V2C post-quantum authentication and key agreement method based on RLWE

Abstract

The present invention discloses a V2C post-quantum authentication and key negotiation method based on RLWE. During system initialization, a master key, public key, hash function, and related parameters are selected. During the registration phase, the vehicle and cloud server CS register with a registration authority RA. During the login phase, the vehicle and CS log in to the local system. During the authentication and key negotiation phase, the vehicle and CS perform identity authentication and key negotiation through the RA, negotiating a session key for subsequent secure communication without revealing their true identity. During the identity and password update phase, users can directly update their identity and password without going through the RA. The present invention is based on ring fault-tolerant learning RLWE and a hash method design, effectively reducing the computational and communication overhead of the AKA process, resisting attacks by quantum adversaries, and ensuring the confidentiality of the true identity of legitimate vehicles. Furthermore, the "fuzzy verifier + honeyword" technology is used in the AKA process to resist signal leakage and key guessing attacks, ensuring key security.

Description

Technical Field

[0001] The present invention relates to vehicle-to-vehicle (V2C) post-quantum authentication and key negotiation methods based on RLWE. Background Art

[0002] With the rapid development of the Internet of Vehicles (IoV), vehicles can collect road information such as weather, speed, and traffic conditions through sensors, radio frequency identification devices, and onboard recorders. This information is then exchanged with infrastructure via wireless networks, improving the efficiency of the transportation system. A typical IoV architecture consists of vehicles, onboard units (OBUs), roadside units (RSUs), trusted authorities (TAs), and cloud or fog servers. Within this architecture, communication methods such as vehicle-to-vehicle (V2V), vehicle-to-remote (V2R), and vehicle-to-consumer (V2C) are commonly used to ensure timely communication between vehicles and various entities in the transportation system.

[0003] While the development of the Internet of Vehicles (IoV) has brought many benefits, the emergence of malicious entities can compromise secure communications. For example, malicious vehicles could provide false traffic information, leading to serious accidents. Other malicious nodes could leak private vehicle information, causing the IoV system's communication system to collapse. Furthermore, with the development of quantum computers, quantum algorithms can break traditional encryption algorithms (such as those based on discrete logarithms and large integer factorization problems). Therefore, designing a quantum-resistant authentication protocol in existing IoV scenarios to ensure the confidentiality and integrity of identity data is a key issue that needs to be addressed.

[0004] Lattice-based cryptography currently holds a significant position in the post-quantum cryptography field. However, existing lattice-based cryptography schemes often suffer from significant computational and communication overhead, failing to meet the high-efficiency requirements of connected vehicle mobile communications and failing to mitigate key leakage threats caused by signaling functions during key exchange.

[0005] Scholars have proposed many solutions to combat the risk of key leakage, but these solutions still exhibit certain shortcomings. Some identity and smart card-based authentication solutions cannot achieve true two-factor security and cannot resist password guessing attacks. Subsequently, scholars proposed the "fuzzy verifier + honeyword" technology, which has been effectively proven to be widely applicable. Fuzzy verifiers can perform matching verification within a certain tolerance range, improving the success rate of verification and user experience. Honeyword technology generates some forged "honeywords" for real data or accounts. These "honeywords" are very similar to the real data. If an attacker uses the honeyword to operate, the system can immediately detect it and take corresponding measures. Therefore, the "fuzzy verifier + honeyword" technology can effectively resist the threat of password guessing attacks and key leakage. However, with the rapid development of quantum computers, these solutions face new challenges and find it difficult to provide effective post-quantum security guarantees.

[0006] However, the existing "fuzzy verifier + honeyword" approach may face the risk of honeyword cracking. If the honeyword generation rules are simple and lack randomness, attackers may be able to distinguish the honeyword from the real password through analysis. This can avoid the honeyword trap and render the honeyword defense mechanism ineffective. Multi-node systems also pose the risk of insider collusion attacks. If honeyword information or key fuzzy verification data is stored and processed on multiple nodes, some insiders may collude with attackers to leak honeywords or interfere with the fuzzy verification process, bypassing the system's security mechanisms. Furthermore, the addition of the fuzzy verifier + honeyword component to existing technologies may further increase computing resources. Therefore, it is necessary to design an appropriate mechanism to strike a balance between security and performance. Summary of the Invention

[0007] Purpose of the Invention: This invention aims to address the shortcomings of the existing technology by providing a V2C post-quantum authentication and key agreement method based on RLWE. Designed using ring fault-tolerant learning (RLWE) and hashing methods, this method effectively reduces the computational and communication overhead of the AKA process, resists attacks by quantum adversaries, and ensures the confidentiality of the legitimate vehicle's true identity. Furthermore, the invention incorporates a "fuzzy verifier + honeyword" technique in the AKA process to mitigate key leakage attacks, ensuring key security.

