Let G 1 and G 2 be an addition cyclic group and a multiplication with the same prime order q. Let g be the generator of group G 1 . Let e : G 1 × G 1 → G 2 denote a bilinear map which has following properties [26].

Bilinear: For all a , b ∈ Z q * , e ( g a , g b ) = e ( g , g ) a b .

Non-degeneracy: e ( g , g ) ≠ 1 .

Computability: For all g 1 , g 2 ∈ G 1 , there is an effective algorithm for calculation e ( g 1 , g 2 ) .

The ElGamal encryption algorithm is a multiplicative homomorphic encryption algorithm. The process of the ElGamal encryption algorithm is as follows [27].

Key generation: Randomly select a large prime number q and a random number s ∈ Z q * . And calculate o = g s mod q . Then the public key is ( o , g , q ) and private key is s.

Encryption: Select a random number r that is relatively prime with q − 1 . And calculate the ciphertext of message M as

C = E ( M ) = ( c 1 , c 2 ) = ( g r mod q , s r M mod ( q − 1 ) ) (1)

Decryption: Decrypt the ciphertext C as

M = D ( C ) = c 2 / c 1 s ( mod q ) = d ( c 1 s ) − 1 mod q (2)

Bloom filter (BF) [28] is a probabilistic data structure that checks set membership and effectively saves space. The false negative rate of the Bloom filter is 0, but the Bloom filter has a certain false positive rate due to the collision rate of the hash function, the false positive rate p is calculated as [28]

p = ( 1 − ( 1 − 1 m ) k ⋅ n ) k ≈ ( 1 − e − k ⋅ n m ) k (3)

where m, k and n are the size of the bloom filter vector, the number of hash functions and the number of elements stored in the Bloom filter, respectively.

Privacy Set Intersection (PSI) [29] can judge whether there is an intersection between the input sets of the two parties without leaking privacy. The execution process of BF-PSI is: two parties A and B whose secret sets are S A = ( a 1 , a 2 , ⋯ , a n ) and S B = ( b 1 , b 2 , ⋯ , b n ) , respectively. A and B choose random value r a and r b , and then use k independent hash functions with the number bits s to represent the set as B F A and B F B . Next, A and B exchange random values and BF. Finally, it determines the intersection of two parties A and B. For example, if A executes P S I ( S A , B F B , r b ) , who uses m e m _ t e s t (   ) to judge whether a i ( i = 1 , 2 , ⋯ , n ) appears in B F B . If it returns a positive result, then a i ∈ B F B , and vice versa. In this way, A and B can learn I A , B = S A ∩ S B without leaking the privacy of the two parties.

The system model of the TPCM scheme proposed in this paper is shown in Figure 1, which includes four entities: Trusted Authority (TA), RSU, vehicle and passenger.

When the TPCM scheme is deployed in the carpooling system, TA assigns public key, private key and reputation certificates to registered entities. Only TA can reveal the true identities of malicious users and punish them when users have malicious behaviors. TA also is responsible for collecting trust feedback and updating the user’s trust information. RSU is responsible for verifying the certificates and information signatures of vehicles and passengers and matching vehicles and passengers in carpooling. Passengers are responsible for sending

encrypted carpooling requests within the communication range of a certain RSU. The vehicles send an encrypted carpooling response after receiving the encrypted carpooling requests.

We assume that the TA is completely trusted, whereas RSU is honest and curious in the threat model of this paper. That is, the RSU honestly performs the steps in carpooling, but it is curious about the carpooling information broadcasted in the carpooling system and the user’s private information. Specifically, RSU may launch passive attacks such as message eavesdropping attacks or privacy digging. Although it does not modify the information, it tries to obtain more private information from carpooling users. Vehicles and passengers may be malicious. They may launch passive attacks to eavesdrop on the private information in carpooling or launch active attacks to disrupt the carpooling network. For example, vehicles or passengers may launch message cheating attacks, and use a false identity to deceive other carpooling entities. And they may launch message modification attacks to modify the carpooling information.

