Automobile lease transaction and trust management system based on block chain

Abstract

The invention discloses an automobile lease transaction and trust management system based on a block chain, and relates to the technical field of data security. The system comprises an identity and key management unit, a digital signature and data encryption unit and a block chain consensus and storage unit. The identity and key management unit is used for being responsible for identity registration of all participants and generating a shared key; the digital signature and data encryption unit is used for performing AES encryption by using a shared key after performing multiple hash perturbation preprocessing on transaction data including a digital signature to generate a final ciphertext; and the block chain consensus and storage unit is used for constructing a hash of a new block, and storing the constructed new block into the block chain after consensus verification to form a non-tampering transaction historical record. According to the invention, the security and transparency of automobile leasing transaction are improved, and the problems of data leakage and fraud caused by centralization risks are effectively reduced through a decentralized trust management mode.

Description

Technical Field

[0001] The present disclosure relates to the field of data security technologies, and particularly to a blockchain-based car rental transaction and trust management system. Background Art

[0002] Currently, with the rapid development of Internet and Internet of Things technologies, traditional car rental businesses are gradually transforming towards digital, networked, and intelligent directions. However, existing car rental transaction systems mostly adopt a centralized architecture, relying on a third-party platform to centrally manage rental information, transaction data, and user identities. Although this architecture improves operational efficiency to a certain extent, it also has serious security risks and trust crises. In traditional systems, user identity authentication, digital signatures, and data encryption all rely on a central server. This not only makes the security of the entire system highly dependent on a single node, but also once the central server is attacked or suffers internal leakage, the data security and transaction trust of the entire system will face huge risks. In addition, the centralized management mode often fails to fully meet users' requirements for privacy protection and data immutability, and is prone to problems such as data tampering, forgery, and replay, resulting in a lack of sufficient trust basis between the two parties in the rental transaction during the actual transaction process.

[0003] In recent years, due to its characteristics such as decentralization, immutability, transparency, etc., blockchain technology has received extensive attention and application in fields such as finance, logistics, supply chain, and sharing economy. Blockchain technology stores transaction data in each node across the network in chronological order through a distributed ledger. Each block is connected by the hash value of the previous block, thus forming an irreversible chain, greatly improving the security and transparency of data storage. Some existing technologies have applied blockchain to the car rental business, attempting to replace the traditional centralized management mode through a distributed trust management mechanism to achieve the goals of reducing transaction costs, improving data security, and preventing forgery and tampering. For example, some blockchain platforms use digital signatures and public key infrastructure (PKI) to encrypt and verify transaction data, thus achieving identity authentication and non-repudiation of transaction data to a certain extent. However, there are still some problems in the practical application of these existing technologies. First, traditional digital signature technologies mostly rely on algorithms such as RSA or ECC. Although these algorithms have been proven to have high security in mathematics, they are still vulnerable to risks such as man-in-the-middle attacks, side-channel attacks, and key forgery during key management and the digital signature process. Second, when generating key pairs, exchanging shared keys, and encrypting transaction data, existing technologies often only rely on traditional asymmetric encryption or symmetric encryption algorithms, lacking multi-level and multi-angle security protection measures. Therefore, in the face of complex network attacks, the anti-attack ability of the overall system is still insufficient. Moreover, in actual rental transactions, it is often difficult to establish and maintain the trust relationship between car owners and rental users. Under the traditional centralized management mode, the leakage or tampering of information in any node may lead to the collapse of the entire transaction system. Although existing blockchain technologies theoretically solve the problem of data immutability, in the actual implementation process, due to the lack of a comprehensive protection mechanism for identity authentication, key exchange, and data encryption, there is still a risk of forgery or tampering of transaction data. Summary of the Invention

[0004] The present disclosure aims to provide a blockchain-based car rental transaction and trust management system. By adopting an extended public key encryption technology combined with polynomial random perturbation, highly random and unpredictable public-private key pairs are generated, effectively preventing man-in-the-middle attacks and key forgery. Using improved digital signature and multiple hash perturbation preprocessing techniques, the transaction data is encrypted to ensure the authenticity, integrity, and non-repudiation of the data during transmission and storage. At the same time, by using a vectorized Diffie-Hellman key exchange protocol and a multi-round iterative integral perturbation method to construct a new block hash, the continuity and immutability of blockchain data are achieved. Overall, the present invention not only greatly improves the security and transparency of car rental transactions, but also effectively reduces data leakage and fraud problems caused by centralized risks through a decentralized trust management model, providing an efficient, trustworthy, and attack-resistant digital trading platform for the car rental industry.

[0005] To solve the above problems, the technical solution of the present invention is implemented as follows:

[0006] A blockchain-based car rental transaction and trust management system, the system includes: an identity and key management unit, a digital signature and data encryption unit, and a blockchain consensus and storage unit; the identity and key management unit is responsible for the identity registration of all participants, generates public-private key pairs through an extended RSA algorithm and polynomial random perturbation, and completes the key exchange between participants and generates a shared key during the rental request phase; the digital signature and data encryption unit is used for the owner to digitally sign the vehicle unique identifier, rental price, and timestamp with its own private key, and after preprocessing the transaction data including the digital signature through multiple hash perturbations, encrypts it with the shared key using AES to generate the final ciphertext; the blockchain consensus and storage unit is responsible for receiving the digital signature and ciphertext, combines them with the hash of the previous block and the perturbation factor generated by the shared key to construct the hash of the new block, and after consensus verification, stores the constructed new block in the blockchain to form an immutable transaction history record.

[0007] Further, the participants include car owners and rental users; for each participant i, the system first randomly generates two large prime numbers p i and q i ; i = 1, 2,..., N; N is the number of participants; define the RSA modulus n i = p i q i ; and satisfy 2 λ ≤ p i , q i <2 λ+1 ; is the set of prime numbers; define the Euler's totient function φ(n i) = (p i - 1)(q i - 1); Define the public key exponent where gcd(·) represents the greatest common divisor operation; is the set of natural numbers; λ is a system - preset security parameter; Define the private key exponent

[0008] Furthermore, the identity and key management unit is responsible for the identity registration of all participants. When generating the public - private key pair by extending the RSA algorithm and polynomial random perturbation, it is achieved by adding a polynomial random perturbation term; for each participant i, the polynomial random perturbation term is represented by the following formula:

[0009]

[0010] where represents the bit - wise exclusive - or operation; both j and k are integer subscript indices; μ is the upper limit of the internal summation of the polynomial, representing the number of terms in each layer of the polynomial expansion; the non - linear perturbation ξ is a predefined large constant; Γ(·) is the gamma function; the formula for the auxiliary term is as follows:

[0011]

[0012] where H i represents the integer value obtained by hashing and mapping the identity ID of the participant; then construct the public key perturbation term as:

[0013]

[0014] Furthermore, the finally obtained public - private key pair is represented by the following formula:

[0015]

[0016] where SK i is the private key of participant i; PK i is the public key of participant i.

[0017] Furthermore, let the car owner be participant o. When publishing car rental information, digitally sign the vehicle unique identifier, rental price, and timestamp. The formula is as follows:

[0018]

[0019] where car_ID is the vehicle unique identifier; price is the rental price; τ is the timestamp; Ω o is the public key perturbation term of participant o; d ois the private key exponent of participant o; Θ o is the polynomial random perturbation term of participant o; n o is the RSA modulus of participant o; m is an integer subscript index; M is the expansion upper limit, represents the floor function; σ o is the digital signature of the participant.