[0008] Technical solution: The present invention provides a V2C post-quantum authentication and key agreement method based on RLWE, comprising the following steps:

[0009] Step (1), system initialization, select the master key s and seed σ1 from the random sample ψ, select the pseudo-random generator to generate the public key pk, and then select the corresponding hash function, and the registration authority RA broadcasts the necessary system parameters;

[0010] Step (2), during the registration phase, the cloud server CS and the vehicle register with the registration authority RA, which generates the identity CID of the CS. j and the private key of the cloud server j , and then calculate A j To hide the private key j ;Storage {s j ,h(·),σ1}, RA generates vehicle related parameters {C i ,B i ,h(·),σ1,e} and stored locally in the vehicle;

[0011] Step (3), login phase, cloud server CS j Choose the secret polynomial s c With random number s c , calculate the relevant security parameters and broadcast {R j ,PIDj ,S j ,FS j}For the vehicle, enter the vehicle ID and password and calculate With local B i Verify and log in successfully.

[0012] Step (4), authentication and key negotiation phase, the vehicle checks the timestamp and selects a random polynomial, calculates the security parameters and sends the message to RA, RA verifies the vehicle identity and sends the corresponding message to CS; CS verifies the identity of the vehicle and RA and calculates the session key SK ij The corresponding message is sent to the vehicle, which verifies it and calculates the session key SK based on its content. ij and verify;

[0013] In step (5), the identity and password update phase, the user enters the original personal information. After the vehicle is successfully verified, the user enters the new personal message. The vehicle records the latest data and updates the honeyword list.

[0014] Furthermore, the detailed process of the initialization phase of step (1) is as follows:

[0015] Step (1-1), the registration structure RA selects s ​​from the sample ψ as the primary key; selects e∈ψ, σ1 as the seed; and selects the pseudo-random generator PRGG(·): Then a=G(σ1); pk=a·s+e is the public key;

[0016] Step (1-2), RA selects hash function Denoted as h i (·);

[0017] Where i = 0, 1, 2, 3, l i Indicates the length of the hash function output;

[0018] Steps (1-3), vehicle selection integer 2 4 ≤n0≤2 8 It is used as a fuzzy verifier to resist offline guessing, and sets m0 = 20 as the number of honey words in the honey word list. The vehicle and cloud server maintain a Nonce list and cache the random numbers in the current time window;

[0019] The final registration authority RA broadcasts {q,σ1,pk,h i (·)} as system parameters.

[0020] Furthermore, the specific process of the registration phase in step (2) is as follows:

[0021] Step (2-1), Cloud Server CS jSelect a unique CID j , register information {CID j}Send to RA;

[0022] Step (2-2), RA generates a random number k j , n0 is an integer selected in the initialization phase 2 4 ≤n0≤2 8 ; Calculate s j =h(h(CID j ||s||k j )mod n0), {A j ,h(·),σ1,e} is sent to CS j Honey_List is CS j Maintained honeyword list, store {h(CID j ||s),k j ,Honey_List=Null}; Honey_List=Null is the honey word list. A honey word list is maintained during the CS registration phase to store the honey words when the vehicle logs in;

[0023] Steps (2-3), CS j Upon receiving {A j ,h(·),σ1}, the private key is recovered Avoid sending the private key directly in plain text, CS j Storage j ,h(·),σ1}, complete the cloud server CS j Registration; Steps (2-4), user enters ID and password UID i ,PW i , the vehicle selects a random sequence α i , calculate UPW i =h(UID i ||PW i ), used for subsequent calculation of security parameters; UID i The ID of the vehicle user; PW i The password corresponding to the user ID, UPW i The hashed result of the user's ID and password is used for subsequent calculation of security parameters;

[0024] The vehicle will Send to RA;