The classification and attributes of travel preferences for the TPCM scheme in this paper are shown in Table 1. Travel preferences are divided into 7 categories, where I 1 ~ I 7 represents the trust value corresponding to travel preferences. The trust value of travel preference I m is T V V i ( I m ) . The vehicle reputation set is composed of trust value, which is used to evaluate the trustworthiness of the vehicle from multi-faceted. Each travel preference has two attributes, x 1 ， 1 ~ x 7 ， 2 represents the 14 attributes corresponding to the 7 travel preferences. The attributes of I 1 ~ I 4 is based on the range of trust values. That is, the attributes of preference I 1 ~ I 4 are converted from continuous variables to characters, where the range of trust values [ ω s , 0.5] is Good and the range (0.5, 1] is Very Good, ω s is the score threshold. The attributes of I 1 ~ I 4 is constantly updated with the changes of the trust value. The attributes of I 5 ~ I 7 is unchanged based on the real information when vehicle registration, and the trust

value reflects the trustworthiness of the corresponding travel preference. One of the attributes of each travel preference constitutes the preference attributes set P A V i of the vehicle V i , which is used to meet the individual needs of passengers.

Given the security parameters 1 τ , TA generates the bilinear parameters ( G 1 , G 2 , e ) , where G 1 , G 2 is the cyclic group with prime order q, g 1 , g 2 is the generator of G 1 and G 2 , respectively. And the bilinear map e : G 1 × G 1 → G 2 . Then TA calculates e ( g 1 , g 2 ) = F . Next, TA generates the master key M S K T = t and calculates P K T = g 1 t to be its public key, where t ∈ Z q * . TA selects two hash function: H 1 : { 0 , 1 } → Z q * , H 2 : { 0 , 1 } × { 0 , 1 } → Z q * , and selects the filter function f, length l, and hash function set H s for the Bloom filter. TA sets the distance threshold φ s and φ d , time threshold ψ t and score threshold ω s . Finally, TA publishes the system parameters Θ = ( τ , G 1 , G 2 , e , q , F , P K T , f , l , H s , φ s , φ d , ψ t , ω s ) .

In order to prevent the vehicle from forging its travel preference attributes, TA will create preference attributes secret value as shown in Table 2, where S v i λ is the secret value corresponding to the preference attribute x i , λ is the time when TA generates all preference attributes secret value. The calculation method of S v i λ is S v i λ = h λ ( x i | | r λ ) , where h λ is the hash function for calculating the secret value and r λ is a random number. Due to the collision rate of the hash function, if the secret value of two different preference attributes is the same, TA recalculates the secret value for all preference attributes until the secret value of all preference attributes is different. In addition, TA regularly updates the preference attributes secret value.

When a passenger P i with the identity R I D P i registers with the carpooling system, TA generates the privacy key S K P i = p and calculates the public key P K P i = g 1 p for passenger P i , where p is a random number and p ∈ Z q * . TA generates the reputation certificate R C e r t P i = g 2 1 / ( H P i + M S K T + S K P i ) , where H P i = H 1 ( R I D P i | | P K P i | | P V P i ) , P V P i is the validity period of the reputation certificate. The anonymous identity of passenger P i is P I D P i = R I D P i ⊕ H 1 ( p | | P K T | | P K R i ) .

When vehicle V i with the identity R I D V i registers with the carpooling system, TA generates the privacy key S K V i = v and calculates the public key P K V i = g 1 v

for vehicle V i , where v is a random number and v ∈ Z q * . TA generates the reputation certificate R C e r t V i = g 2 1 / ( H V i + M S K T + S K V i ) , where H V i = H 1 ( R I D V i | | P K V i | | P V V i ) .The anonymous identity of vehicle V i is P I D V i = R I D V i ⊕ H 1 ( v | | P K T | | P K R i ) . The reputation set of the vehicle V i is R S V i = ( T V V i ( I 1 ) ~ T V V i ( I 7 ) ) , where T V V i ( I 1 ) ~ T V V i ( I 7 ) represents the trust value of the 7 travel preference types of V i , and the reputation set is used to evaluate the trustworthiness of V i from multi-faceted. Since the travel preference I 1 ~ I 4 ’s trust value is initialized to 0.5 and the corresponding attributes are x 1 , 2 , x 2 , 2 , x 3 , 2 , x 4 , 2 , so the initial vehicle preference attribute set is P A V i = ( x 1 , 2 , x 2 , 2 , x 3 , 2 , x 4 , 2 x a , x b , x c ) , where x a , x b and x c are the real information registered by the vehicle V i . P A V i is used to meet the individual travel preferences needs of passengers. TA retrieves the secret value corresponding to the preference attribute from Table 2, and then sends the preference attribute secret value set P A S V i to the vehicle V i , where P A S V i = ( S v 1 , 2 β , S v 2 , 2 β , S v 3 , 2 β , S v 4 , 2 β , S v a β , S v b β , S v c β ) .

When RSU registers with the carpooling system, TA generates the privacy key S K R i = r and calculates the public key P K R i = g 1 r for R i , where r is a random number and r ∈ Z q * .

