TriNymAuth: Triple Pseudonym Authentication Scheme for VANETs Based on Cuckoo Filter and Paillier Homomorphic Encryption
Abstract
:1. Introduction
1.1. Motivation and Contributions
- The idea of using triple pseudonyms is one of the main contributions of this paper.
- HomoNym realizes the correspondence between the vehicle’s real identity and multiple HomoNyms, such as OBU’s . HomoNyms is updated synchronously by the HPP and OBU.
- LocNym implements the correspondence between HomoNym and LocNym, such as OBU’s . LocNym is generated by the OBU and registered with the RSU.
- VirNym implements the correspondence between LocNym and multiple VirNyms, such as OBU’s , and the OBU periodically updates a set of virtual pseudonyms to be used during V2V communication. Each virtual pseudonym becomes invalid when it is used up.
The triple pseudonyms are updated synchronously. There are two update opportunities for triple pseudonyms: (1) update in accordance with the suggested updated cycle in 5GAA [2], and (2) update when OBU drives across RSU regions. - The update of the vehicle’s HomoNyms does not depend on the preloading or online update of TA, which reduces the storage and communication overhead.
- A two-stage HomoNym enrollment protocol is based on the CF. Fresh vehicles joining VANETs must apply to the RSU for HomoNym enrollment, the RSU forwards the enrollment message to the HPP, and the HPP verifies the validity of the vehicle’s HomoNym using an efficient CF query service. The vehicle does not need to sign with the root certificate private key, and the HPP does not need to verify the signature of the vehicle, which reduces the computational overhead. Inside the VANETs, vehicles use LocNyms and local private keys that are regularly updated for identity authentication and do not rely on the HPP, which improves the authentication efficiency. This separation of internal and external identity authentication in VANETs achieves identity privacy protection, unlinkability of HomoNyms, non-repudiation, and message integrity.
- The HomoNym revocation protocol is based on Paillier homomorphic encryption and the CF. In the aspect of identity tracing (revocation), because all the HomoNyms generated in the life cycle of the vehicle are stored in the HPP, the HPP can quickly obtain the malicious vehicle’s true identity based on Paillier homomorphic decryption by using the additive property of homomorphic encryption in the abnormal situation, which realizes the traceability of vehicle identity and reduces the storage overhead. Different from other traditional authentication schemes that distribute Certificate Revocation Lists (CRL) for vehicles, TriNymAuth maintains the CRL in the CF to store revoked HomoNyms and verifies the validity of the HomoNyms by querying the CRL. This reduces the overhead of CRL distribution management.
- The V2V authentication mechanism is based on VirNyms’ exchange and usage. A series of VirNyms are generated and exchanged between vehicles for subsequent communication. The vehicle uses the Elliptic Curve Digital Signature Algorithm (ECDSA) [3] to sign VirNyms to realize identity authentication, which not only reduces the dependence on the RSU and the HPP but also solves the key escrow problem, which is the most common problem in identity-based authentication schemes. It improves the efficiency of authentication while ensuring the privacy protection of vehicle identity, non-repudiation, and message integrity. In addition, TriNymAuth also satisfies the security and privacy requirements of unlinkability, traceability, and avoiding impersonation attacks in VANETs.
1.2. Paper Organization
2. Related Works
2.1. Identity-Based Authentication Scheme
2.2. BF-Based Authentication Scheme
2.3. CF-Based Authentication Scheme
3. Preliminaries
3.1. System Model
- HPP
- RSU
- OBU
3.2. Cuckoo Filter
Algorithm 1 Insert(x) |
Input. Output. true/false 1: 2: 3: for to do 4: calculate hash values 5: acquiring buckets corresponding to hash values from a hash ring 6: if contains an empty entry e then 7: 8: return true 9: end if 10: select a fingerprint e from any bucket 11: 12: 13: end for 14: return false |
Algorithm 2 Query(x) |
Input. Output. true/falsev 1: 2: calculate hash values 3: acquiring buckets corresponding to hash values from a hash ring 4: if and then 5: return true 6: end if 7: return false |
Algorithm 3 Delete (x) |
Input. Output. true/false 1: 2: calculate hash values 3: obtain the bucket 4: if and then. 5: remove f form 6: return true 7: end if 8: return false |
3.3. Paillier Homomorphic Encryption
- PKGA()(1) First, choose two large prime numbers, and , for which gcd() = 1, and calculate .(2) Second, define L(x) = , select , where gcd(L( mod .(3) Third, calculate = (L( mod mod N, and = LCM, where LCM represents the least common multiple.(4) Finally, the public key is , and the private key is .
- Paillier_Enc_PKThe Paillier homomorphic encryption Paillier_Enc_PK is represented in Equation (1). For any plaintext message , a random number is chosen to calculate the ciphertext C.