[0025] Step (2-5): After receiving the vehicle request message, RA generates a random sequence k i , calculate vehicle V i Private key i =h(IDi ||s||k i ||h(ID i ||s)mod n0), calculate {A i ,h(·),σ1,e} is sent to the registered vehicle, and RA stores {h(ID i ||s),k i , Honey_List = Null} in the ID database T ID middle;

[0026] T ID Store the ID database list for RA; The vehicle's private key is not directly stored locally. i , but with C i The form is stored in the vehicle local security module TTP;

[0027] Steps (2-6), Vehicle V i Calculate the private key and C i Used to protect the private key from being stored in plain text;

[0028] V i Select the fuzzy verifier parameter n0 and calculate B i =h(s i ||ID i ||h(UID i ||PW i )mod n0);2 4 ≤n0≤2 8 ;

[0029] V i In the security module TTP, the tuple {C i ,B i ,h(·),σ1,e}, completing vehicle registration.

[0030] Furthermore, the specific process of the login phase in step (3) is as follows:

[0031] Step (3-1), CS j Randomly sample s from the sample ψ c and s c , select Nonce n j , using seed σ1 to generate polynomial a, timestamp TS j , then the current freshness is FS j =TS j ||n j , then calculate R j =a·sc +e c , Participate in the subsequent calculation of θ, where θ is used for CS j Verify the identity of RA and ensure that the message M2 has not been tampered with by a malicious adversary; CS j Calculate pseudonyms Within the expiration time of TS j , CS j Periodically broadcast {R j , PID j , FS j};

[0032] Here, R j Is the calculation result of the RLWE hard problem, which is used for RA to calculate in the subsequent authentication and key negotiation process Participate in the subsequent calculation of θ, where θ is used for CS j Verify the identity of RA and ensure that the message M2 has not been tampered with by a malicious adversary; B i Is the data stored in TTP during the vehicle registration phase;

[0033] Step (3-2), V i After receiving {R j , PID j , FS j}, input the login credentials UID i , ID i , PW i , calculate Then check Whether it is equal to B stored in the vehicle TTP i ; If they are equal, continue, otherwise check SUM < m0. If SUM < m0, then SUM + 1, Insert it into the honey word list, otherwise terminate. This operation can prevent the threat brought by key mismatch attacks; In this invention, m0 = 20 is set as the maximum capacity of the honey word list, and a counter SUM is maintained to record the number of session terminations between the vehicle and CS, preventing possible key mismatch attacks.

[0034] Furthermore, the specific process of the authentication and key negotiation phase in step (4) is as follows:

[0035] Step (4-1), V i Check the current freshness FS j = TS j ||n j , where is the time when V i receives the CS j message, check the Nonce n jIs this the first time sending? If n already exists in the Nonce list j , then reject the message;

[0036] If the above conditions are met, then select a small polynomial s from the binomial distribution ψ v ,e v ,s′ v ,e′ v ,e′ c , according to the seed σ1, the polynomial a=G(σ1) is generated. In order to ensure the temporary secret s v ,e v ,,s′ v , e′ v Security, computing E i =a·s v +e v ,E′ i =a·s′ v +e′ v , used to participate in subsequent F i Calculation of F i RA is used to verify that the message M1 sent by the vehicle has not been tampered with by the adversary. Calculate c1 = pk·s′ v +e′ c +Encode(v1), μ1=h(v1), μ1 is used to calculate the vehicle's real ID i Important parameters of

[0037] Here, E i and E′ i They are all intermediate quantities used to participate in subsequent vehicle calculations, F i RA is used to verify that the message M1 sent by the vehicle has not been tampered with by the adversary, c1 is used to hide the secret polynomial v1, and μ1 is the RA's calculation of the vehicle's true identity ID i Important parameters of

[0038] To ensure the security of the vehicle's true identity, choose Noncen i , calculate the freshness FS of the current vehicle i =TS i ||n i and Kana Then calculate the hash value F i =h(PID i ||s i ||E i ||E′ i ||FS i ) for RA verification vehicle V i The identity of J i =R j ·s iand A=h(J i ||PID i ||PID j ||FS i ) is used for subsequent identity verification, where J i is the final session key SK ij An important part of

[0039] Finally, the vehicle V i Send a request message M1 to RA through the open channel = {E i ,E′ i ,c1,PID i ,F i ,A,TS i ,FS j};

