A Dynamic Privacy-Regulated Cross-Chain Payment Method Based on Lattice Cryptography

Abstract

This invention discloses a dynamic privacy-monitored cross-chain payment method based on lattice cryptography, relating to the fields of blockchain cross-chain payment and post-quantum cryptography. The method includes the following steps: S1: System initialization; S2: User key generation and transaction privacy protection; S3: Cross-chain consistency verification; S4: Dynamic parameter and key management; S5: Monitoring and auditing mechanism. The technical problem this invention aims to solve is to provide a dynamic privacy-monitored cross-chain payment method based on lattice cryptography, addressing the issues of quantum security threats, the incompatibility between privacy and regulation, and low cross-chain verification efficiency in existing cross-chain payment methods.

Description

Technical Field

[0001] This invention relates to the fields of blockchain cross-chain payment and post-quantum cryptography, specifically to a dynamic privacy-monitoring cross-chain payment method based on lattice cryptography. Background Technology

[0002] With the rapid development of blockchain technology, multi-chain ecosystems are gradually becoming an important infrastructure for the digital economy. Against this backdrop, the demand for inter-chain value circulation is constantly growing. Cross-chain payments, as a key mechanism for achieving interoperability between different blockchains, are playing a central role in several key scenarios such as cross-border finance, supply chain settlement, and digital asset trading. However, current cross-chain payment systems face three major, irreconcilable contradictions: first, the conflict between privacy protection and quantum security; second, the opposition between user anonymity and regulatory compliance; and third, the trade-off between cross-chain efficiency and verification reliability.

[0003] Most current mainstream cross-chain systems are based on traditional public-key encryption algorithms, such as elliptic curve cryptography and large integer factorization. However, these algorithms are extremely vulnerable to quantum computing—quantum algorithms can crack keys in a short time, leading to systemic risks to transaction funds. Although some solutions introduce homomorphic encryption to hide transaction amounts, their security foundation is also limited by the ability to resist quantum attacks, failing to fundamentally close the security gap. Furthermore, while blockchain anonymity protects user privacy, it also provides opportunities for illegal activities such as money laundering and extortion. Most existing privacy protection mechanisms (such as ring signatures and zero-knowledge proofs) adopt an "all-or-nothing" privacy model, either completely anonymizing and hindering regulatory tracking, or disclosing all information and sacrificing privacy. Financial regulatory agencies often have to conduct full-chain scans when performing anti-money laundering audits, which is not only inefficient but also fails to meet dynamic and refined compliance strategies.

[0004] Meanwhile, verification mechanisms in cross-chain communication remain immature. Interoperability between heterogeneous blockchains typically relies on solutions such as hash time locks and sidechain relays, but these mechanisms involve frequent interactions and complex processes, leading to significant transaction delays and failing to meet real-time requirements. More seriously, the plaintext amount comparison method used to ensure transaction consistency often directly exposes sensitive business information, posing a risk of privacy breaches. To address this issue, existing privacy verification protocols attempt to hide transaction amounts using homomorphic encryption and other techniques, but these still face significant bottlenecks in practical deployment: the rapid increase in ciphertext size significantly increases communication overhead, limiting system throughput and making it difficult to support high-concurrency application scenarios. Furthermore, the current industry also exhibits significant shortcomings in its technological evolution. On the one hand, while mainstream post-quantum cryptography schemes offer strong long-term security guarantees, they often neglect the practical need for a balance between privacy protection and regulatory compliance in cross-chain scenarios; on the other hand, emerging cryptographic components such as dynamic accumulators have not yet been deeply integrated with key lifecycle management mechanisms, meaning that if keys are leaked, historical data remains at risk of being decrypted. Therefore, there is an urgent need to build a new cross-chain payment solution that can simultaneously resist quantum threats, support dynamic privacy regulation, and have efficient verification capabilities, so as to lay a secure, efficient and compliant technical foundation for the next generation of trusted blockchain infrastructure. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a dynamic privacy-regulated cross-chain payment method based on lattice cryptography, which solves the problems of quantum security threats, the incompatibility between privacy and regulation, and low cross-chain verification efficiency in existing cross-chain payments.

