carries the cumulative phase information formed by the superposition of phase parameters of all voters. In this step, each voter only uses the quantum state corresponding to their data slot to perform interferometric measurement to obtain an estimate of the cumulative phase. Step S5 only forms an output time-coded quantum state carrying the cumulative phase information, and uses this to recover the final total vote count. Each voter estimates the cumulative phase based on their data slot, and recovers the final total vote count based on the cumulative phase estimation result. Specifically:

[0084] The time slot sequence is obtained after running for one week: ,in And because Therefore, the cumulative phase satisfies .

[0085] Voter i performs interferometry on the time-coded quantum state corresponding to its data slot and statistically obtains an estimate of the cumulative phase. .in, The corresponding theoretical value is the aforementioned global cumulative phase estimate. Ideally there is When statistical error exists around fluctuation.

[0086] Each Use your own segment's data slots Interferometry is performed on the time-coded quantum states to estimate the cumulative phase. A reference phase parameter is selected to estimate the relative phase of the two time-slot components. Constructing a measurement base: The probability of getting a "+" or "-" result is: Voters have different opinions The measurement results are statistically analyzed, and the estimated value of the cumulative phase is obtained by inversion based on the probability distribution. Then, according to the modulus mapping rules agreed upon during system initialization, the phase estimate is converted into a vote estimate. Select two or three different And the number of recoverable votes for each data slot is counted: .in, Indicates voters The final estimated total number of votes obtained after restoration This represents the modulus used to prevent overflow. Indicates voters The cumulative phase estimate is obtained based on the data slot measurement statistics. The reference phase parameter selected during interferometry. To measure the base The probability of getting a "+" or "-" result.

[0087] S8: Each voter uses the QDBA protocol to verify the final total number of votes to ensure that honest nodes receive a consistent number of votes.

[0088] The QDBA protocol is used to confirm the final result through consensus. This includes each voting node generating a message msg=(RoundID,S(i)) containing the round identifier for the recovered total number of votes S and broadcasting it to all voting nodes. Byzantine error nodes are eliminated through a multi-round interactive verification algorithm to ensure that all honest participants obtain a consistent final number of votes.

[0089] In summary, this invention utilizes the quantum detectable Byzantine protocol to establish decentralized parameter consensus, uses high-dimensional entangled state distribution and local measurement to generate a dynamic invisible mask, and combines the voting information with the mask. Through the phase evolution of time-encoded quantum states in a ring topology, anonymous voting results are generated. This result ensures the accuracy of the overall network vote count while effectively hiding the voting intentions of individual nodes and possessing detectability against malicious attacks.

[0090] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A quantum voting method based on the quantum detectable Byzantine protocol, characterized in that, Includes the following steps: S1: Initialize the system, randomly select a leader from the voters and confirm the order of the circular voters, and the leader performs consensus negotiation; S2: Voters generate local masks; S3: Voters merge the ballot with the local mask to obtain the phase parameters; S4: Construct a time slot sequence, divide the time slot sequence into segments according to the number of voters, and assign each time segment to a voter one-to-one; voters select data slots, reference slots, and trap slots from the corresponding time segments and prepare time-encoded quantum states for the corresponding slots; S5: The time slot sequence is transmitted along the loop. Each voter performs phase loading on the time-coded quantum state according to the phase parameter during their own time period, so that the late time slot component of the time-coded quantum state produces a phase shift corresponding to the phase parameter. After the time slot sequence is transmitted for one cycle, an output time-coded quantum state carrying the accumulated phase information is obtained. S6: Identify the abnormal trap slots and calculate the detection probability. If the detection probability exceeds the preset threshold, stop the voting process for this round and discard the measurement results of the time slot sequence for this round; otherwise, execute steps S7~S8 to complete the vote counting and consistency verification for this round. S7: For the time slot sequence after one cycle of transmission along the loop in step S5, perform interferometry on the output time-coded quantum state in the data slot to obtain the estimated value of the cumulative phase and convert it into the final total number of votes; S8: Each voter uses the QDBA protocol to verify the final total number of votes to ensure that honest nodes receive a consistent number of votes.

2. The quantum voting method based on the quantum detectable Byzantine protocol according to claim 1, characterized in that, Step S1 includes: Construct a ring-shaped topology network, including N voters, a quantum state distributor Bob, and a vote counter Charlie; A leader is randomly selected from the voters, and the order of the circular voters is determined. The leader generates consensus parameters and uses the QDBA protocol to reach consensus parameters with all voters.

3. A quantum voting method based on the quantum detectable Byzantine protocol according to claim 2, characterized in that, Step S2 includes: Bob prepares N pairs of M-dimensional generalized Bell states; For each pair of adjacent voters Bob will put a pair of entangled particles In Distributed to ,Will Distribute to ; Each voter Generate a private key locally; determine the node type of the voter based on the private key and calculate the local mask.

4. A quantum voting method based on the quantum detectable Byzantine protocol according to claim 3, characterized in that, The process of calculating the local mask includes: When voters Generate private key According to the local mask calculation formula Calculate the local mask; When voters Generate private key According to the local mask calculation formula Calculate the local mask; All local masks satisfy the constraints. ; Where M represents the modulus to prevent overflow. This represents the first entangled particle measurement value for voter i. This represents the second entangled particle measurement value for voter i.

5. A quantum voting method based on the quantum detectable Byzantine protocol according to claim 1, characterized in that, The formula for calculating the phase parameter is: ； in, This represents the phase parameter of voter i. This represents the modulus used to prevent overflow. This represents the ballot information of voter i. This represents the local mask of voter i.

6. A quantum voting method based on the quantum detectable Byzantine protocol according to claim 1, characterized in that, The formula for calculating the detection probability is: ； in, This indicates the probability that the system successfully detected an active attack. This indicates the proportion of anomaly trap slots in the time slot sequence. This indicates the number of time slots the attacker attempted to tamper with.

7. A quantum voting method based on the quantum detectable Byzantine protocol according to claim 1, characterized in that, The formula for obtaining the estimated value of the cumulative phase is expressed as: ； in, This represents the estimated value of the cumulative phase. This represents the modulus used to prevent overflow. Indicates the number of voters. This represents the ballot information of voter i.

8. A quantum voting method based on the quantum detectable Byzantine protocol according to claim 1, characterized in that, The formula for converting the final total number of votes is: ； in, This represents the final total number of votes obtained by the i-th voter after decoding. This represents the modulus used to prevent overflow. This represents the estimated cumulative phase of the i-th voter, and the round function represents the rounding operation.

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