[0040] Step (4-2): After receiving the request message M1, RA first checks the timestamp TS i Is it satisfied n i Is it the first time to send, calculate the polynomial a=G(σ1) again, if it is satisfied, calculate the check If they are not equal, then F i Insert honeyword list, otherwise check timestamp TS j , Calculate v1 = Decode(c1-E′ i ·s), μ1=h(v1), from V i Pseudonymous PID i Extract calculate

[0041] Next, RA calculates and For CS j Verification, at the same time, RA calculation and ρ = h(A||CID" j ||CID j ||s i ||E′ i ) for V i Verification;

[0042] Finally, RA sends a message M2 = {E″ i ,PID i ,CID″ j ,θ,ρ,FS i} to CS j ;

[0043] Step (4-3), after receiving message M2, CS jFirst check the freshness of the current timestamp FS i , calculate the polynomial a=G(σ1) again, according to E″ i recover Calculate J i =E i ·s c =(a·s i +e i )·s c and A=h(J i ||PID i ||PID j ||FS i ); then CS j verify If verification fails, the CS j Reject message M2, otherwise, CS j Select n ij , calculate the current freshness FS ij =TS ij ||n ij and session key SK ij =h(J i ||PID i ||CID j ||FS ij ) and for vehicles V i Verified message L j =h(SK ij ||CID″ j ||ρ||CID j ||FS ij ); Finally, CS j The message M3 = {L j ,CID″ j ,ρ,FS ij}Send to V i ;

[0044] Step (4-4), vehicle V i After receiving message M3, check the freshness FS ij , according to CID″ j Recover from CS j of Then verify If they are equal, the session key is calculated Finally, verify

[0045] Furthermore, the specific process of the identity and password update phase in step (5) is as follows:

[0046] Step (5-1), user enters original personal information {UID i,ID i ,PW i}, then the vehicle calculates B i =h(s i ||ID i ||h(UID i ||PW i )mod n0), then check If they are equal, the user is asked to enter the information that needs to be updated, otherwise, B i Insert the honeyword list and deny the request;

[0047] Step (5-2), user enters new personal information Vehicle calculation new

[0048]

[0049] Step (5-3), the vehicle successfully updates the user's identity and password At the same time, the vehicle is updated in TTP and Replace B i and C i

[0050] Beneficial Effects: This paper uses the lattice-based RLWE problem to propose a post-quantum authentication and key agreement scheme for V2C. This scheme is resistant to quantum computer attacks and effectively mitigates the threats of offline password guessing and key mismatch attacks. The innovative use of fuzzy verifiers and honeyword technology achieves perfect forward secrecy and anonymity, while also providing some resistance to side-channel attacks and providing more reliable security. This scheme has lower computational and communication overhead, making it suitable for V2C scenarios with high efficiency requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a system model diagram of the present invention;

[0052] Figure 2 This is a flowchart of authentication and key agreement in the embodiment;

[0053] Figure 3 This is a comparison chart of computing overhead in the embodiment;

[0054] Figure 4 2 is a comparison chart of communication overhead in the embodiment. DETAILED DESCRIPTION

[0055] The technical solution of the present invention is described in detail below, but the protection scope of the present invention is not limited to the embodiments.

[0056] like Figure 1 As shown, the present invention involves three participating entities, vehicles, registration agencies RA and cloud servers CS. Each vehicle is equipped with an on-board unit OBU. It is assumed that the storage and computing capabilities of each vehicle are limited. Before communication, it is necessary to register with the RA through a secure channel. In addition, the vehicle is also deployed with a trusted platform module (TPM) for storing encryption keys and performing encryption operations to ensure the security and integrity of the system. RA is a highly secure and trusted entity. Assuming that RA has sufficient computing power and storage space to generate and distribute the parameters required by the system, all vehicles and CS need to register with RA to generate unique long-term session keys to ensure the privacy of the vehicle. RA is controlled by the traffic management department, ensuring reliability and security. RA is the only entity that can track the true identity of the vehicle. CS is an honest and curious entity. CS is responsible for storing security parameters and performing corresponding encryption and decryption operations. CS has powerful computing and storage capabilities. Before communication, CS also needs to register with RA.