[0006] The present invention achieves its objective by employing the following technical solution:

[0007] A dynamic privacy-regulated cross-chain payment method based on lattice cryptography, characterized by the following steps: S1: System initialization;

[0008] S2: User key generation and transaction privacy protection;

[0009] S3: Cross-chain consistency verification;

[0010] S4: Dynamic parameters and key management;

[0011] S5: Regulatory and auditing mechanisms.

[0012] As a further limitation of this technical solution, step S1 is as follows:

[0013] S11: During system startup, relay nodes generate global common parameters and set grid dimensions. and modulus To ensure compliance with NIST's post-quantum security standards;

[0014] S12: Generate a uniform random matrix by calling the trapdoor generation algorithm. And its corresponding short basis trap gate S, making This indicates that each element of the matrix product must be... Integer division, modulo of each element The result is 0;

[0015] in: It represents the set of integers;

[0016] , Indicates rounding up;

[0017] S13: Error distribution is selected from discrete Gaussian distribution. Standard deviation ;

[0018] S14: Collision-resistant hash functions are mainly used to bind user identity information and transaction data;

[0019] S15: Master Key It is held secretly by the regulatory agency for subsequent key management and tracing.

[0020] As a further limitation of this technical solution, step S2 is as follows:

[0021] S21: User key generation involves embedding identity information into a lattice structure to achieve uniqueness;

[0022] First, calculate the identity hash. And construct an identity association matrix , ;

[0023] Calling the lattice-based homomorphic proxy re-encryption algorithm Generate private key Ensure that the requirements are met. private key To satisfy the short vector property and prevent attacks;

[0024] Public Key Once made public, users participate in transactions through it, and the process of generating private keys is to ensure that the keys of different users are not statistically correlated;

[0025] S22: Transaction encryption protects monetary privacy through LWE's difficulty mechanism;

[0026] First, the amount Encode into a binary vector and generate a random matrix. With error vector The ciphertext is constructed as follows , Indicates rounding down to the nearest integer;

[0027] The ring signature module invokes zero-knowledge proofs to generate a signature; signature proof. The user has satisfied The sender's valid private key is hidden, while its specific location in the ring is concealed, ensuring the sender's anonymity.

[0028] The transaction was ultimately completed Submitted to the blockchain network in the form of [submission method];

[0029] Ring signatures achieve strong anonymity through zero-knowledge proofs; the signer chooses to include themselves as an anonymity signer. Construct a ring using public keys to generate commitments. and through non-interactive proof This indicates that they possess a valid private key.

[0030] As a further limitation of this technical solution, step S3 is as follows:

[0031] Cross-chain verification ensures transaction consistency through random linear transformations;

[0032] S31: Relay nodes generate random matrices Calculate the challenge vector , The ciphertext is sent to chain A and then to chain B;

[0033] S32: Chain B generates random vectors With error , return response and , For the response parameters of chain B;

[0034] S33: Decrypt Chain A to calculate the scalar product ,verify , These are the response parameters related to the transaction that are calculated.

[0035] S34: The dynamic accumulator is used to maintain the global ledger state. After each transaction is generated, its hash value is calculated. , Transaction information, || indicates a join operation, and the accumulator is updated. , This indicates the current value of the accumulator. The updated value of the accumulator;

[0036] S35: Membership Certificate , For the first The member proof value calculated by each member, This represents a product operation, allowing nodes to quickly verify whether a transaction is included;

[0037] S36: Based on the one-wayness of lattice hashing, an adversary cannot... The specific details of the transaction are deduced in reverse.

[0038] As a further limitation of this technical solution, step S4 is as follows:

[0039] By leveraging the unpredictability of random matrices and error terms, the correlation between cross-chain transactions is severed, while ensuring the credibility of the verification results.

[0040] S41: Call the ReKeyGen() algorithm to regenerate the key, and call the ReEnc() algorithm to re-encrypt the ciphertext;

[0041] S42: The system dynamically adjusts the grid dimensions when monitoring security threats in real time. and modulus Grid dimensions expanded to , For safety parameters, The adjusted safety parameters are modulo scaling. The standard deviation of the error is updated to Parameter scaling preserves the difficulty of the LWE problem, that is: Furthermore, it enables seamless upgrades across the entire network through relay broadcasting, avoiding hard forks and thus addressing the evolution of quantum computing capabilities;

[0042] S43: Upon detecting malicious activity, the regulatory authority generates a certificate revocation. And division operation via accumulator Remove the related transactions.