[0020] Furthermore, when generating the shared key, the identity and key management unit uses the Diffie–Hellman key exchange algorithm to conduct key negotiation for the car owner and the rental user to generate the shared key; let the car owner vector be a = (a 1 , a 2 ,..., a v ,..., a L ): the rental user vector is b = (b 1 , b 2 ,..., b v ,..., b L ); L is the dimension of the Diffie–Hellman key exchange; both the car owner vector and the rental user vector are random vectors; a v is the v-th element in the car owner vector; b v is the v-th element in the rental user vector; the shared key k shared is generated through the following formula:

[0021]

[0022] where p o and q o are two large prime numbers of participant o corresponding to the car owner; p u and q u are two large prime numbers of participant u corresponding to the rental user; v is an integer subscript index; g is a generator.

[0023] Furthermore, let the digital signature of participant o corresponding to the car owner be σ o , then the transaction data is T = Encode(car_ID, price, τ, σ o ); the transaction data including the digital signature is preprocessed through adding multiple hash perturbation terms, and the multiple hash perturbation term Ψ(T, k shared ) is defined as:

[0024]

[0025] Among them, R is the expansion series of the set multiple hash perturbation term; r is an integer subscript index; || is the concatenation operator; |T| represents the length of the transaction data; H(·) is a hash function; through the following formula, AES encryption is performed using the shared key to generate the final ciphertext C:

[0026]

[0027] Among them, represents the AES encryption algorithm with k shared as the key.

[0028] Furthermore, let the hash of the previous block be prev_hash; through multiple rounds of iteration, the digital signature, ciphertext, the hash of the previous block, and the perturbation factor generated by the shared key are combined to construct the hash of the new block. In the j-th round of iteration, the intermediate function F j (s, t):

[0029] F j (s, t) = SHA256(H j-1 ||C||τ||j||s||t);

[0030] Among them, j = 1, 2,..., J; J is the total number of iteration rounds; let the initial intermediate value be H 0 = prev_hash, H j-1 is the intermediate value of the (j - 1)-th round of iteration; both s and t are integral variables, taking values in the interval [0, |T|], and the multiple integral term I j in the perturbation factor of the j-th round of iteration is:

[0031]

[0032] The single integral term J j in the perturbation factor of the j-th round of iteration is:

[0033]

[0034] Among them, SHA256(·) is the standard SHA-256 hash function; the perturbation factor is I j + J j .

[0035] Furthermore, the hash of the new block is calculated through the following formula:

[0036]

[0037] Among them, H block is the hash of the new block.

[0038] The blockchain-based car rental transaction and trust management system of the present invention has the following beneficial effects: By organically combining blockchain technology with advanced cryptographic algorithms, the present invention constructs a brand-new car rental transaction and trust management system, greatly enhancing the security, transparency, and reliability of the transaction process. First, the present invention adopts an improved asymmetric encryption algorithm. By introducing polynomial random perturbation technology on the basis of traditional public-key cryptography, the key pair generation process has higher randomness and unpredictability, effectively preventing man-in-the-middle attacks and key forgery problems. Compared with the existing centralized transaction system, the key management mechanism of the present invention no longer relies on a single trusted third party, but establishes a secure communication channel among various participants in a decentralized manner, enabling the identity authentication and key exchange of each user to be protected by multiple encryptions, thus significantly reducing the risk of data leakage and tampering. Secondly, the present invention has made significant improvements in digital signature technology. By performing multiple hash perturbation preprocessing on transaction data, complex nonlinear processing is carried out on key data such as vehicle identity, rental price, timestamp, and user signature information, and then encrypted using a symmetric encryption algorithm, ensuring that the data not only passes digital signature verification during transmission, but also introduces multiple perturbations and confusion effects during the encryption process, making it impossible for any unauthorized third party to reverse-engineer the original transaction content. This design not only improves the confidentiality of the data, but also provides an irrefutable transaction voucher for all parties, effectively preventing forgery and replay attacks, and protecting the legitimate rights and interests of both parties to the transaction. In addition, during the shared key negotiation process, the present invention adopts an improved key exchange protocol. By introducing quantization and multi-dimensional random numbers, secure and fast key negotiation is achieved in a distributed network environment. This solution makes full use of the multi-dimensional characteristics and nonlinear perturbation effects of random vectors, making the generated shared key highly random and attack-resistant mathematically, thus ensuring the security of all subsequent transaction data transmissions between the car owner and the rental user. Thus, a solid trust foundation is established at the initial communication stage of the system, providing a solid security guarantee for subsequent digital signatures, data encryption, and blockchain storage. In terms of blockchain data storage, the present invention designs a block hash construction method with multiple rounds of iteration and integral perturbation, enabling each new block to not only inherit the information of the previous block, but also greatly enhance the randomness and unpredictability of the block hash through multi-layer nonlinear operations and integral averaging. This method effectively solves the problems in the prior art that blockchain data is vulnerable to replay attacks or being tampered with, ensuring the continuity and integrity of the entire chain. At the same time, the blockchain technology itself has the characteristics of decentralization, openness, transparency, and immutability, enabling all transaction records to be permanently stored on a distributed ledger, and any transaction can be traced and verified, providing strong technical support for the secure operation of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a schematic structural diagram of a blockchain-based car rental transaction and trust management system provided by an embodiment of the present invention. Detailed implementation manners

[0040] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present disclosure clearer and more understandable, the present disclosure will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present disclosure and are not used to limit the present disclosure.

[0041] Embodiment 1, refer to Figure 1 : A blockchain-based car rental transaction and trust management system, the system includes: an identity and key management unit, a digital signature and data encryption unit, and a blockchain consensus and storage unit; the identity and key management unit is responsible for the identity registration of all participants, generates a public-private key pair by extending the RSA algorithm and polynomial random perturbation, and completes the key exchange between participants and generates a shared key during the rental request phase; the digital signature and data encryption unit is used for the car owner to digitally sign the vehicle unique identifier, rental price and timestamp with its own private key, and after preprocessing the transaction data including the digital signature through multiple hash perturbations, encrypts it with the shared key using AES to generate the final ciphertext; the blockchain consensus and storage unit is responsible for receiving the digital signature and ciphertext, combines them with the hash of the previous block and the perturbation factor generated by the shared key to construct the hash of the new block, and after consensus verification, stores the constructed new block in the blockchain to form an immutable transaction history record.

[0042] Specifically, the identity and key management unit is used to ensure the identity legitimacy of all participants and the data confidentiality during the communication process, thus building a solid security defense line for the entire system. By comprehensively registering and authenticating the identities of participants, this unit binds the identity information of each car owner and renter to a unique digital identifier, avoiding forgery and misappropriation problems, and making the entire rental process have a trustworthy identity basis from the initial request stage. During identity authentication, the system introduces an improved RSA algorithm and combines it with polynomial random perturbation to generate public-private key pairs. This method adds additional randomness to the traditional RSA algorithm, making the key generation process more complex and unpredictable. Specifically, this method not only relies on the mathematical problem of large prime factorization but also perturbs the key parameters by introducing randomly generated polynomial perturbation factors, making it difficult for attackers to recover valid key information due to the interference of multiple random factors even if they try to crack through the known RSA theory. At the same time, during the rental request stage, the participants need to securely exchange keys. The system successfully implements the key exchange process using the above-extended RSA algorithm and generates an encryption key shared only by both parties during this process, ensuring that the symmetric encryption algorithm (such as AES) used in subsequent data transmission can achieve the best balance between confidentiality and efficiency. The design of the entire identity and key management unit not only solves the man-in-the-middle attack and eavesdropping risks existing in traditional key exchange protocols but also introduces multiple perturbations in the key generation link, making the key structure more complex and enhancing the overall anti-attack ability of the system.