[0057] like Figure 2 As shown, the RLWE-based V2C post-quantum authentication and key agreement method of this embodiment includes the following steps:

[0058] Step (1) System initialization: select the master key s and seed σ1 from the random sample ψ, select the pseudo-random generator to generate the public key pk, and then select the corresponding hash function. The registration authority RA broadcasts the corresponding system parameters.

[0059] Step (2), during the registration phase, the cloud server CS and the vehicle register with the registration authority RA, which generates the identity CID of the CS. j and the private key of the cloud server j , and then calculate A j To hide the private key j ;Storage {s j ,h(·),σ 1};

[0060] Step (3), login phase, cloud server CS j Choose the secret polynomial s c With random number s c , calculate the relevant security parameters and broadcast them to the vehicle, the vehicle enters the ID and password and calculates the data With local data B i Verify and log in successfully.

[0061] Step (4), authentication and key negotiation phase, the vehicle checks the timestamp and selects a random polynomial, calculates the security parameters and sends the message to RA, RA verifies the vehicle identity and sends the corresponding message to CS; CS verifies the identity of the vehicle and RA and calculates the session key SK ij The corresponding message is sent to the vehicle, which verifies it and calculates the session key SK based on its content. ij and verify;

[0062] In step (5), the identity and password update phase, the user enters the original personal information. After the vehicle is successfully verified, the user enters the new personal message. The vehicle records the latest data and updates the honeyword list.

[0063] The detailed process of the initialization phase of step (1) of this embodiment is as follows:

[0064] Step (1-1), the registration structure RA selects s ​​from the sample ψ as the primary key; selects e∈ψ, σ1 as the seed; and selects the pseudo-random generator PRGG(·): Then a=G(σ1); pk=a·s+e is the public key;

[0065] Step (1-2), RA selects hash function Denoted as h i (·);

[0066] Where i = 0, 1, 2, 3, l i Indicates the length of the hash function output;

[0067] Steps (1-3), vehicle selection integer 2 4 ≤n0≤2 8 It is used as a fuzzy verifier to resist offline guessing, and sets m0 = 20 as the number of honey words in the honey word list. The vehicle and cloud server maintain a Nonce list and cache the random numbers in the current time window;

[0068] The final registration authority RA broadcasts {q,σ1,pk,h i (·)} as system parameters.

[0069] The specific process of the registration phase in step (2) of this embodiment is as follows:

[0070] Step (2-1), Cloud Server CS j Select a unique CID j , register information {CID j}Send to RA;

[0071] Step (2-2), RA generates a random number k j , n0 is an integer selected in the initialization phase, and 2 4 ≤n0≤28 ; Calculate s j =h(h(CID j ||s||k j )mod n0), {A j ,h(·),σ1,e} is sent to CS j , Honey_List is CS j Maintained honeyword list, store {h(CID j ||s),k j ,Honey_List=Null};

[0072] Steps (2-3), CS j Upon receiving {A j ,h(·),σ1}, the private key is recovered CS j Storage j ,h(·),σ1}, complete the cloud server CS j registration;

[0073] Steps (2-4), user enters ID and password UID i ,PW i , the vehicle selects a random sequence α i , calculate UPW i =h(UID i ||PW i ), used for subsequent calculation of security parameters; here, UID i PW is the ID of the vehicle user; i The password corresponding to the user ID, UPW i The hashed result of the user's ID and password;

[0074] The vehicle will then Send to RA;

[0075] Step (2-5): After receiving the vehicle request message, RA generates a random sequence k i , calculate vehicle V i Private key i =h(ID i ||s||k i ||h(ID i ||s)mod n0), calculate {A i ,h(·),σ1,e} is sent to the registered vehicle, and RA stores {h(ID i ||s),k i , Honey_List = Null} in the ID database T ID middle;

[0076] Steps (2-6), Vehicle V i Calculate the private key and C i Used to protect the private key from being stored in plain text;

[0077] V i Select the fuzzy verifier parameter n0 and calculate B i =h(s i ||ID i ||h(UID i ||PW i )mod n0);2 4 ≤n0≤2 8 ;

[0078] V i In the security module TTP, the tuple {C i ,B i ,h(·),σ1,e}, completing vehicle registration.