[0043] As a further limitation of this technical solution, step S5 is as follows:

[0044] S51: Regulators use traps Decrypting Tags: Encrypted tags , Basic transaction ciphertext, Verify the ciphertext of the response for cross-chain verification, and verify the index. and accumulator relationship , For transaction information;

[0045] S52: The public audit module periodically verifies the global consistency of the accumulator. And randomly select a subset ,implement ;

[0046] S53: The error control decryption module mainly decrypts and calculates intermediate values. , It is encrypted; and it is rounded down. Plaintext recovery, error constraints , Representing vectors The infinite norm ensures the correctness of decryption, and dynamic parameter adjustment further optimizes the error tolerance.

[0047] As a further limitation of this technical solution, the method includes user nodes, blockchain nodes, cross-chain relay nodes, and regulatory agencies.

[0048] As a further limitation of this technical solution, the blockchain node:

[0049] S61: Transaction Submission: Receives encrypted transaction or response parameters submitted by the user, verifies the format validity, and then forwards them to the relay node;

[0050] S62: State Synchronization: Maintain the latest block hash of this chain and receive the global state broadcast by the relay node. ;

[0051] S63: Local Ledger Management: Stores verified cross-chain transaction records, supporting fast querying and auditing;

[0052] Cross-chain relay node:

[0053] S71: State Synchronization: Maintain global state G, and record the latest block hash value of each chain. ;

[0054] S72: Transaction Verification: Perform cross-chain privacy-preserving scalar product to generate a random matrix. Calculate the challenge value Receive response Post-verification To ensure transaction consistency;

[0055] Regulatory authorities:

[0056] S81: Holder of the Trapdoor: Possesses the master trapdoor key Transaction tags can be decrypted ,in For transaction indexing;

[0057] S82: Anomaly Tracing: Invoking the tracing algorithm Generate verifiable proof To confirm the source of the transaction;

[0058] S83: Key Revocation: Issue Revocation Certificate Trigger accumulator update This renders the revoked key invalid.

[0059] Compared with related technologies, the dynamic privacy-monitoring cross-chain payment method based on lattice cryptography provided by this invention has the following beneficial effects:

[0060] 1. Quantum-resistant security: This invention employs a lattice cryptography system based on the LWE (Low-Weighted Equation) problem to replace traditional public-key encryption algorithms, fundamentally resisting the security threats posed by quantum computing. Existing encryption schemes mainly rely on large integer factorization or discrete logarithm problems, whose security will rapidly collapse in a quantum environment due to Shor's algorithm. This scheme, through lattice basis trapdoor functions and fault-tolerant learning mechanisms, achieves long-term security with a private key recovery probability approaching zero, providing quantum-era security guarantees for cross-chain payments.

[0061] 2. Highly Efficient Cross-Chain Verification Architecture: This invention designs a privacy-preserving scalar product (PPSP) protocol based on lattice basis optimization, effectively alleviating the ciphertext expansion problem commonly found in traditional PPSP implementations. Compared to the high overhead caused by excessively large ciphertext during the communication phase in existing homomorphic encryption schemes, this scheme fully leverages the parallelism of lattice cryptography in matrix operations and the compactness of the ciphertext structure, achieving compression of single verification data, improving system throughput, and meeting the performance requirements of high-concurrency commercial scenarios.

[0062] 3. Dynamic Privacy Regulatory Balance: This invention innovatively proposes a strategy-driven regulatory trapdoor mechanism that generates zero-knowledge compliance proofs through knowledge signatures (SoK), effectively overcoming the rigid limitations of existing "fully anonymous" or "fully exposed" privacy solutions. This technology activates the traceability function only when risk control rules are triggered (such as large-amount transfers), achieving a precise balance between "default privacy and exceptional regulation." This mechanism can both prevent the abuse of anonymity for illegal activities such as money laundering and effectively protect the transaction privacy of ordinary users from excessive infringement, thus balancing regulatory compliance and data privacy.