[0043] Combined with blockchain technology, this unit provides a solid foundation for subsequent digital signatures, encryption, and blockchain storage of transaction data while conducting identity authentication and key management, ensuring a high level of data integrity and immutability in the process of initiating, transmitting, and recording each car rental transaction. In the system, each rental request undergoes strict verification by the identity and key management unit, and only legitimate participants can enter the subsequent signature and encryption processes. This mechanism not only prevents illegal transactions from occurring but also constructs an identity-based trust chain for the system. Through this mechanism, all interactions between car owners and renters are carried out under the protection of cryptography, and the success rate of any attempt to forge identities or steal keys is greatly reduced due to the random perturbation of the key management strategy. In addition, the identity and key management unit is closely integrated with the entire blockchain system. By generating shared keys, it ensures that each block in the blockchain can incorporate additional security parameters when being generated and linked. This not only improves the tamper resistance of blockchain transaction data but also enables the overall system to maintain a high level of security and credibility even in the presence of malicious nodes. Due to this innovative design that combines advanced cryptography technology and distributed ledger technology, the blockchain-based car rental transaction and trust management system can achieve a very high security standard in ensuring identity authentication, data transmission, and transaction recording, while also realizing the efficiency and transparency of the entire rental process, providing a secure and convenient service platform for rental transaction participants.

[0044] The digital signature and data encryption unit is used to ensure that transaction data can verify the authenticity and integrity of information during transmission and storage, and can also prevent the data from being stolen or tampered with. The working process of this unit starts from the car owner initiating a transaction. First, it uses the private key of the car owner to digitally sign key data such as the vehicle's unique identifier, rental price, and timestamp. The signature generated in this way can not only prove that the data was indeed initiated by the car owner but also enable each node in the system to verify it through the public key of the car owner after receiving the data, thus preventing the risk of forgery and tampering. The digital signature process uses an asymmetric encryption algorithm and combines traditional cryptography principles. While ensuring the security of the signature, it also realizes the immutability of transaction records by combining blockchain technology, ensuring that once the signature is recorded in the blockchain, it cannot be maliciously modified or forged. Subsequently, the system preprocesses the transaction data containing the digital signature. During this process, a multiple hash perturbation technique is used to perform a series of encryption conversions on the data. This process utilizes the irreversibility of the hash function and the introduction of random perturbation factors, greatly enhancing the security of the data and making it impossible for attackers to obtain the original content through reverse operations even if the data is intercepted during transmission. This multiple hash perturbation preprocessing not only makes each transaction data unique and random but also provides a solid foundation for subsequent data encryption.

[0045] After preprocessing, the system adopts the AES algorithm in the symmetric encryption algorithm to encrypt the preprocessed data. The AES encryption process depends on the shared key previously generated by the Identity and Key Management Unit, ensuring that only legitimate communication parties can correctly decrypt the data, thus achieving strict confidentiality during the information transmission process. The entire data encryption process integrates the advantages of asymmetric and symmetric encryption technologies. It ensures the reliability of the data source through digital signatures, and then protects the data content through multiple hash perturbations and AES symmetric encryption, forming a dual protection barrier, enabling the transaction data to meet extremely high security standards before entering the blockchain for storage. More importantly, the design of this unit is combined with the blockchain consensus mechanism. After the transaction data is encrypted, it participates in the hash construction of the new block together with the hash of the previous block and the perturbation factor generated by the shared key, forming a unique and irreversible blockchain structure, thus achieving end-to-end security protection. The operating mechanism of the entire digital signature and data encryption unit not only ensures the authenticity, integrity, and confidentiality of the data for each car rental transaction, but also provides a trustworthy, secure, and efficient transaction environment for traditional car rental businesses through deep integration with blockchain technology. With this design, each transaction between car owners and renters can be recorded on a transparent, public, and immutable ledger, making any attempt to tamper with data or commit fraud impossible to hide, and at the same time providing technical support for the future large-scale and cross-regional expansion of car rental businesses. In the entire system, the digital signature and data encryption unit, as the last line of defense for data security, the complex encryption and perturbation technologies used inside ensure the high security of the data during transmission, storage, and subsequent verification processes, and closely cooperate with modules such as identity authentication, key management, and blockchain storage to jointly form a secure, trustworthy, and efficient car rental transaction and trust management platform.

[0046] In this system, after each transaction is processed through multiple links such as identity authentication, key management, digital signature, and data encryption, it will be submitted to the blockchain network. The blockchain consensus and storage unit is responsible for uniformly summarizing and verifying this strictly encrypted and preprocessed data to ensure that it has not been tampered with or forged during the transmission process. Specifically, when the system receives transaction data protected by multiple encryptions, it combines it with the hash value of the previous block and the perturbation factor generated by the shared key, and constructs the hash of the current new block through hash operation. This design not only ensures that each block has a strong correlation with the previous block, making any data change in a single block destroy the integrity of the entire chain, but also uses the perturbation factor to increase the unpredictability of the hash calculation, thus greatly enhancing the ability to prevent replay attacks, collision attacks, and tampering attacks. At the same time, the blockchain consensus mechanism plays a key role in this process. Each node in the system participates in the consensus algorithm (such as proof of work, proof of stake, or other innovative consensus protocols) to reach an agreement on the legality of the new block. After being repeatedly verified and confirmed by multiple nodes, the new block is officially written into the blockchain, realizing the consistency and integrity of data in the distributed network. This consensus process not only prevents the risks brought by single-point failures and centralized management, but also makes full use of the distributed ledger feature of blockchain technology, enabling the entire car rental transaction system to automatically generate, verify, and store transaction records without the participation of a centralized third-party institution, providing an open, transparent, and trustworthy transaction platform for car owners and renters. In addition, the storage unit adopts a distributed storage architecture in the whole system, organically connecting each new block with the previous blocks according to the time sequence and logical relationship, forming an irreversible transaction chain. This not only ensures the permanent preservation and public query of historical transaction data, but also makes any attempt to tamper with the data must simultaneously modify all subsequent blocks on the entire chain, thus becoming extremely difficult economically and computationally. Throughout the process, the consensus and storage unit use cryptographic technology to ensure that each piece of data in the blockchain has high credibility and integrity, and at the same time, through distributed storage and decentralized architecture design, reduce the risk of the system being attacked by the network and internally tampered with. With the help of this technical architecture, all key information in car rental transactions, such as vehicle unique identification, rental price, timestamp, and digital signature, can be permanently recorded on the blockchain in an immutable manner by the system. Any subsequent disputes or disputes can be traced and verified through the data on the public ledger, thus providing strong legal and technical support for both parties to the transaction. It is precisely because of the excellent performance of the blockchain consensus and storage unit in ensuring data transmission security, information synchronization between nodes, and reaching consensus across the network that the entire blockchain-based car rental transaction and trust management system can effectively prevent forgery, tampering, and attack behaviors, and establish an efficient and trustworthy transaction environment for both rental parties.

[0047] Example 2: The participants include car owners and rental users; for each participant i, the system first randomly generates two large prime numbers p i and q i ; i = 1, 2,..., N; N is the number of participants; define the RSA modulus n i = p i q i ; and satisfy 2 λ ≤ p i , q i < 2 λ+1 ; is the set of prime numbers; define the Euler's totient function φ(n i ) = (p i - 1)(q i - 1); define the public key exponent where gcd(·) represents the greatest common divisor operation; is the set of natural numbers; λ is a security parameter preset by the system; define the private key exponent

[0048] Specifically, first, the process of randomly selecting two large prime numbers p i and q i relies on the statistical law of prime number distribution. That is, although the distribution of prime numbers seems disordered in a sufficiently large interval, according to the prime number theorem, its density is roughly proportional to 1 / ln(x). Thus, given the security parameter λ, prime numbers that satisfy 2 λ ≤ p i , q i < 2 λ+1 can be selected with a relatively high probability. This selection ensures that both factors that make up the RSA modulus n i = p i ·q i have enough digits, making it computationally infeasible to factorize n i using existing computing resources, thus ensuring the anti-attack ability of the system against man-in-the-middle attacks and key forgery. Then, by constructing the Euler's totient function φ(n i ) = (p i - 1)(q i - 1), the structural characteristics of the multiplicative group of integers modulo in group theory are reflected. The significance of the Euler's totient function is that it gives the number of integers that are relatively prime to n i under the modulus n i . This number-theoretic function not only reveals the periodicity of operations under the modulus n i , but also provides a theoretical guarantee for the existence of the subsequent inverse element. When selecting the public key exponent e iWhen it is required to be greater than 2 λ-1 and relatively prime to φ(n i ), that is, it satisfies gcd(e i , φ(n i )) = 1. This choice ensures that e i has an inverse element in the multiplicative group modulo φ(n i ), and further ensures that there exists a unique private key d i satisfying e i· d i ≡ 1 (mod φ(n i ). This modular inverse operation process depends on the extended Euclidean algorithm, which not only effectively calculates the greatest common divisor of two integers, but also can find a unique inverse element under the condition of relatively prime. This property stems from the concepts of unit elements and invertible elements in ring theory.