When a passenger P i wants to carpool, who first chooses individual travel preferences, and then selects preference attributes from the attributes corresponding to the selected travel preferences. It is noted that passengers can only choose one of the two attributes corresponding to each travel preference. We assume that the preference attributes selected by the passenger are x m ~ x n , I m ′ ~ I n ′ are the corresponding travel preferences. Next, the passenger P i requests the secret value corresponding to the selected preference attributes from TA, and TA returns the corresponding secret value S v m α ~ S v n α to the passenger P i . We assume P S P i = ( S v m α ~ S v n α ) , then the passenger P i selects a random number r 1 and injects P S P i into Bloom filter by using B f P i = I n s e r t ( H s ( P S P i | | r 1 ) , B f P i ) . The passenger sets a preference score threshold χ m ∼ n . Finally, passenger P i selects the starting position and destination to form a carpooling request

Q M P i = ( P I D P i , R C e r t P i , B f P i , χ m ∼ n , l o c P i , d e s P i , α , T Q M P i ) (4)

where T Q M P i denotes the timestamp when the carpooling request is generated. And then passenger calculates the signature δ Q M P i = g 2 1 / ( H 2 ( Q M P i | | P K P i | | P K R i ) + S K P i ) . When the passenger is within the communication range of a certain RSU, who uses ElGamal encryption and parameter ( g 1 , P K R i ) to encrypt Q M P i to form a ciphertext

C P i = E ( Q M P i ) = ( c 1 , c 2 ) = ( g 1 w 1 mod q , P K R i w 1 Q M P i mod ( q − 1 ) ) (5)

Eventually passenger P i sends { C P i , R C e r t P i , δ Q M P i } to R i . After the R i receives the information { C P i , R C e r t P i , δ Q M P i } , which uses the decryption algorithm and the private key to decrypt ciphertext C P i to obtain the passenger’s carpooling request information, Q M P i = D ( C P i ) = c 2 ( c 1 S K R i ) − 1 mod q . Then R i obtains the current timestamp from the clock and verifies the freshness of the message by | T 1 − T Q M P i | < ψ t . If it holds, then R i verifies the validity of the passenger’s reputation certificate and information signature by (6) and (7).

e ( g 1 H P i ⋅ P K T ⋅ P K P i , R C e r t P i ) = F (6)

e ( g 1 H 2 ( Q M P i | | P K P i | | P K R i ) ⋅ P K P i , δ Q M P i ) = F (7)

when all verifications are passed, R i will broadcast M s g R i to the nearby vehicles, where T M s g R i is the timestamp when M s g R i is generated.

M s g R i = ( P I D P i , B f P i , l o c P i , d e s P i , α , T M s g R i ) (8)

When the vehicle V i is within the communication range of R i , who first obtains the current timestamp from the clock after receiving the information M s g R i , and then checks the freshness of the message by | T 2 − T M s g R i | < ψ t . If it holds, we assume the preference attribute secret value set of the vehicle V i is P A S V i = ( S v p β ~ S v q β ) . In order to ensure the time consistency of the preference attribute secret value of the vehicle V i and the passenger P i , the vehicle first checks whether α is equal to β that in P A S V i . If it holds, the vehicle selects a random number r 2 and inserts P A S V i into the Bloom filter by using B f V i = I n s e r t ( H s ( P A S V i | | r 2 ) , B f V i ) ; Otherwise, the vehicle requests to update secret value in P A S V i from TA, and then injects the updated P A S V i into the Bloom filter. Finally, vehicle sets the maximum number of carpooling to form a carpooling response

S M V i = ( P I D V i , R S V i , R C e r t V i , B f V i , l o c V i , d e s V i , C N max , T S M V i ) (9)

where l o c V i , d e s V i denotes the starting point and destination of vehicle, respectively, and T S M V i denotes the timestamps when the carpooling responding is generated. The vehicle calculates the signature δ S M V i = g 2 1 / ( H 2 ( S M V i | | P K V i | | P K R i ) + S K V i ) . Then vehicle V i adopts ElGamal encryption and uses the parameter ( g 1 , P K R i ) to encrypt the carpooling response of the vehicle to form ciphertext

C V i = E ( S M V i ) = ( c 3 , c 4 ) = ( g 1 w 2 mod q , P K R i w 2 S M V i mod ( q − 1 ) ) (10)

Eventually vehicle V i sends { C V i , R C e r t V i , δ S M V i } to R i .