[0063] 4. Trustworthy Lightweight Auditing: This invention integrates dynamic accumulators and zero-knowledge proof technology to achieve a highly efficient and compliant auditing mechanism. Compared to traditional solutions that rely on full-node on-chain scanning and have processing delays in the minutes range, this mechanism can trace a single transaction within milliseconds. Regulators can quickly verify the consistency of the ledger through the dynamic accumulator, and the entire auditing process does not expose transaction information unrelated to the audit objective, thus ensuring data privacy while meeting the dual requirements of audit efficiency and compliance in various scenarios.

[0064] 5. Evolvable Quantum Resistance: This invention supports seamless upgrades to key revocation and quantum resistance parameters through a dynamic parameter adjustment mechanism. Compared to existing quantum-resistant encryption schemes that require reconstructing the entire encryption system to improve security, thus exposing historical data to decryption risks, this solution introduces proxy re-encryption technology. This allows historical transactions to be smoothly migrated within the ciphertext domain, achieving "hot upgrade" security enhancement without interrupting system operation. This ensures the system maintains continuous and reliable security as quantum computing technology evolves. Attached Figure Description

[0065] Figure 1 This is a schematic diagram of the structure of the present invention.

[0066] Figure 2 This is the system framework of the present invention. Detailed Implementation

[0067] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0068] A dynamic privacy-regulated cross-chain payment method based on lattice cryptography includes the following steps:

[0069] S1: System initialization;

[0070] S2: User key generation and transaction privacy protection;

[0071] S3: Cross-chain consistency verification;

[0072] S4: Dynamic parameters and key management;

[0073] S5: Regulatory and auditing mechanisms.

[0074] The steps in S1 are as follows:

[0075] S11: During system startup, relay nodes generate global common parameters and set grid dimensions. and modulus To ensure compliance with NIST's post-quantum security standards;

[0076] S12: Generate a uniform random matrix by calling the trapdoor generation algorithm. And its corresponding short basis trap gate S, making This indicates that each element of the matrix product must be... Integer division, modulo of each element The result is 0;

[0077] in: It represents the set of integers;

[0078] , Indicates rounding up;

[0079] S13: Error distribution is selected from discrete Gaussian distribution. Standard deviation This balances the correctness and security of decryption.

[0080] S14: Collision-resistant hash functions are mainly used to bind user identity information and transaction data;

[0081] The collision-resistant hash function is: ; Represents the set of all possible binary strings. Represents a set consisting of 0s and 1s. This indicates that the elements in the set can be strings of any length, including empty strings.

[0082] S15: Master Key It is held secretly by the regulatory agency for subsequent key management and tracing.

[0083] This phase ensures that all participants operate based on the same set of quantum-resistant parameters, thereby resisting potential quantum computing attacks.

[0084] The steps in S2 are as follows:

[0085] S21: User key generation involves embedding identity information into a lattice structure to achieve uniqueness;

[0086] First, calculate the identity hash. And construct an identity association matrix , , and All are generated random matrices;

[0087] Calling the lattice-based homomorphic proxy re-encryption algorithm Generate private key Ensure that the requirements are met. ,in For public vectors, private keys To satisfy the short vector property ( , For vectors (norm), to prevent attacks;

[0088] Public Key Once made public, users participate in transactions through it, and the process of generating private keys is to ensure that the keys of different users are not statistically correlated;

[0089] S22: Transaction encryption protects monetary privacy through the LWE (Learning With Errors) difficulty mechanism;

[0090] First, the amount Encode into a binary vector and generate a random matrix. With error vector The ciphertext is constructed as follows , This represents rounding down to the nearest integer, where It is used to enhance randomness, thereby resisting statistical attacks;

[0091] The ring signature module invokes zero-knowledge proofs to generate a signature; signature proof. The user has satisfied The sender's valid private key is hidden, while its specific location in the ring is concealed, ensuring the sender's anonymity.