[0049] In a finite ring , any element relatively prime to the modulus must be invertible. This structural property provides a mathematical basis for the RSA algorithm. It should be noted that the relationship between the public key e i and the private key d i determines the security of the RSA system. Even if e i and the modulus n i are both public, due to the fact that the problem of factoring large numbers is considered to be a problem with extremely high computational complexity under the current computing power, it is difficult for an attacker to factor p i and q i from n i and thus deduce φ(n i ) and d i . This irreversibility is exactly a security defense line constructed based on difficult problems in algorithm complexity theory. It is generally considered that factoring large integers is an NP-hard problem. Combining these mathematical principles, the entire process of generating RSA key pairs not only demonstrates the probabilistic characteristics of large number random selection and prime number distribution, but also reflects the strict proof of the existence of inverse elements in the multiplicative group in group theory and finite fields. At the same time, the congruence relationship and modular operation characteristics in ring theory are used to ensure the correctness of encryption and decryption. The key system constructed in this way plays an important role in the blockchain-based car rental transaction and trust management system, because each participant (whether it is the car owner or the rental user) has a unique and non-forgeable identity identifier. These keys are not only used for digital signatures to verify the legality of transaction data, but also ensure the confidentiality of information transmission during the data encryption process. With the help of this mathematical construction, every transaction information is strictly encrypted before being sent to the blockchain, and only the holder of the corresponding private key can decrypt it. Thus, while the transaction data is permanently stored in the publicly transparent distributed ledger, it can also ensure that the data content is not illegally tampered with.

[0050] Example 3: The identity and key management unit is responsible for the identity registration of all participants. When generating the public and private key pairs by extending the RSA algorithm and polynomial random perturbation, it is achieved by adding polynomial random perturbation terms. For each participant i, the polynomial random perturbation term is represented by the following formula:

[0051]

[0052] where, denotes the bitwise exclusive OR operation; both j and k are integer subscript indices; μ is the upper limit of the internal summation of the polynomial, representing the number of terms in each layer of the polynomial expansion; the non - linear perturbation ξ is a predefined large constant; Γ(·) is the gamma function; the formula for the auxiliary term is as follows:

[0053]

[0054] where, H i represents the integer value obtained by hashing and mapping the identity ID of the participant; then the public key perturbation term is constructed as:

[0055]

[0056] Specifically, by introducing the perturbation term Θ i and the public key perturbation term Ω i the identity information of the participant, the randomly generated prime number, and other auxiliary parameters are mixed in a multi - layer non - linear operation manner to form a key correction value that is both closely related to the participant's identity and has high randomness and irreversibility. The symbol appearing first in the formula denotes the bitwise exclusive OR operation, which has the characteristics of non - linearity and data confusion in information security. It can mix the binary representations of multiple data streams in an unpredictable way, making it difficult to reverse - deduce the overall result even if some input values are known. Therefore, the operation is used multiple times in the formula to synthesize different calculation results, thereby achieving the purpose of secure confusion. For each participant i, the construction expression of its perturbation term Θ i contains a nested multiple operation. The inner - layer product operation represents the cumulative multiplication effect of the number of terms in each layer in the polynomial expansion. Here, μ defines the upper limit of the internal summation of the polynomial, controlling the number of terms included in each layer, making the overall expression show a polynomial - level non - linear growth in structure. The numerator part of the product contains the product of the participant identity hash value H i and (p i +q i ) k , where p i and qi They are two large prime numbers used for RSA key generation. The sum of them, after exponentiation, further amplifies the initial prime number information, making the perturbation term closely related to the RSA parameters and increasing the difficulty for attackers to decompose the key by reverse deduction.

[0057] The denominator part introduces the gamma function Γ(j + k + ζ i ). As a continuous generalization of the factorial function, the gamma function has smooth and non-linear characteristics. Its parameters are composed of the sum of the indices j and k plus a non-linear perturbation amount ζ i , where ζ i is defined as (ξ is a predefined large constant). This design makes the input of the gamma function not only depend on fixed index values but also on the specific RSA parameters of the participants, thus introducing a difficult-to-predict perturbation scale mathematically and further strengthening the randomness of the entire formula. On the outer layer, the product result is exponentiated with the exponent j. Such exponentiation not only makes the influence of each layer result show an exponential amplification effect but also magnifies the subtle differences in the initial value to an irreversible degree through multiple superpositions. The XOR operation on the outer layer then XORs and synthesizes the calculation results from different j layers one by one. This way of layer-by-layer mixing effectively combines the non-linear results of each layer calculation into a comprehensive perturbation value Θ i , making the final result show high entropy and complexity in statistical distribution, far exceeding simple linear combinations or simple products. In addition, an auxiliary term is introduced in the formula, and its expression is . Here, the alternating sign is used to introduce the property of the alternating series, which can produce an oscillating and partially canceling effect mathematically. This ensures the numerical balance and convergence of the auxiliary term to some extent and makes the overall structure of the perturbation term more complex; in the numerator, introduces the prime number information generated by RSA through exponentiation, so that this term is complementary to p i +q i in the main perturbation term. The factorial (j + k)! in the denominator uses the rapidly growing property of the factorial function to decay and regulate each term to ensure that the summation result will not get out of control due to exponentiation; at the same time, the parameter a i , as a participant-specific auxiliary scaling factor, further gives the perturbation terms between different participants numerical characteristics. After completing the summation of the auxiliary term, it is XORed again bit by bit with the main perturbation part obtained previously through multiple XOR operations to obtain the final perturbation value Θ iThis process mathematically embodies the superposition effect of multi-layer non-linear operations, enabling the perturbation value to contain all the information of identity hash, RSA prime numbers, and their combinations, and forming a complex value that is difficult to restore the original parameters through linear inverse operations after operations of alternation, normalization, and exponential amplification.

[0058] Next, the public key perturbation term Ω i is constructed by the formula Here, n i is the RSA modulus, and the product part of its λ power and extends the traditional RSA parameters with power and multi-level product operations. In this way, the original key information shows a very high diffusion effect numerically, further increasing the difficulty of recovering the original prime number information from the public parameters; finally, the bitwise exclusive OR operation is used to combine with the perturbation value Θ i so that the entire public key perturbation term not only retains the security of the original RSA construction but also integrates the non-linear characteristics of polynomial random perturbations, thus providing an additional layer of encryption protection for the key system. From a scientific theory perspective, this design makes full use of the characteristics of large prime numbers and their random distributions in number theory, the advantages of the gamma function in continuous extension and normalization processing, and the mathematical characteristics of alternating series and factorial functions in controlling numerical scale and oscillation effects. At the same time, through a large number of non-linear operations and exclusive OR mixing, the entire perturbation structure shows a high degree of irreversibility in algorithm complexity. It is precisely this superposition effect of multi-layer mathematical functions and operations that makes it difficult for attackers to obtain the core random perturbation term used to generate the key through reverse calculation even if they can obtain some public key parameters, thus providing a solid and unbreakable security guarantee for identity authentication and data transmission in the blockchain-based car rental transaction and trust management system. In practical applications, when the car owner and the rental user perform identity registration and key generation, the system will, according to the identity information of each participant (obtained through hash mapping as H i ), randomly generated RSA large prime numbers p i and q i and auxiliary parameters, calculate the perturbation term Θ i through the above complex polynomial random perturbation formula and further construct the public key perturbation term Ω i ; this process ensures that even if the transaction information and some key parameters are leaked on the public blockchain, attackers cannot use the public information to reverse deduce the complete private key information or interference term, thus greatly improving the security and credibility of the entire system.