- Paillier_Dec_SKThe Paillier homomorphic decryption Paillier_Dec_SK is represented in Equation (2). For the ciphertext , the plaintext message is computed as follows:
3.4. Elliptic Curve Digital Signature Algorithm
Algorithm 4 EKGA() |
Input., Output. 1: select a random integer 2: calculate , obtain a solution point Q on the curve 3: return vehicle’s local pseudonym is Q, local private key is d |
Algorithm 5 ECDSA_Sign_SK |
Input., Output. 1: select a random integer or a pseudo-random integer 2: calculate the solution point of the curve , and . If , then skip to step 1 3: calculate 4: calculate , where H is the hash function SHA-256, which produces a 256-bit hash value 5: calculate . If , then skip to step 1 6: return the signature of is |
Algorithm 6 ECDSA_Verify_PK |
Input. Output. accept/reject 1: check whether r and s are integers between 1 and 2: calculate a 256-bit Hash value using hash function SHA-256 3: calculate 4: calculate and 5: calculate solution point 6: if , reject , otherwise compute 7: if and only if , accept |
4. Pseudonym Management Scheme Based on Paillier Homomorphic Encryption and the CF
- HomoNym issuance. The HPP issues the HomoNym of the vehicle and sends it to the vehicle through a secure channel. After that, the vehicle and the HPP update the pseudonym synchronously, and the HPP calls the insert algorithm of the CF to save the HomoNym in the filter.
- Two-stage HomoNym enrollment. The two-stage HomoNym enrollment consists of: HomoNym verification and LocNym advertisement. Firstly, after the fresh vehicle enters the RSU area, it applies for HomoNym enrollment at the RSU. The RSU forwards the HomoNym to the HPP, and the HPP queries the CF to verify the validity of the HomoNym. After that, the RSU broadcasts the LList in the jurisdiction.
- HomoNym revocation. When there is a malicious vehicle, the vehicle sends the reporting message to the RSU, and the RSU verifies and forwards the HomoNym of the reported vehicle to the HPP, and the HPP performs a revocation operation on the malicious vehicle. In addition, the CF update service is used to update the HomoNym status.
- VirNym exchange. Before V2V communication, vehicles generated VList and exchanged it.
- VirNym usage. For V2V communication, vehicles use VirNym to achieve vehicle identity authentication inside VANETs.
4.1. System Initialization
- HPP selects the cryptographic hash function h.
- HPP constructs a multiplicative cyclic group G of prime order l and generates a random public prime z and its public generator . The HPP constructs Paillier homomorphic encryption Paillier_Enc_PK.
- Finally, the HPP publishes the public system parameters, params = .
- HPP Key generation. By using PKGA(), the HPP generates its own public key and private key .
- RSU Key generation. The HPP chooses a random number as the private key of the RSU and computes as the public key of the RSU. Based on the secure channel between the HPP and the RSU, the HPP encrypts and with the symmetric key between them and transmits the ciphertext to the RSU. After receiving it, the RSU decrypts and using .
4.2. Homomorphic Pseudonym Generation and SELF-Update Protocol Based on Paillier Homomorphic Encryption
- Initial information issuance:
- The first random seed of the OBU.The HPP randomly selects the first random seed to the OBU, which is used to update the HomoNym simultaneously between the OBU and the HPP.
- Update cycle. The HPP specifies the update cycle [2] for HomoNyms. When the OBU receives the initial HomoNym issued by the HPP, it will self-update HomoNym strictly according to the update cycle specified by the HPP.
- Initial HomoNym. The HPP employs Paillier homomorphic encryption Paillier_Enc_PK to generate the OBU’s initial HomoNym, along with its own public key and randomized seed . The calculation formula of the initial HomoNym is represented in Equation (5):
- Finally, based on the AES-CCM symmetric encryption algorithm, the HPP encrypts by using the symmetric key , then sends AES_Enc_ sym{} to the OBU through a secure channel. OBU executes AES_Dec_sym{} to decrypt and obtain the initial information issued by the HPP and saves in its own TPD.
- HomoNyms self-updateBased on the update cycle, the vehicles self-update the shared random number and HomoNym synchronously with the HPP, and the calculation formula for the random number and HomoNym is introduced as follows:
4.3. Two-Stage Homomorphic Pseudonym Enrollment Protocol Based on the CF
4.3.1. Homomorphic Pseudonym Verification Protocol Based on the CF
- After entering the jurisdiction of the RSU or updating and , based on the ECIES public key encryption algorithm, OBU uses the of the RSU to encrypt and and sends ECIES_Enc_PK to the RSU. After receiving it, the RSU decrypts ECIES_Dec_SK to obtain and .