[0079] The specific process of the login phase in step (3) of this embodiment is as follows:

[0080] Step (3-1), CS j Randomly sample s from the sample ψ c and s c , select Nonce n j , using seed σ1 to generate polynomial a, timestamp TS j , then the current freshness is FS j =TS j ||n j , then calculate R j =a·s c +e c , Participate in the subsequent calculation of θ, θ is used for CS j Verify the identity of RA and ensure that the message M2 has not been tampered with by a malicious adversary; CS j Calculating pseudonyms In TS j Within the expiration time, CS j Periodic broadcast {R j ,PID j ,FS j};

[0081] Step (3-2), vehicle V i Upon receiving {R j ,PID j ,FS j}, input the login credential UID i , ID i , PW i , calculate Then check whether it is equal to B stored in the vehicle TTP i ; if equal, continue, otherwise check SUM < m0, if SUM < m0, then SUM + 1, Insert it into the honey word list, otherwise terminate.

[0082] The specific process of the authentication and key negotiation phase in step (4) of this embodiment is as follows:

[0083] Step (4-1), V i Check the current freshness FS j = TS j ||n j , where is the time when V i receives the CS j message, check whether the Nonce n j is sent for the first time. If n already exists in the Nonce list j , then reject the message;

[0084] If the above conditions are satisfied, select a small polynomial s from the binomial distribution ψ v , e v , s′ v , e′ v , e′ c , and generate the polynomial a = G(σ1) according to the seed σ1. To ensure the security of the temporary secret s v , e v ,, s′ v , e′ v i calculate E= a·s v + e v , E′ i = a·s′ v + e′ v , for participating in the subsequent calculation of F i , F i is used by RA to verify that the message M1 sent by the vehicle has not been tampered with by the adversary, calculate c1 = pk·s′ v + e′ c + Encode(v1), μ1 = h(v1), μ1 is an important parameter for calculating the true identity ID of the vehicle i ;

[0085] Select Nonce n i, calculate the freshness FS of the current vehicle i =TS i ||n i and Kana Then calculate the hash value F i =h(PID i ||s i ||E i ||E′ i ||FS i ) for RA verification vehicle V i The identity of J i =R j ·s i and a=h(J i ||PID i ||PID j ||FS i ) is used for subsequent identity verification, where J i is the final session key SK ij An important part of

[0086] Finally, the vehicle V i Send a request message M1 to RA via the open channel = {E i ,E′ i ,c1,PID i ,F i ,A,TS i ,FS j};

[0087] Step (4-2): After receiving the request message M1, RA first checks the timestamp TS i Is it satisfied n i Is it the first time to send, calculate the polynomial a=G(σ1) again, if it is satisfied, calculate the check If they are not equal, then D i Insert honeyword list, otherwise check timestamp Calculate v1 = Decode(c1-E′ i ·s), μ1=h(v1), from V i Pseudonymous PID i Extract calculate

[0088] Next, RA calculates and For CS j Verification, at the same time, RA calculation and ρ = h(A||CID" j ||CIDj ||s i ||E′ i ) for V i Verification;

[0089] Finally, RA sends a message M2 = {E″ i ,PID i ,CID″ j ,θ,ρ,FS i} to CS j ;

[0090] Step (4-3), after receiving message M2, CS j First check the freshness of the current timestamp FS i , calculate the polynomial a=G(σ1) again, according to E″ i recover Calculate J i =E i ·s c =(a·s i +e i )·s c and A=h(J i ||PID i ||PID j ||FS i ); then CS j verify If verification fails, the CS j Reject message M2, otherwise, CS j Select n ij , calculate the current freshness FS ij =TS ij ||n ij and session key SK ij =h(J i ||PID i ||CID j ||FS ij ) and for vehicles V i Verified message L j =h(SK ij ||CID″ j ||ρ||CID j ||FS ij ); Finally, cS j The message M3 = {L j ,CID″ j ,ρ,FS ij}Send to V i ;

[0091] Step (4-4), vehicle V iAfter receiving message M3, check the freshness FS ij , according to CID″ j Recover from CS j of Then verify If they are equal, the session key is calculated Finally, verify

[0092] The specific process of identity and password update in step (5) of this embodiment is as follows:

[0093] Step (5-1), user enters original personal information {UID i ,ID i ,PW i}, then the vehicle calculates B i =h(s i ||ID i ||h(UID i ||PW i )mod n0), then check If they are equal, the user is asked to enter the information that needs to be updated, otherwise, B i Insert the honeyword list and deny the request;

[0094] Step (5-2), user enters new personal information Vehicle calculation new

[0095]

[0096] Step (5-3), the vehicle successfully updates the user's identity and password At the same time, the vehicle is updated in TTP and Replace B i and C i .