[0059] Example 4: The finally obtained public and private key pairs are represented by the following formula:

[0060]

[0061] Among them, SK i is the private key of participant i; PK i is the public key of participant i.

[0062] Specifically, d i is the private exponent generated by using large prime numbers p i and q i in the traditional RSA algorithm. Its mathematical principle is based on modular inverse operation, that is, it satisfies d i ·e i ≡1 (mod φ(n i ))), which ensures that only the participant with the correct private key can decrypt the ciphertext. And Θ i is a polynomial random perturbation term introduced by extending the RSA algorithm. This perturbation term mixes the identity information H i of the participant (i.e., the hash mapping value of the identity ID), the combined characteristics of the prime numbers p i and q i involved in the RSA generation process, and other auxiliary parameters through multi-layer non-linear operations. Its core idea is to construct a high-entropy and unpredictable value by using bitwise XOR operation products, exponential operations, and continuous and discrete mathematical tools such as the gamma function. This perturbation term makes it difficult for an attacker to deduce the complete key information even if they can partially obtain or guess the traditional RSA parameters, because the complex non-linear functions and the effects of multiple alternating series contained in the perturbation term greatly increase the computational difficulty of recovering the private key from the public key information. At the same time, the public key part contains the classical RSA modulus n i = p i ·q i and the public key exponent e i , and these two items constitute the basis of the traditional RSA encryption algorithm, and its security depends on the computational complexity of the large number factorization problem; however, in order to further enhance the security, the system also additionally introduces a perturbation term Ω i in the public key. Its construction method is to combine a certain power of n i with the sum of p and q i ((p i +q i +q i )) through multiple products, and then mix it with the perturbation term Θ i through bitwise XOR operation. Such a design makes the public key not only carry the encryption information of the traditional RSA, but also further hides the internal relationship between the key parameters by introducing additional non-linear perturbations, thereby preventing potential side-channel analysis and key recovery attacks. From the perspective of scientific theory, the construction of the entire key pair deeply integrates the core principles of number theory, combinatorics, and complexity theory.

[0063] First, when generating n i and calculating d i , it depends on the random selection of large prime numbers and the construction of the Euler's totient function φ(n i ). This process ensures the computational difficulty based on large number factorization. Secondly, by combining the identity information H i with the operation results of prime numbers p i and q i to generate the perturbation term Θ i , using the normalization effect of the gamma function in continuous extension and the positive and negative oscillation effects introduced in the alternating series, the perturbation term shows extremely high uncertainty and non-linear characteristics numerically, which greatly enhances the system's ability to resist statistical attacks and reverse calculations mathematically. Finally, when constructing the public key perturbation term Ω i , the power operation results of traditional RSA parameters are bitwise XOR mixed with the perturbation term, thus forming a multi-level, non-linear and highly diffusive key expression method. Even after n i and e i are made public, attackers still cannot easily derive any useful information about the private key from them. This design not only ensures a strict mathematical correspondence between the private key and the public key of each participant, but also enhances the anti-attack ability of the key pair by introducing an additional perturbation layer, so that even in the face of high-performance computers and advanced algorithm attacks, the system can still maintain an extremely high security standard. In practical applications, when the car owner or rental user conducts transactions on the blockchain network, the generated digital signatures and data encryption both rely on the two components in the private key SK i =(d i , Θ i ), and the verification of these operations is completed through the public key PK i =(n i , e i , Ω i ), ensuring that the transaction information not only undergoes traditional RSA encryption protection during transmission and storage, but also incorporates an additional random perturbation protection layer, so that the entire blockchain-based car rental transaction and trust management system can obtain multiple guarantees in all aspects such as identity authentication, digital signature, and data encryption. Through this dual-key construction method, while the system utilizes the security of classical RSA, it adds an additional line of defense through the mathematically difficult-to-invert perturbation term, making the key difficult to be maliciously calculated or forged even in the case of partial information leakage, thus providing an efficient and unbreakable security platform for both trading parties.

[0064] Example 5: Assume that the car owner is participant o. When publishing car rental information, the unique vehicle identifier, rental price, and timestamp are digitally signed. The formula is as follows:

[0065]

[0066] where car_ID is the unique vehicle identifier; price is the rental price; τ is the timestamp; Ω o is the public key perturbation term of participant o; d o is the private key exponent of participant o; Θ o is the polynomial random perturbation term of participant o; n o is the RSA modulus of participant o; m is an integer subscript index; M is the expansion upper limit, represents the floor function; σ o is the digital signature of the participant.

[0067] Specifically, in the blockchain-based car rental transaction and trust management system, the digital signature not only undertakes the task of verifying the authenticity of transaction data but also serves as an important guarantee to ensure that the identity of the car owner cannot be forged. In Example 5, when the car owner publishes car rental information, the unique vehicle identifier, rental price, and timestamp are signed. Its mathematical expression reflects an improvement on the traditional RSA signature method and incorporates series expansion and perturbation techniques to enhance overall security. The entire signature formula can be regarded as consisting of two major parts: First, through a summation process similar to Taylor series expansion, the vehicle information data is non-linearly transformed, and then combined with the specific public key perturbation term of the car owner; Second, the summation result is exponentiated with the sum of the private key exponent and the additional perturbation term, and then modular exponentiation is performed on it to obtain the final signature. Each term involved in the summation part of the formula uses a coefficient This coefficient structure is derived from the expansion of the exponential function, and its alternating sign (-1) m introduces a positive and negative oscillation effect in mathematics, which helps to balance the values of each term, making the expansion result more dispersed and avoiding a single-directional offset caused by data concentration; the m! in the denominator effectively attenuates the high-order terms using the characteristic of rapid growth of factorial, enabling the entire series to converge rapidly after reaching the predetermined expansion upper limit M, ensuring the stability and rationality of the calculation. Here, the expansion upper limit M is defined as This setting not only depends on the overall magnitude of the data to be signed, but also balances the expansion depth and computational complexity, enabling each signature to fully capture the data characteristics while avoiding arithmetic overflow or unnecessary resource waste caused by excessive high-order terms. After the data to be signed undergoes exponentiation, the unique vehicle identifier is first squared. This processing method can amplify the role of the vehicle identifier in the entire signed data on the one hand, and on the other hand, it also ensures that even if there is a slight change in the vehicle identifier, its impact on the overall data structure will be significantly amplified. At the same time, the rental price and timestamp are involved as dynamic information, making each signature not only related to the vehicle itself, but also closely bound to the specific moment when the transaction occurs and the pricing strategy, thus endowing the signature with higher uniqueness and timeliness. To further enhance security, after each data processing in the formula, the result is mixed with the public key perturbation term Ω of the vehicle owner o . The exclusive OR operation is widely used in information security. Its irreversibility and confusion effect make it difficult for an attacker to directly restore any useful plaintext information from the exclusive OR result even if they partially know the relevant parameters after the original data is combined with the perturbation value.