- Based on the AES-CCM symmetric encryption algorithm, the RSU encrypts its with the symmetric key and sends the encrypted AES_Enc_sym to the HPP. The HPP uses to decrypt AES_Dec_sym to obtain . Then the HPP calls the CF’s Query() (as shown in Algorithm 2) to query . If found, it proves that the is valid, not “expired” or “revoked”. The HPP returns the verification result to the RSU. The RSU keeps the LocNyma of OBU in and the table of correspondence between and locally. If the cannot be found or is expired or revoked, it will be discarded.
4.3.2. Local Pseudonym Advertisement Protocol
4.4. Homomorphic Pseudonym Revocation Protocol Based on Paillier Homomorphic Encryption and the CF
- When OBU discovers illegal behavior by OBU, OBU uses the of the RSU to encrypt the evidence of violation and the , of OBU and OBU and sends the ECIES_Enc_PK to the RSU.
- The RSU decrypts ECIES_Dec_SK and obtains the report message, then looks up and in the local . If the LocNyms are discovered, the identities of OBU and OBU are established.
- The RSU finds the of the OBU corresponding to in the relation table of HomoNym and LocNym stored locally. The RSU encrypts with the symmetric key and sends AES_Enc_sym to the HPP, which decrypts AES_Dec_sym and obtains using the AES-CCM symmetric encryption algorithm.
- According to the of the reported OBU, the HPP calculates its true identity and all HomoNyms in the revocation period t and calls the CF’s pseudonym state change service to set the status of all HomoNyms in the revocation period to “revoked”.
- According to the additive property of homomorphic encryption, the HPP can obtain the real identity of OBU by using Paillier homomorphic decryption Paillier_Dec_SK, which is represented in Equation (8).
4.5. V2V Authentication Protocol Based on Virtual Pseudonyms Exchange and Usage
4.5.1. V2V Authentication Protocol Based on Virtual Pseudonyms Exchange
- Before the first communication between OBU and OBU, based on the ECDSA digital signature algorithm, by using OBU’s local private key , OBU executes ECDSA_Sign_ (as shown in Algorithm 5), the VirNym hash list of OBU is signed as , and then the signature is sent to OBU.
- After receiving it, OBU uses the of OBU to verify the signature , executes ECDSA_Verify_LocNym (as shown in Algorithm 6) to obtain the VirNym hash list of OBU, and saves it locally.
- Similarly, by using OBU’s local private key , OBU executes ECDSA_Sign_ (as shown in Algorithm 5), the VirNym hash list of OBU is signed as , and then the signature is sent to OBU.
- After receiving it, OBU uses the of OBU to verify the signature , executes ECDSA_Verify_LocNym (as shown in Algorithm 6) to obtain the VirNym hash list of OBU and saves it locally.
4.5.2. V2V Authentication Protocol Based on Virtual Pseudonyms Usage
- Based on the ECDSA algorithm, OBU uses its own local private key to sign , and after ECDSA_Sign_ (as shown in Algorithm 5), sends the signature and message to OBU.
- After receiving them, OBU locally queries to find LocNym that can verify the signature, and then OBU uses the queried that corresponds to to verify the signature , executes ECDSA_Verify_LocNym (as shown in Algorithm 6), and obtains . Since both and are from OBU, it shows that OBU did not carry out an impersonation attack.
- Similarly, based on the ECDSA algorithm, OBU uses its own local private key to sign , and after ECDSA_Sign_ (as shown in Algorithm 5), sends the signature and message to OBU.
- After receiving them, OBU queries locally to find LocNym that can verify the signature, and then OBU uses the queried that corresponds to to verify the signature , executes ECDSA_Verify_LocNym (as shown in Algorithm 6), and obtains . Since both and are from OBU, it shows that OBU did not carry out an impersonation attack. OBU and OBU complete the communication.
5. Security and Privacy Analysis
5.1. Security Analysis
- In the two-stage HomoNym enrollment phase. The adversary OBU generates an invalid HomoNym and sends it to the RSU for HomoNym enrollment. The RSU receives it and forwards it to the HPP. The HPP verifies the HomoNym of OBU. By comparing the HomoNym with the HomoNym stored locally in the HPP, it can be known that the HomoNym used by the OBU is invalid, so as to effectively avoid the possible impersonation attack launched by a fresh vehicle in the two-stage HomoNym enrollment phase.
- In the VirNym exchange phase. The VirNym impersonation attack cannot be carried out in this phase because the OBU is a fresh vehicle and cannot obtain the VirNym of other vehicles. In addition, TriNymAuth can effectively avoid the impersonation attack launched by a fresh vehicle in the VirNym exchange phase because the vehicle generates its own local private key based on the EKGA () algorithm, which cannot be obtained by other vehicles through monitoring.