[0092] The transaction was ultimately completed Submitted to the blockchain network in the form of [submission method];

[0093] Ring signatures achieve strong anonymity through zero-knowledge proofs (SoK); the signer selects a signer that includes themselves. Construct a ring using public keys to generate commitments. , For a hash function, For a series of hash values, and through non-interactive proof This indicates that they possess a valid private key.

[0094] sign The actual signer index is hidden, making it impossible for an adversary to distinguish the real signer from other ring members in polynomial time. During signature verification, the node checks... The validity and consistency of commitments are ensured to guarantee the legality of transactions. The encrypted transaction is submitted to the target chain and synchronized to the cross-chain relay node, thus forming the first layer of privacy protection.

[0095] The steps in S3 are as follows:

[0096] Cross-chain verification ensures transaction consistency through random linear transformations;

[0097] S31: Relay nodes generate random matrices Calculate the challenge vector , The ciphertext is sent to chain A and then to chain B;

[0098] S32: Chain B generates random vectors With error , return response and , For the response parameters of chain B;

[0099] S33: Decrypt Chain A to calculate the scalar product ,verify , These are the response parameters related to the transaction that are calculated.

[0100] S34: The dynamic accumulator is used to maintain the global ledger state. After each transaction is generated, its hash value is calculated. , Transaction information, || indicates a join operation, and the accumulator is updated. , This indicates the current value of the accumulator. The updated value of the accumulator;

[0101] S35: Membership Certificate , For the first The member proof value calculated by each member, This represents a product operation, allowing nodes to quickly verify whether a transaction is included;

[0102] S36: Based on the one-wayness of lattice hashing, an adversary cannot... The specific details of the transaction are deduced in reverse.

[0103] The steps in S4 are as follows:

[0104] By leveraging the unpredictability of random matrices and error terms, the correlation between cross-chain transactions is severed, while ensuring the credibility of the verification results.

[0105] S41: Call the ReKeyGen() algorithm to regenerate the key and call the ReEnc() algorithm to re-encrypt the ciphertext. This process does not require decrypting the original data, thus ensuring privacy protection during key rotation and making it more suitable for the long-term operation of cross-chain systems.

[0106] S42: The system dynamically adjusts the grid dimensions when monitoring security threats in real time. and modulus Grid dimensions expanded to , For safety parameters, The adjusted safety parameters are modulo scaling. The standard deviation of the error is updated to Parameter scaling preserves the difficulty of the LWE problem, that is: Furthermore, it enables seamless upgrades across the entire network through relay broadcasting, avoiding hard forks and thus addressing the evolution of quantum computing capabilities;

[0107] S43: Upon detecting malicious activity, the regulatory authority generates a certificate revocation. And division operation via accumulator Remove the associated transactions. Historical transactions corresponding to the revoked key will fail subsequent verification, preventing double-spending attacks.

[0108] The steps in S5 are as follows:

[0109] S51: Regulators use traps Decrypting Tags: Encrypted tags , Basic transaction ciphertext, Verify the ciphertext of the response for cross-chain verification, and verify the index. and accumulator relationship , For transaction information;

[0110] The tracing process is carried out only under judicial authorization and only exposes malicious transaction indexes; the privacy of legitimate users remains unaffected.

[0111] S52: The public audit module periodically verifies the global consistency of the accumulator. And randomly select a subset ,implement Cross-chain scalar product verification S31-S36;

[0112] The one-way nature and random sampling mechanism of the accumulator are mainly to ensure the transparency and credibility of the ledger and to defend against Sybil attacks.

[0113] S53: The error control decryption module mainly decrypts and calculates intermediate values. , It is encrypted; and it is rounded down. Plaintext recovery, error constraints , Representing vectors The infinite norm ensures the correctness of decryption, and dynamic parameter adjustments further optimize the error tolerance. The regulatory process is independent of transaction verification, intervening only when necessary, balancing privacy protection and compliance requirements.

[0114] Regarding the LWE distribution: for a given secret vector From LWE distribution From a sample, a vector is randomly and uniformly selected. A small error term and output .

[0115] The LWE distribution can be used to define two versions of the LWE problem.

