Vehicle Ad Hoc Network (VANET) is a self-organizing multi-hop network. It establishes a traffic network with information sharing through wireless communication between vehicles and road infrastructure and between vehicles. It has the characteristics of openness, high-speed change of topology and so on.

Because of the limited communication radius of the vehicle, the vehicle node not only transmits its own message, but also forwards the message to other vehicle nodes as a wireless router node. In this open self-organizing network, in order to avoid unsafe communication environment, efficient, reliable inter-vehicle authentication scheme with less delay is essential. Therefore, efficient and reliable inter-vehicle authentication scheme is the focus of VANET research.

The IEEE 1609.2 standard [1] addresses security services for applications and management messages in wireless vehicular environment. It suggests the Secure Elliptic Curve Digital Signature Algorithm (ECDSA) [2] signatures should be used for wireless access. ECDSA ensures vehicular authentication and message integrity. However, it also brings huge signature verification overhead.

Due to this, Grover et al. [3] propose an efficient authentication scheme for highly dynamic VANET. They use probabilistic verification approach to reduce packet ratio in the highly dynamic traffic. They implement a complete solution in a realistic VANET scenario, which shows their scheme decreases message loss by an overall average of 68% compared to ECDSA.

To change the one by one verification way between vehicles, Lee [4] propose a batch authentication scheme for VANETs. They use a bilinear pairing to verify the vehicles’ identities. At the same time, it can resist replay attacks and achieve non-repudiation effect. However, Bayat et al. [5] find the above scheme is vulnerable to the impersonation attack. That is to say, a malicious vehicle node can create a valid signature faking the identities of other vehicles. Therefore, they adopt a discrete logarithm problem to make malicious vehicles cannot compute the secret values of other vehicles. However, neither of the two Scheme’s computational speed is fast enough to adapt to the real high-speed traffic environment.

Considering the requirement of quick verification when vehicles meet, Liu et al. [6] propose a proxy-based authentication scheme to assist roadside units in verifying a large number of vehicles simultaneously. They also present a novel key negotiation scheme for the transmitting of sensitive messages. Using such an authentication scheme, every RSU can verify more than 26000 signatures per second simultaneously with the assistance of some proxy vehicles.

To ensure certification service availability under the high dynamicity of VANETs, Oulhaci et al. [7] propose a distributed and secure certification system architecture for vehicular authentication. They use the concept of delegation and threshold cryptography to build collaborative-based certification approach in order to resist against compromised RSUs.

While some researchers focus on vehicle authentication, others begin to pay attention to vehicle privacy. For the driver, the identity and location information of the vehicle impacts his privacy rights and he does not want it to be disclosed.

Song et al. [8] address the advances in mobile networks and positioning technologies make vehicular location information leaked. Then, some adversaries will launch unauthorized tracking to a valid vehicle in VANET. They propose a vehicle density-based location privacy (DLP) scheme providing location privacy by utilizing the neighboring vehicle density as a threshold to change the pseudonyms. The proposed DLP scheme has a lower probability of successful tracking by an adversary than conventional schemes.

In addition to location privacy, identity privacy is also important. Hwang et al. [9] use Identity-Based Encryption (IBE) to design a secure message-broadcasting method in VANET, which can protect vehicular privacy and trail. Their proposal has some functionality such as integrity, authentication, non-repudiation, confidentiality, forward secrecy, anonymity, untraceability. It is more able to meet the needs of VANET communication.

However, a large number of malicious attacks are accompanied by the development of privacy preserving.

As presented in Bouali et al. paper [10], it regards that there are a large number of malicious users in existing VANET. They divided conventional methods into two categories. One is that the central authority (CA) uses CRL to discover compromised certificates to revoke users’ certificates, and the other is to use intrusion detection methods to discover malicious users. The former approach with high overhead is not practical. The latter is a passive approach and cannot predict malicious behavior. They design a classification method to divide vehicles into three lists, namely black list, gray list, and white list. This classification offers the possibility for the system to predict an attack before it happens by detecting vehicles in the gray list in the routing process.

In many privacy protection schemes, the identity information of vehicles is completely hidden, so it is not practical to use the above anti-malicious attack scheme based on real identity.

Recently, some schemes protecting vehicular privacy in VANET, which focuses on conditional anonymous authentication based on anonymous certificates and signatures. Common techniques used in these schemes include group or ring signature scheme [11,12], ID-based encryption scheme [13–16], blind signature [17] or commitment zero-knowledge proof and so on [18].

Wang et al. [12] point out that most of privacy-preserving authentication schemes depend on central certificate and has the single point failure problem, and then propose a VANET privacy protection scheme without a trusted third party. The proposal satisfies the most of security requirements, such as authentication security, good anonymity, and anti single point attack.

Tzeng et al. [15] regard that the conventional IBV scheme has some security risks and cannot be proved in the random oracle model. Therefore, they propose an identity-based batch verification for VANETs. Using a small constant number of pairing and point multiplication computations, their proposal has lower computation delay and transmission overhead because the verification processing is dependent on the number of messages.

But the above methods cannot resist collusion attack.

Recently, we proposed an anonymous identity authentication scheme, which not only guarantees users’ privacy but also achieves anonymous identity authentication.