[0068] After the above multi-layer mixing of the sum of accumulations, the result is raised to the power exponent formed by the sum of the private key exponent d and the polynomial random perturbation term Θ o . Here, d o is the private exponent generated based on the RSA algorithm, and its security relies on the computational difficulty of the large number factorization problem. The additional perturbation term Θ o further disrupts the structure of the power exponent, making the signature generation process not only depend on the traditional RSA private key, but also incorporate randomness and non-linear effects, thus greatly increasing the difficulty of reverse calculation by attackers. Finally, by performing a modulo n o operation on the above result (where n oFor the RSA modulus of the car owner), it ensures that the signature value is within a predetermined finite range, which is exactly the core role of modular arithmetic in the RSA system. It not only controls the size of the data but also ensures the interoperability of signatures between different devices and the consistency of verification. Scientifically speaking, this entire digital signature construction method fully combines the Taylor series expansion of the exponential function, the convergence of alternating series, the attenuation effect of the factorial function in high-order terms, and the confusion characteristics of bitwise exclusive-or operations. Each mathematical operation link aims to break up the direct linear relationship of the original data and create a signature result that is highly dispersed and irreversible numerically. Especially in the application scenario of blockchain, once any transaction record is published, it will be permanently stored on the public ledger. Therefore, the security of the signature is directly related to the trust level of the entire car rental transaction system. By simultaneously introducing vehicle identification, rental price, and timestamp, multiple mixed perturbations, and strict modular arithmetic restrictions into the signature formula, not only does each digital signature have uniqueness and timeliness, but also it ensures that even if the signature data is intercepted or partially disclosed in a distributed network, attackers cannot reverse-deduce the private key information of the car owner through any mathematical means.

[0069] Embodiment 6: Identity and Key Management Unit. When generating a shared key, for the car owner and the rental user, the Diffie–Hellman key exchange algorithm is used for key negotiation to generate a shared key; let the car owner vector be a = (a 1 , a 2 ,..., a v ,..., a L ): The rental user vector is b = (b 1 , b 2 ,..., b v ,..., b L ); L is the dimension of the Diffie–Hellman key exchange; both the car owner vector and the rental user vector are random vectors; a v is the v-th element in the car owner vector; b v is the v-th element of the rental user vector; through the following formula, the shared key k shared is generated:

[0070]

[0071] where p o and q o are two large prime numbers of the participant o corresponding to the car owner; p u and q u are two large prime numbers of the participant u corresponding to the rental user; v is an integer subscript index; g is a generator.

[0072] Specifically, in the blockchain-based car rental transaction and trust management system, to achieve secure communication and key sharing between car owners and rental users, an improved Diffie–Hellman key exchange algorithm is adopted. Its mathematical formula not only continues the basic idea of the traditional Diffie–Hellman method but also significantly enhances the entropy value and anti-attack ability of the shared key through vectorization, multi-dimensional expansion, and the introduction of additional perturbation factors. Specifically, the system constructs random vectors a = (a 1 , a 2 ,..., a L ) and b = (b 1 , b 2 ,..., b L ) for car owners and rental users respectively, where L is the dimension of the key exchange. The randomness ensures the unpredictability of each component, and this multi-dimensional structure makes the shared key affected by independent random numbers in each dimension, thus forming a high-dimensional and difficult-to-analyze key space as a whole. In the traditional Diffie–Hellman protocol, the two parties usually negotiate the shared key by calculating the exponential power g ab of the generator g. In this embodiment, each vector component a v and b v respectively participate in the calculation . This step utilizes the one-wayness and irreversibility of the exponential operation under modular arithmetic, ensuring that even if part of the information is leaked, it is impossible to easily recover their respective private random numbers. However, to further enhance security and prevent side-channel attacks, an additional perturbation factor is introduced into the formula. This perturbation factor is reflected in the additional term in the product . Among them, the parameter α v is a unique weighting coefficient for each dimension, which can flexibly adjust the influence of the perturbation term. The polynomial expansion and summation part is based on (a v + b v ) j and is normalized by dividing by τ + j, ensuring that the high-order terms will not get out of control due to exponential growth and making the perturbation term show a multi-level and non-linear mixing characteristic. Mathematically, this processing effectively introduces additional uncertainty, making it difficult for attackers to analyze the true vector components even if they can capture some exponential information. Next, take the natural logarithm of the operation result of each dimension and then average it, that is, use the in the formula.The operation is equivalent to calculating the geometric mean for all dimensions. This processing method not only maintains the product relationship between dimensions but also achieves smoothing and normalization numerically, helping to resist security risks caused by abnormal data in a certain dimension. Subsequently, the exponential function is used to restore the logarithmic value to the original product domain, forming a shared secret value that combines the random contributions of all dimensions and the non-linear perturbation effect. Finally, to ensure that the generated shared key is within a reasonable and secure numerical range, the formula restricts the result through modular arithmetic, and the modulus is selected as where p o and q o are two large prime numbers corresponding to the car owner respectively, p u and q u are two large prime numbers corresponding to the rental user respectively. This choice not only makes the modulus have the properties of being large enough and random but also integrates the respective RSA parameters of both parties, so that the final value of the shared key is closely related to the identities and key generation histories of both parties, further increasing the security in the key negotiation process.

[0073] This formula comprehensively utilizes the inverse property of exponential and logarithmic functions, the non-linear superposition of polynomial expansion, normalization technology, and the characteristic of modular arithmetic to construct a closed loop in a finite field. It not only retains the security foundation based on the difficulty of large number factorization in the traditional Diffie–Hellman key exchange but also makes the shared key highly complex and resistant to analysis in terms of mathematical structure by introducing random vectors, multi-dimensional averaging, and perturbation terms. Specifically, the operation on each dimension is based on the one-way property of the generator and exponential operation in group theory, and the additional This item utilizes the convergence characteristics of polynomial series in function approximation and the oscillation effect of alternating series, effectively increasing the uncertainty of the calculation results. Taking the natural logarithm and then averaging is equivalent to calculating the arithmetic mean of each dimension in the logarithmic space, which not only smooths the data distribution but also cancels out the abnormal deviations in certain dimensions. Finally, taking the exponential restoration ensures the integrity of the product structure of the shared key. Modular arithmetic is a common technique in cryptography. It maps the result to a fixed integer range, not only ensuring the fixed-length and transmissibility of the output data but also further leveraging the randomness and large-number characteristics of RSA parameters. Even if an attacker attempts to restore the shared key through brute force or other mathematical methods, the required computational effort will be infeasible due to the huge modulus. Overall, this scheme based on vectorized Diffie–Hellman key exchange constructs a shared key generation process that not only has the security of traditional large-number factorization but also higher entropy value and structural complexity by superimposing non-linear perturbations and multi-dimensional averaging mechanisms in traditional exponential operations. For the car rental transaction system, this key negotiation mechanism can ensure that the car owner and the rental user reach a highly secure shared secret in the initial communication stage, enabling subsequent transaction data transmission, digital signature verification, and blockchain storage to be based on a solid encryption foundation, preventing security threats such as man-in-the-middle attacks and replay attacks, and also providing a flexible and efficient key management strategy for the entire system.

[0074] Example 7: Let the digital signature of the participant o corresponding to the car owner be σ o , then the transaction data is T = Encode(car_ID, price, τ, σ o ); The transaction data including the digital signature is preprocessed by adding multiple hash perturbation terms through multiple hash perturbations. The multiple hash perturbation term Ψ(T, k shared ) is defined as:

[0075]

[0076] where R is the set expansion series of the multiple hash perturbation term; r is the integer subscript index; || is the concatenation operator; |T| represents the length of the transaction data; H(·) is the hash function; Using the following formula, AES encryption is performed using the shared key to generate the final ciphertext C:

[0077]

[0078] where, represents the AES encryption algorithm with k shared as the key.