[0116] (1) Search version. Given the LWE distribution mentioned above m independent samples obtained from For uniform random (Since the vector is fixed for all samples), it is difficult to find a vector. .

[0117] (2) Decision version. Given m independent samples Each sample is distributed according to any of the following conditions: ① For uniform random If the distribution is fixed for all samples or ② uniformly distributed, then distinguishing which case is difficult.

[0118] From the two LWE problems mentioned above, the following observations can be drawn.

[0119] 1) In the absence of error terms In this case, the search for the LWE problem can be easily solved using Gaussian elimination, and the secret vector can be recovered. .

[0120] 2) Similarly, for the decision-making LWE problem, if there is no error term... Gaussian elimination will likely reveal that no solution vector exists if sampling is not performed from the LWE distribution. .

[0121] 3) If there are m LWE samples For a uniformly random (Since all samples are fixed), all Combined into a matrix, , Combined into vectors and will Combined into vectors Combined into a vector-matrix linear equation: .

[0122] The method includes user nodes, blockchain nodes, cross-chain relay nodes, and regulatory agencies.

[0123] Blockchain nodes serve as the interface between users and cross-chain relays, and are responsible for on-chain operations.

[0124] S61: Transaction Submission: Receives encrypted transaction or response parameters submitted by the user, verifies the format validity, and then forwards them to the relay node;

[0125] S62: State Synchronization: Maintain the latest block hash of this chain and receive the global state broadcast by the relay node. ;

[0126] S63: Local Ledger Management: Stores verified cross-chain transaction records, supporting fast querying and auditing;

[0127] Cross-chain relay nodes: Relay nodes serve as hubs for multi-chain interactions, undertaking the responsibilities of state synchronization, transaction verification, and dynamic accumulator management;

[0128] S71: State Synchronization: Maintain global state G, and record the latest block hash value of each chain. ;

[0129] S72: Transaction Verification: Perform cross-chain privacy-preserving scalar product to generate a random matrix. Calculate the challenge value Receive response Post-verification To ensure transaction consistency;

[0130] Regulatory agencies: The main role of regulatory agencies is to intervene in the system when necessary to achieve controlled privacy;

[0131] S81: Holder of the Trapdoor: Possesses the master trapdoor key Transaction tags can be decrypted ,in For transaction indexing;

[0132] S82: Anomaly Tracing: Invoking the tracing algorithm Generate verifiable proof To confirm the source of the transaction;

[0133] The generated verifiable proof contains sufficient information to trace and confirm the original sender or relevant party of the transaction;

[0134] S83: Key Revocation: Issue Revocation Certificate Trigger accumulator update This renders the revoked key invalid. The public key of the user whose account has been revoked.

[0135] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A dynamic privacy-monitoring cross-chain payment method based on lattice cryptography, characterized in that, Includes the following steps: S1: System initialization; S2: User key generation and transaction privacy protection; S3: Cross-chain consistency verification; S4: Dynamic parameters and key management; S5: Regulatory and auditing mechanisms; The steps in S3 are as follows: Cross-chain verification ensures transaction consistency through random linear transformations; S31: Relay nodes generate random matrices Calculate the challenge vector , The ciphertext is sent to chain A and then to chain B; S32: Chain B generates random vectors With error , return response and , For the response parameters of chain B; S33: Decrypt Chain A to calculate the scalar product ,verify , These are the response parameters related to the transaction that are calculated. S34: The dynamic accumulator is used to maintain the global ledger state. After each transaction is generated, its hash value is calculated. , Transaction information, || indicates a join operation, and the accumulator is updated. , This indicates the current value of the accumulator. The updated value of the accumulator; S35: Membership Certificate , For the first The member proof value calculated by each member, This represents a product operation, allowing nodes to quickly verify whether a transaction is included; The steps in S4 are as follows: S41: Call the ReKeyGen() algorithm to regenerate the key, and call the ReEnc() algorithm to re-encrypt the ciphertext; S42: The system dynamically adjusts the grid dimensions when monitoring security threats in real time. and modulus Grid dimensions expanded to , The adjusted safety parameters are modulo scaling. The standard deviation of the error is updated to Parameter scaling is: ; S43: Upon detecting malicious activity, the regulatory authority generates a certificate revocation. , Represents the master key and is used for division operations via accumulator. Remove the related transactions.