In recent years, there are some authors put forward some methods for privacy protection [24–30]. In [24], the authors design a novel anonymous authentication scheme based on edge computing in internet of vehicles. In [25], the authors put forward a location prediction method based on ga-lstm networks and associated movement behavior information. In [26], the authors research on copyright protection method of material genome engineering data based on zero-watermarking. In [27], the authors plan a plc protection system based on verification separation. H. Geng etc. design an efficient routing protection algorithm in large-scale networks [28]. In [29], the authors design a mutual authentication and key agreement protocol for wbans. In [30], X. Jin etc. design a reversible data hiding algorithm based on secret sharing.

As we mentioned above, there are also some weaknesses existing in current studies, such as single point failure, anonymity abuse. So we propose a novel mechanism based on fair blind signature and secret sharing algorithm to improve them [19].

In this section, we use similar BAN logic ideology [23] to briefly demonstrate the validity of the proposed scheme. Although BAN logic has some limitations, it is still a widely used tool for the analysis of security-sensitive schemes and applications.

We transform the process of our protocol to the following idealized form (including plaintext).

Msg 1: V→AC:{IDV,n,{IDV,n}dV,CertV}.

Goal 1: AC|≡V|∼{IDV,n}.

Proof: According to Msg 1, we could get the following statement by applying the Message Meaning Rules of BAN logic: AC|≡↦eVV,AC◃{IDV,n}dVAC|≡V|∼{IDV,n}

Msg2:AC→V:{IDAC,IDV,ts,{IDAC,IDV,ts}dAC}

Initial assumption 2: V|≡#(ts)

Goal 2: V|≡AC|≡{IDAC,IDV,ts}.

Proof: According to assumption 2, we could get the following statement by applying the Freshness Rules of BAN logic: (1)V|≡#(ts)V|≡#{IDAC,IDV,ts}

Then, we could get the following statement by applying the Nonce Verification Rules to (1): (2)V|≡#{IDAC,IDV,ts},V|≡AC|∼{IDAC,IDV,ts}V|≡AC|≡{IDAC,IDV,ts}

Finally, we could get the following statement by applying the Jurisdiction Rule to (2): V|≡AC|⇒{IDAC,IDV,ts},V|≡AC|≡{IDAC,IDV,ts}V|≡{IDAC,IDV,ts}

Msg 3: V→AC:BieACAi.

Goal 3: AC◃Bi.

Proof: According to Msg 3, we could get the following statement by applying the Seeing Rules of BAN logic: AC|≡↦eACAC,AC◃{Bi}eACAC◃Bi

Msg 4: AC→V:{{{Bi}eACAi∙(i,IDV,ts)}dAC,{{i,IDV,ts}eTC}dAC}

Goal 4-1: AC|≡V|∼{{Bi}eACAi∙(i,IDV,ts)}

Goal 4-2: AC|≡V|∼{i,IDV,ts}eTC

Proof: According to Msg 4, we could get the following statement by applying the Seeing Rules of BAN logic: (3)V◃{{{Bi}eACAi∙(i,IDV,ts)}dAC,{{i,IDV,ts}eTC}dAC}V◃{{Bi}eACAi∙(i,IDV,ts)}dAC

Then, we could get the following statement by applying the Message Meaning Rules to (3):

V|≡↦eAVAC,V◃{{Bi}eACAi∙(i,IDV,ts)}dACV|≡AC|∼{{Bi}eACAi∙(i,IDV,ts)}dAC Similarly, we could get another goal: AC|≡V|∼{i,IDV,ts}eTC

Msg 5: V→PAC:{IDAC,{ IDPVi,Ei,1,Ei,2,ePVi,NPVi,SPVi} }ePAC

Goal 5: PAC◃{IDAC,{ IDPVi,Ei,1,Ei,2,ePVi,NPVi,SPVi} }

Proof: According to Msg 3, we could get the following statement by applying the Seeing Rules of BAN logic: PAC|≡↦ePACPAC,AC◃{IDAC,{ IDPVi,Ei,1,Ei,2,ePVi,NPVi,SPVi} }ePACAC◃{IDAC,{ IDPVi,Ei,1,Ei,2,ePVi,NPVi,SPVi} }

Msg 6: PAC→V:{IDPAC,IDPVi,ts,ePVi,NPVi,SPAC}eV

Goal 6: V◃{IDPAC,IDPVi,ts,ePVi,NPVi,SPAC}.

Proof: According to Msg 3, we could get the following statement by applying the Seeing Rules of BAN logic: V|≡↦eVV,V◃{IDPAC,IDPVi,ts,ePVi,NPVi,SPAC}eVV◃{IDPAC,IDPVi,ts,ePVi,NPVi,SPAC}

It must be noted that the BAN logic is to achieve the trustworthiness of each other. In view of the number of relative entities in this scheme and the limited length of the paper, we only give and prove the local goal of each step in the certificate generation process. However, from these goals, the trustworthiness of each other can be further deduced.

In this paper, we use BAN logic ideology to prove our previous algorithm. Further experiments will be carried out in future work. By security analysis, the scheme has been proved to be available.