[0097] This example uses the widely accepted cryptographic library NTL to measure the execution time of primitives on the following platform: "CPU Architecture: 64-bit, Processor: Intel(R) Core(TM) i7-12700 @ 2.10 GHz, Memory: 32 GB, Operating System: Windows 11 Professional." The NTL library is a high-performance, portable, and flexible C++ library for performing number theory operations, particularly those involving multiple-precision arithmetic and polynomial arithmetic. We executed these operations 5000 times to obtain the average time. The results are shown in Table 1.

[0098] Table 1

[0099] Cryptographic operations Overhead (milliseconds) Hash operation AHA3-256 0.0019 <![CDATA[Hash operation {0, 1} * →{0, 1} l > 0.0002 <![CDATA[Hash operation {0, 1} l →R q > 0.0025 <![CDATA[Hash operation R q →χ γ > 0.0070 <![CDATA[R q Execution time of the above two polynomial multiplications (n=512,q=12289) 3.5418 <![CDATA[R q Execution time for adding the above two polynomials (n=512,q=12289) 0.0852 <![CDATA[R q Execution time for multiplying the above two polynomials (n=512,q=7557773) 4.8863 <![CDATA[R q Execution time for adding the above two polynomials (n=512,q=7557773) 0.0861 <![CDATA[R q Execution time of the above two polynomial multiplications (n=512,q=1073479709) 5.0578 <![CDATA[R q Execution time for adding the above two polynomials (n=512,q=1073479709) 0.0945 <![CDATA[R q Execution time of the Cha(*) function in 0.0343 <![CDATA[R q Execution time of Mod2(*) function in 0.0650 Signature function Sgnl execution time 0.0008

[0100] The actual application calculation cost of the technical solution of the present invention is compared with the calculation cost of other solutions. The results are as follows: Figure 3 As shown, the present invention has obvious advantages in terms of both the vehicle user end, the cloud server end and the total computational overhead. The actual application communication overhead of the technical solution of the present invention is compared with the communication overhead of other solutions. Figure 4 As shown, the total communication overhead of the technical solution of the present invention is the lowest.

[0101] In summary, the present invention solves two major defects of the existing technology: first, it does not consider the threat of quantum computers to existing public key encryption schemes; second, the computing and communication overheads are high, which cannot meet the needs of low-latency sensitive devices in the Internet of Vehicles environment.

Claims

1. A V2C post-quantum authentication and key agreement method based on RLWE, characterized in that: The following steps are involved: Step (1), system initialization, from random samples Select the master key and seeds , select a pseudo-random generator to generate a public key Then the corresponding hash function is selected and the registration authority RA broadcasts the corresponding system parameters; Step (2), during the registration phase, the cloud server CS and the vehicle register with the registration authority RA, which generates the identity of the CS. and the private key of the cloud server , and then calculate To hide the private key ;storage{ }; Step (3), login phase, cloud server Choosing a secret polynomial With random numbers , calculate the relevant security parameters and broadcast them to the vehicle, the vehicle enters the ID and password and calculates the data With local data Verify and log in successfully. Step (4), authentication and key negotiation phase, the vehicle checks the timestamp and selects a random polynomial, calculates the security parameters and sends the message to RA, RA verifies the identity of the vehicle and sends the corresponding message to CS; CS verifies the identity of the vehicle and RA and calculates the session key The corresponding message is sent to the vehicle, which verifies it and calculates the session key based on its content. And verify, the specific method is: Step (4-1), Check current freshness , ,in yes Received Time of the message, check Nonce Is this the first time sending? If the Nonce list already exists , then reject the message; If the above conditions are met, then from the binomial distribution Select a small polynomial , , , according to the seed Generator polynomial ), ,calculate , for participation in subsequent Calculation, RA is used to verify the message sent by the vehicle Not tampered by the adversary, calculation , , It is used to calculate the real identity of the vehicle Important parameters of Select Nonce Calculate the freshness of the current vehicle and Kana , then calculate the hash value For RA verification vehicles identity, calculation and For subsequent identity verification, is the final session key An important part of Finally, the vehicle Send a request message to RA via an open channel { }; Step (4-2): RA receives the request message After that, first check the timestamp Is it satisfied , Is this the first time sending? Calculate the polynomial again. ), if satisfied, then calculate the test Is it established? If not, then Insert honeyword list, otherwise check timestamp , ,calculate = Decode( ), ,from pseudonym Extract ,calculate ; Next, RA calculates )and Used for Verification, at the same time, RA calculation and Used for Verification; Finally, RA sends the message to ; Step (4-3), receiving the message back, First check the freshness of the current timestamp , and calculate the polynomial again ),according to recover ; calculate = and ;Then verify Is it true? If not, then Reject Message ,otherwise, choose , calculate the current freshness and session key and for vehicles Verified message ;at last, The message Send to ; Step (4-4), Vehicle Received the message Afterwards, check for freshness ,according to Restore of , then verify the equation Is it true? If they are equal, calculate the session key Finally, verify ; In step (5), the identity and password update phase, the user enters the original personal information. After the vehicle is successfully verified, the user enters the new personal message. The vehicle records the latest data and updates the honeyword list.