2. The dynamic privacy-monitoring cross-chain payment method based on lattice cryptography according to claim 1, characterized in that: The steps in S1 are as follows: S11: During system startup, relay nodes generate global common parameters and set grid dimensions. and modulus To ensure compliance with NIST's post-quantum security standards; S12: Generate a uniform random matrix by calling the trapdoor generation algorithm. And its corresponding short basis trap gate S, making This indicates that each element of the matrix product must be... Integer division, modulo of each element The result is 0; in: It represents the set of integers; , Indicates rounding up; S13: Error distribution is selected as discrete Gaussian distribution. Standard deviation ; S14: Collision-resistant hash functions are mainly used to bind user identity information and transaction data; S15: Master Key It is held secretly by the regulatory agency for subsequent key management and tracing.

3. The dynamic privacy-monitoring cross-chain payment method based on lattice cryptography according to claim 2, characterized in that: The steps in S2 are as follows: S21: User key generation involves embedding identity information into a lattice structure to achieve uniqueness; First, calculate the identity hash. And construct an identity association matrix , ; Calling the lattice-based homomorphic proxy re-encryption algorithm Generate private key Ensure that the requirements are met. private key To satisfy the short vector property and prevent attacks; Public Key Once made public, users participate in transactions through it, and the process of generating private keys is to ensure that the keys of different users are not statistically correlated; S22: Transaction encryption protects monetary privacy through LWE's difficulty mechanism; First, the amount Encode into a binary vector and generate a random matrix. With error vector The ciphertext is constructed as follows , Indicates rounding down to the nearest integer; The ring signature module invokes zero-knowledge proofs to generate a signature; signature proof. The user has satisfied The sender's valid private key is hidden, while its specific location in the ring is concealed, ensuring the sender's anonymity. The transaction was ultimately completed Submitted to the blockchain network in the form of [submission / transmission]; Ring signatures achieve strong anonymity through zero-knowledge proofs; the signer chooses to include themselves as an anonymity signer. Construct a ring using public keys to generate commitments. and through non-interactive proof This indicates that they possess a valid private key.

4. The dynamic privacy-monitoring cross-chain payment method based on lattice cryptography according to claim 3, characterized in that: The steps in S5 are as follows: S51: Regulators use traps Decrypting Tags: Encrypted tags , Basic transaction ciphertext, Verify the ciphertext of the response for cross-chain verification, and verify the index. and accumulator relationship , For transaction information; S52: The public audit module periodically verifies the global consistency of the accumulator. And randomly select a subset ,implement ; S53: The error control decryption module mainly decrypts and calculates intermediate values. , It is encrypted; and it is rounded down. Plaintext recovery, error constraints , Representing vectors The infinite norm ensures the correctness of decryption, and dynamic parameter adjustment further optimizes the error tolerance.

5. An apparatus utilizing the lattice-based dynamic privacy-monitoring cross-chain payment method of claim 4, characterized in that: This includes user nodes, blockchain nodes, cross-chain relay nodes, and regulatory agencies; Blockchain node: S61: Transaction Submission: Receives encrypted transaction or response parameters submitted by the user, verifies the format validity, and then forwards them to the relay node; S62: State Synchronization: Maintain the latest block hash of this chain and receive the global state broadcast by the relay node. ; S63: Local Ledger Management: Stores verified cross-chain transaction records, supporting fast querying and auditing; Cross-chain relay node: S71: State Synchronization: Maintain global state G, and record the latest block hash value of each chain. ; S72: Transaction Verification: Perform cross-chain privacy-preserving scalar product to generate a random matrix. Calculate the challenge value Receive response Post-verification To ensure transaction consistency; Regulatory authorities: S81: Holder of the Trapdoor: Possesses the master trapdoor key Transaction tags can be decrypted ,in For transaction indexing; S82: Anomaly Tracing: Invoking the tracing algorithm Generate verifiable proof To confirm the source of the transaction; S83: Key Revocation: Issue Revocation Certificate Trigger accumulator update This renders the revoked key invalid.

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