- In the VirNym usage phase. OBU obtains a series of VirNyms of OBU in the VirNym exchange phase. If OBU wants to pretend to be OBU, in the VirNym usage phase, OBU signs using its own local private key and sends the signature and message to OBU. Following receipt of the signature, OBU searches locally for LocNym that can verify the signature, and then OBU uses the queried to verify the signature and obtain . OBU’s impersonation attack failed because OBU discovered that was not from OBU. So, TriNymAuth can effectively avoid the possible impersonation attack launched by a fresh vehicle joining VANETs during the VirNym usage phase.
- In the VirNym exchange phase. The adversary OBU sends the of OBU to OBU as its own VirNym hash list. However, the adversary OBU cannot obtain the local private key of OBU and can only sign the using its own local private key , so the impersonation of OBU by the adversary OBU cannot be successfully implemented.
- In the VirNym usage phase. The adversary OBU obtains the of OBU in the VirNym exchange phase. In the VirNym usage phase, OBU signs using its own local private key and sends the signature and message to OBU. After receiving them, OBU queries locally to find LocNym that can verify the signature, and then OBU uses the queried to verify the signature and obtain . OBUB’s impersonation attack failed because OBU discovered that is not from OBU. Therefore, TriNymAuth can effectively avoid the possible impersonation attacks launched by vehicles in the VirNym usage phase.
5.2. Privacy Analysis
- Identity privacy protection
- Unlinkability
- Traceability
6. Performance Analysis
6.1. Advantage of the CF
6.1.1. Query Overhead
6.1.2. Insert Overhead
6.1.3. Space Overhead
6.1.4. False Positive Rate
6.2. Enrollment Cost Analysis and Comparison
6.3. Computational Cost Analysis and Comparison
6.4. Communication Cost Analysis and Comparison
6.4.1. VirNym Exchange Communication Cost
6.4.2. Single Beacon Transfer Communication Cost
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Notation | Description |
---|---|
A hash list of HomoNyms of OBU | |
A hash list of VirNyms of OBU | |
A hash list of LocNyms of OBU under the jurisdiction of an RSU | |
The first random seed of OBU | |
The symmetric key between X and Y | |
AES_Enc_sym | Using the symmetric key to encrypt message |
AES_Dec_sym | Using the symmetric key to decrypt ciphertext C |
ECIES_Enc_PK | Using the public key of X to encrypt message |
ECIES_Dec_SK | Using the private key of X to decrypt ciphertext C |
Paillier_Enc_PK | Using the public key to Paillier homomorphic encrypt message |
Paillier_Dec_SK | Using the private key of X to Paillier homomorphic decrypt ciphertext C |
ECDSA_Sign_/SK | Using the local private key of OBU or the manufacturer private key of OBU to sign with ECDSA |
ECDSA_Verify_LocNym/PK | Using the local public key of OBU or the manufacturer public key of OBU to do ECDSA signature verification on |
Security | SPECS [5] | b-SPECS+ [7] | SPACF [13] | VPPCS [6] | TriNymAuth |
---|---|---|---|---|---|
Resistance to impersonation attack | - | ✓ | - | ✓ | ✓ |
Identity privacy protection | ✓ | ✓ | ✓ | ✓ | ✓ |
Traceability | ✓ | ✓ | ✓ | ✓ | ✓ |
Unlinkability | - | - | ✓ | ✓ | ✓ |
CF | Query Time (ns) |
---|---|
CCF | 2934 |
CCF | 1689 |
CF | Insert Time (s) |
---|---|
CCF | 2.5 |
CCF | 11.7 |
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Zhuang, L.; Guo, N.; Chen, Y. TriNymAuth: Triple Pseudonym Authentication Scheme for VANETs Based on Cuckoo Filter and Paillier Homomorphic Encryption. Sensors 2023, 23, 1164. https://doi.org/10.3390/s23031164
Zhuang L, Guo N, Chen Y. TriNymAuth: Triple Pseudonym Authentication Scheme for VANETs Based on Cuckoo Filter and Paillier Homomorphic Encryption. Sensors. 2023; 23(3):1164. https://doi.org/10.3390/s23031164
Chicago/Turabian StyleZhuang, Luyuan, Nan Guo, and Yufan Chen. 2023. "TriNymAuth: Triple Pseudonym Authentication Scheme for VANETs Based on Cuckoo Filter and Paillier Homomorphic Encryption" Sensors 23, no. 3: 1164. https://doi.org/10.3390/s23031164
APA StyleZhuang, L., Guo, N., & Chen, Y. (2023). TriNymAuth: Triple Pseudonym Authentication Scheme for VANETs Based on Cuckoo Filter and Paillier Homomorphic Encryption. Sensors, 23(3), 1164. https://doi.org/10.3390/s23031164