2. The RLWE-based V2C post-quantum authentication and key agreement method according to claim 1, characterized in that: The detailed process of the initialization phase of step (1) is as follows: Step (1-1), register structure RA from sample Select is the master key; select , For the seed; select the pseudo-random generator PRG ,but ) ; is the public key; Step (1-2), RA selects hash function Recorded as (·); in , Indicates the length of the hash function output; Steps (1-3), vehicle selection integer Used as a fuzzy verifier to resist offline guessing, and set For the number of honey words in the honey word list, the vehicle and cloud server maintain a Nonce list and cache the random numbers in the current time window; The final registration authority RA broadcasts { } as system parameters.

3. The RLWE-based V2C post-quantum authentication and key agreement method according to claim 1, characterized in that: The specific process of the registration phase in step (2) is as follows: Step (2-1), cloud server Choose a unique identity , register information { }Send to RA; Step (2-2), RA generates a random number , is an integer selected during the initialization phase, and ;calculate mod ), ,Will{ }Send to , for Maintained honeyword list, storage { , , }; Steps (2-3), Upon receiving { }, recover the private key , storage{ }, complete the cloud server registration; Steps (2-4), user enters ID and password , the vehicle selects a random sequence ,calculate = ), used for the subsequent calculation of safety parameters; here, The ID of the vehicle user; is the password corresponding to the user ID, The hashed result of the user's ID and password; The vehicle will then { }Send to RA; Steps (2-5): After receiving the vehicle request message, RA generates a random sequence , calculate vehicle Private key ,calculate ,Will{ }Sent to registered vehicle, RA stores { }In the ID database middle; Steps (2-6), Vehicle Calculate the private key and , Used to protect the private key from being stored in plain text; Select the fuzzy validator parameters ,calculate ; ; In the security module TTP, the tuple { }, complete the vehicle registration.

4. The RLWE-based V2C post-quantum authentication and key agreement method according to claim 1, characterized in that: The specific process of the login phase in step (3) is as follows: Step (3-1), From the sample Random sampling and , select Nonce , using seeds Generator polynomial , timestamp , then the current freshness is = , then calculate , , participate in the follow-up Calculation, The identity of the RA and the assurance of the message Has not been tampered with by malicious adversaries; Calculating pseudonyms ;exist Within the expiration period, Periodic broadcast { }; Step (3-2), Vehicle Upon receiving { }, enter the login credentials ,calculate h ( , = , then check Is it equal to the one stored in the vehicle TTP? ; If equal, continue, otherwise check if SUM < , if SUM < , then SUM +1, Insert into the honeyword list, otherwise terminate.

5. The RLWE-based V2C post-quantum authentication and key agreement method according to claim 1, characterized in that: The specific process of the identity and password update phase in step (5) is as follows: Step (5-1), user enters original personal information { }, then the vehicle calculates , , then check the equation If they are equal, the user is required to enter the information that needs to be updated. Otherwise, Insert a list of honey words and deny the request; Step (5-2), user enters new personal information { , the vehicle calculates the new , ; Step (5-3), the vehicle successfully updates the user's identity and password , at the same time, the vehicle is updated in TTP and replace and .

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