[0079] Specifically, the whole process starts with constructing transaction data. The transaction data T is generated after encoding the vehicle's unique identifier, rental price, timestamp, and the digital signature of the vehicle owner. The encoded data ensures that all key information is logically closely connected and inseparable. On this basis, to prevent the transaction data from being exploited by attackers through statistical analysis or reverse derivation of sensitive information during transmission, the system introduces a multiple hash perturbation term, denoted as Ψ(T, k shared ). In the construction of this perturbation term, first, the transaction data T, the shared key k shared negotiated by both parties, and the current expansion subscript r are concatenated together through the concatenation operator "||" to form a new input string, and then processed through the hash function H(·) to obtain a hash value of a fixed length. Since the hash function has the properties of one-wayness and collision resistance, its output cannot be reversed to deduce the input data. Therefore, this part of the processing ensures a strong coupling relationship between the perturbation term and the original transaction data and the shared key. On this basis, each term of the perturbation term is multiplied by a coefficient This coefficient design is derived from the Taylor series expansion. The introduction of the alternating sign (-1) r makes the terms show an alternating positive and negative trend in value, thus playing a role of balancing and partially canceling during the accumulation process. And the r! in the denominator utilizes the characteristic that the factorial function grows rapidly to effectively attenuate the high-order terms and ensure that the entire series converges rapidly within a finite number of terms. The upper limit of the summation R is set as where |T| represents the length of the transaction data T. This setting makes the expansion depth related to the data scale, which not only ensures that the perturbation effect is introduced sufficiently when the data volume is large but also avoids unnecessary computational complexity when the data is small, making the system have good self-adaptability. The calculation of the entire perturbation term Ψ(T, k shared ) is based on the mathematical idea of thoroughly confusing each information component in the transaction data and the influence of the shared key through non-linear superposition, making the perturbation result have extremely high randomness and unpredictability in value, further dispersing the statistical characteristics of the original data and preventing attackers from analyzing it using any known patterns. Next, to ensure that the transaction data is not directly stolen during transmission and storage, the system mixes the original transaction data T and the perturbation term Ψ(T, k shared ) through the bitwise XOR operation . As a basic binary operation, the bitwise XOR is characterized by a simple and irreversible operation process. Once mixed, the information of the original data and the perturbation term is highly integrated. Even if any party obtains the mixed result, it is difficult to split it into independent parts. The mixed result is then used as the input of the AES encryption algorithm. The AES encryption algorithm uses the shared key k sharedEncrypt the data using a symmetric key pair. It performs complex operations of permutation and substitution internally, achieving thorough confusion of the data. Coupled with the combined effect of the aforementioned perturbation terms, the finally generated ciphertext C is approximately random in statistical distribution, greatly enhancing the confidentiality and anti - attack ability of the data.

[0080] Example 8: Let the hash of the previous block be prev_hash; through multiple - round iteration, combine the digital signature, ciphertext, the hash of the previous block, and the perturbation factor generated from the shared key to construct the hash of the new block. In the j - th round of iteration, define the intermediate function F j (s, t):

[0081] F j (s, t) = SHA256(H j-1 ||C||τ||j||s||t);

[0082] where j = 1, 2,..., J; J is the total number of iteration rounds; let the initial intermediate value be H 0 = prev_hash, H j-1 is the intermediate value of the (j - 1)-th round of iteration; both s and t are integral variables, taking values in the interval [0, |T|], and obtain the multiple - integral term I j in the perturbation factor of the j - th round of iteration as:

[0083]

[0084] Obtain the single - integral term J j in the perturbation factor of the j - th round of iteration as:

[0085]

[0086] where SHA256(·) is the standard SHA - 256 hash function; obtain the perturbation factor as I j + J j .

[0087] Specifically, in the first round of iteration, use the hash value of the previous block as the initial intermediate value H 0 = prev_hash, and the system constructs the intermediate function F j (s, t) = SHA256(H j-1 ||C||τ||j||s||t) (where "||" represents the concatenation operator), and this function takes the intermediate value H j-1, the ciphertext C stored in the current block, the timestamp τ of the transaction, the current iteration round j, and two integral variables s and t are combined into a whole through a concatenation operation, and then the SHA-256 hash function is used to operate on it to generate a fixed-length output. As a standard hash function, SHA-256 is characterized in that the output value is extremely sensitive to small changes in the input, and has strong collision resistance and irreversibility. Therefore, hashing the concatenated data from these different sources can make the intermediate value of each round not only closely depend on the information of the previous block, but also contain all the characteristics of the current transaction data and time information. After obtaining F j (s, t), the system calculates the multiple integral term by performing a double integral on variables s and t in the interval [0, |T|] Here, |T| represents the length of the transaction data T. The integral operation is equivalent to taking the global average of the data, so that the values of the multi-dimensional variables s and t in the entire data interval are taken into account, thereby capturing the overall characteristics of the transaction data. At the same time, the shared key k shared is introduced in a concatenated form to ensure that the perturbation factor is closely related to the key negotiated by both parties. The purpose of taking the natural logarithm function is to convert the exponential growth trend of the hash function output into a linear scale, which is convenient for subsequent mathematical processing and makes the change of the data smoother. Correspondingly, the single integral term J j is obtained by integrating the variable t in the same interval, and its calculation formula is Here, only the integral of the single variable t is involved. Although it lacks the global characteristics brought by one-dimensional integration, it can still capture some local characteristics and provide another layer of supplement for the construction of the perturbation factor. The sum of the two integral terms I j and J j is used as the perturbation factor for this round of iteration, which reflects the multiple mathematical processing of the transaction data and the ciphertext. Its role is to further disrupt and confuse the statistical characteristics of the input data, so that in the subsequent iterations, the intermediate hash value H j calculated in each round will contain a large number of non-linear factors and randomness, making the entire blockchain structure have a very high entropy value mathematically.

[0088] This design ensures that even if an attacker can obtain part of the information of the previous block, it is impossible to restore the complete transaction data or the shared key through simple linear operations or reverse engineering. The entire iteration process is carried out for J rounds, and the intermediate value H jBoth rely on the results of the previous round and the perturbation factors calculated currently, thus achieving layer-by-layer superimposed security protection; during the iterative process, the introduction of the timestamp τ and the round number j ensures that the calculation results of each round are unique and closely related to the current moment, thereby further preventing replay attacks and forgery attacks. Thus, the hash value of the new block is ultimately determined by the results of multiple rounds of iteration. Its mathematical structure not only inherits the continuity of the previous block but also exhibits extremely high uncertainty due to the multi-dimensional non-linear mixing of the integral perturbation factors. Combining the theme of the present invention, the entire design scheme not only ensures that the hash value of each block in the blockchain has high randomness and unpredictability, but also through integrating the transaction ciphertext C, the timestamp τ, and the shared key k shared into the hash calculation process, so that the information of each car rental transaction is encrypted multiple times and protected against tampering when generating a block, thereby building an indestructible security barrier for the car rental transaction and trust management system. The whole process makes full use of the one-wayness and collision resistance of the SHA-256 hash function, the role of the natural logarithm in data smoothing processing, the mean effect of integral operation in capturing global features, and the advantages of multiple rounds of iteration in constructing continuous dependence. These mathematical tools cooperate with each other, not only making the hash chain of the blockchain maintain continuity and integrity, but also greatly increasing the computational difficulty for crackers in the reverse solution process, ensuring that all transaction data maintains a high degree of confidentiality and integrity during storage and transmission. It is precisely this mathematical method based on multiple integral perturbations and iterative hash construction that endows the hash value of the new block with randomness and tamper-proof characteristics, enabling the blockchain-based car rental transaction system to remain highly stable and secure in the face of various modern cryptographic attacks, thereby providing a solid theoretical guarantee for the long-term operation of the system and the protection of user information.

[0089] Example 9: The hash of the new block is calculated by the following formula:

[0090]

[0091] where H block is the hash of the new block.

[0092] Specifically, first, the intermediate values H j (where j = 1, 2,..., J) obtained during the previous multiple rounds of iteration form a set of data. These intermediate values are calculated by continuously introducing the perturbation factors generated by the hash of the previous block, the transaction ciphertext, the timestamp, and the shared key. Its basic characteristic is that each iteration makes the result contain all the information of the previous round, and due to the use of the SHA-256 hash function, its output is extremely sensitive to small changes in the input, reflecting the characteristic of information entropy diffusion. Then, the formula performs power normalization processing on the iterative values of each round, that is, for each round of H jTaking the 1 / j power, such a process can balance the information contributed in each round, restore the influence weakened by exponential decay in later rounds, and also make the overall calculation result numerically stable; during this process, the alternating sign (-1) j-1 is introduced to achieve the superposition effect of positive and negative alternation, avoid the deviation or cumulative error that may be caused by monotonic accumulation, and thus increase the unpredictability of the overall output. Subsequently, all these normalized intermediate values are combined by summation, and then through the normalized power operation, that is, taking the reciprocal of the summation result as the exponent for the overall power operation. This step is essentially a comprehensive adjustment of all iterative information, making the data of each layer reach equilibrium in scale, and at the same time making the output value more non-linear and chaotic mathematically, greatly increasing the difficulty of reverse engineering. At the same time, the pre-factor I j +J j in the formula comes from the aforementioned multiple integral perturbation term, where I j and J j respectively capture the global and local information by taking the natural logarithm of the hash outputs related to transaction data and shared keys and then performing integral averaging in different dimensions. This method can not only extract the overall characteristics of the data, but also introduce the smoothing and normalization effects during the integration process, ensuring that the perturbation factor has high entropy and irreversibility. Finally, the entire result is further subjected to a modulo operation, and the modulus is taken from the linear combination of the RSA large prime number parameters p o and q o generated by the car owner and the rental user respectively, p u and q u , usually expressed as This design of the modulo operation can not only limit the final hash value within a fixed numerical range, ensure the fixed length and consistency of the output data, but also introduce the identity information of each participant into the new block hash, making each block on the blockchain associated with the key generation history of both parties, thus constructing a multi-level protection network as a whole.

[0093] The preferred embodiments of the present disclosure have been described above with reference to the accompanying drawings, and thus do not limit the scope of rights of the present disclosure. Any modifications, equivalent replacements, and improvements made by those skilled in the art without departing from the scope and essence of the present disclosure shall fall within the scope of rights of the present disclosure.

Claims

1. A car rental transaction and trust management system based on blockchain, characterized by: The system includes: an identity and key management unit, a digital signature and data encryption unit, and a blockchain consensus and storage unit; the identity and key management unit is used to be responsible for the identity registration of all participants, generate a public-private key pair by extending the RSA algorithm and polynomial random perturbation, complete the key exchange between the participants in the rental request stage, and generate a shared key; the digital signature and data encryption unit is used for the car owner to use his own private key to digitally sign the vehicle unique identification, rental price and timestamp, and after pre-processing the transaction data including the digital signature with multiple hash perturbations, use the shared key to perform AES encryption to generate the final ciphertext; the blockchain consensus and storage unit is used to be responsible for receiving the digital signature and ciphertext, combining it with the hash of the previous block and the perturbation factor generated by the shared key to construct the hash of the new block, and storing the constructed new block in the blockchain after consensus verification to form an unalterable transaction history record.

2. The blockchain-based car rental transaction and trust management system according to claim 1, characterized in that: Participants include car owners and rental users; for each participant i, the system first randomly generates two large prime numbers p i With q i ; i = 1, 2, ..., N; N is the number of participants; define the RSA modulus n i =p i q i ; And satisfy 2 λ ≤p i ,q i <2 λ+1 ; is a set of prime numbers; define the Euler function φ(n i )=(p i -1)(q i -1); define the public key exponent Where gcd(·) represents the greatest common divisor operation; is a set of natural numbers; λ is the security parameter preset by the system; define the private key exponent 3. The blockchain-based car rental transaction and trust management system as claimed in claim 2, characterized in that: The identity and key management unit is responsible for the identity registration of all participants. When generating a public-private key pair through the extended RSA algorithm and polynomial random perturbation, it is achieved by adding a polynomial random perturbation term; for each participant i, the polynomial random perturbation term is expressed using the following formula: Where ⊕ represents a bitwise XOR operation; j and k are both integer subscript indices; μ is the upper limit of the internal summation of the polynomial, representing the number of terms in each layer of the polynomial expansion; nonlinear perturbation ξ is a predefined large constant; Γ(·) is the gamma function; the auxiliary term The formula is as follows: Among them, H i Represents the integer value obtained by hashing the participant's identity ID; the public key perturbation term is then constructed as:

4. The blockchain-based car rental transaction and trust management system as claimed in claim 3, characterized in that: The final public-private key pair is expressed using the following formula: Among them, SK i is the private key of participant i; PK i is the public key of participant i.

5. The blockchain-based car rental transaction and trust management system as claimed in claim 4, characterized in that: The car owner is participant o. When publishing car rental information, the vehicle unique identifier, rental price and timestamp are digitally signed. The formula is as follows: Among them, car_ID is the unique identifier of the vehicle; price is the rental price; τ is the timestamp; Ω o is the public key perturbation term of participant o; d o is the private key index of participant o; Θ o is the polynomial random perturbation term of participant o; n o is the RSA modulus of participant o; m is the integer subscript index; M is the expansion upper limit, represents the floor function; σ o Digital signatures for participants.

6. The blockchain-based car rental transaction and trust management system as claimed in claim 5, characterized in that: When generating a shared key, the identity and key management unit uses the Diffie-Hellman key exchange algorithm to negotiate the key between the car owner and the rental user to generate a shared key; let the car owner vector be a=(a1, a2, ..., a v , ..., a L ): The rental user vector is b = (b1, b2, ..., b v , ..., b L ); L is the dimension of Diffie–Hellman key exchange; both the owner vector and the rental user vector are random vectors; a v is the vth element in the owner vector; b v is the vth element of the rental user vector; the shared key k is generated by the following formula shared : Among them, p o and q o are two large prime numbers of participant o corresponding to the car owner; p u and q u are two large prime numbers of participant u corresponding to the leasing user; v is the integer subscript index; g is the generator.

7. The car rental transaction and trust management system based on blockchain as claimed in claim 6, characterized in that: The digital signature of participant o corresponding to the car owner is σ o , then the transaction data is T = Encode (car_ID, price, τ, σ o ); The transaction data including the digital signature is preprocessed by adding multiple hash perturbation terms, wherein the multiple hash perturbation terms Ψ(T, k shared ) is defined as: Where R is the expansion level of the set multi-hash perturbation term; r is the integer subscript index; || is the connection operator; |T| represents the length of the transaction data; H(·) is the hash function; the following formula is used to perform AES encryption using the shared key to generate the final ciphertext C: in, Indicated by k shared AES encryption algorithm for the key.

8. The blockchain-based car rental transaction and trust management system as claimed in claim 7, characterized in that: Let the hash of the previous block be prev_hash; through multi-round iteration, the digital signature and ciphertext are combined with the hash of the previous block and the perturbation factor generated by the shared key to construct the hash of the new block. In the jth iteration, define the intermediate function F j (s, t): F j (s,t)=SHA256(H j-1 ∥C∥τ∥j∥s∥t); Where j = 1, 2, ..., J; J is the total number of iterations; let the initial intermediate value be H0 = prev_hash, H j- 1 is the middle value of the j-1th iteration; s and t are both integral variables, with values ​​in the interval [0, |T|], and the multiple integral terms I in the perturbation factor of the jth iteration are obtained. j for: Get the single integral term J in the perturbation factor of the jth iteration j for: Among them, SHA256(·) is the standard SHA-256 hash function; the perturbation factor is I j +J j .

9. The blockchain-based car rental transaction and trust management system as claimed in claim 8, characterized in that: The hash of a new block is calculated using the following formula: Among them, H block The hash of the new block.

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