After receiving the information { C V i , R C e r t V i , δ S M V i } , R i first uses the decryption algorithm and private key to decrypt the vehicle’s carpooling response ciphertext C V i to obtain S M V i = D ( C V i ) = c 4 ( c 3 S K R i ) − 1 mod q . Then it checks the freshness of carpooling response information by | T 3 − T S M V i | < ψ t . If it holds, R i verifies the validity of V i ’s reputation certificate and information signature by (11) and (12).

e ( g 1 H V i ⋅ P K T ⋅ P K V i , R C e r t V i ) = F (11)

e ( g 1 H 2 ( S M V i | | P K V i | | P K R i ) ⋅ P K V i , δ S M V i ) = F (12)

After above verifications are passed, R i verifies (13) to match the starting position and destination of the vehicle and passengers. Then it checks whether all the T V V i ( I 1 ) ~ T V V i ( I 7 ) in R S V i is greater than χ m ~ n . In other words, it is to check whether the trust value corresponding to V i ’s travel preference categories selected by the passenger meets the passenger’s multi-faceted trust needs.

( | l o c P i − l o c V i | < φ s ) ∧ ( | d e s P i − d e s V i | < φ d ) (13)

Finally, R i uses BF-PSI to determine whether there is an intersection I n P i , V i between V i ’s preference attribute secret value set P A S V i and the set P S P i selected by P i . If I n P i , V i and P S P i are the same, V i fulfills all individual carpooling needs of passenger P i . Then the vehicle and passengers are successfully matched and the message M P i , V i is sent to the vehicle and passengers.

M P i , V i = ( P I D P i , P I D V i , S P i , V i , T M P i , V i ) (14)

where S P i , V i is the communication key between the vehicle and the passenger, and T M P i , V i is the timestamp of the successful carpooling matching. In order to understand the process of carpooling matching in our TPCM scheme, Algorithm 1 describes the carpooling matching scheme based on BF-PSI in Table 3.

When the passenger P i arrives at the destination, who will calculate the feedback score F s P i → V i ( I m ′ ) ~ F s P i → V i ( I n ′ ) for the selected preference attribute ( x m ~ x n ) corresponds to the travel preferences ( I m ′ ~ I n ′ ) based on the actual experience in the carpooling journal. For ∀ I i ∈ ( I m ′ ~ I n ′ ) , the corresponding feedback score is F s P i → V i ( I i ) ∈ { 0 , 1 } , where 1 represents positive feedback and 0 represents negative feedback. Passenger P i calculates feedback scores for all selected travel preferences by using above method and generates a travel preference feedback set F s P i → V i = ( F s P i → V i ( I m ′ ) , ⋯ , F s P i → V i ( I n ′ ) ) , which forms the passenger P i ’s trust feedback tuple T f P i → V i = ( P I D P i , F s P i → V i , P I D V i , M P i , V i ) for the vehicle V i .

Since there is more than one carpooling passenger, multiple trust feedback tuples about the vehicle V i will be generated. These trust feedback tuples are aggregated by the RSU and sent to the TA in a safe manner. After the TA receives them, who first classifies and integrates this information into multiple preference feedback information sets about the vehicle based on the type of travel preference, for example

P F M V i ( I m ′ ) = ( P I D P i , F s P i → V i ( I m ′ ) , ⋯ , P I D P n , F s P n → V i ( I m ′ ) , P I D V i ) (15)

TA updates the trust value of the travel preferences type selected by passengers

in the reputation set R S V i of vehicle V i based on ( P F M V i ( I m ′ ) ~ P F M V i ( I n ′ ) ) , the updating method is as follows:

T V V i ( I i ) t + 1 = { ∑ P I D P i ∈ P F M V i ( I i ) F s P i → V i ( I i ) ⋅ R s P i t ∑ P I D P i ∈ P F M V i ( I i ) R s P i t ,   if     ∑ P I D P i ∈ P F M V i ( I i ) R s P i t > ω s ξ ⋅ T V V i ( I i ) t ,   otherwise (16)

where R s P i is the reputation score of passengers P i , ξ is a decay factor. If a vehicle does not carpool for a long time, the trust value corresponding to its travel preference will decay over time.

Then TA updates the attributes of the first four items in the vehicle V i ’s preference attribute set based on the updated trust value. Finally, TA sends the updated R S V i and P A S V i to the vehicle. In order to evaluate the overall trustworthiness of the vehicle, we use the weighted average method to calculate the average reputation score of the vehicle, the calculation method is as follows:

R s V i t + 1 = w s M ∑ ( T V V i ( I m ′ ) t + 1 + ⋯ + T V V i ( I n ′ ) t + 1 ) + w t N ∑ ( T V V i ( I p ′ ) t + ⋯ + T V V i ( I q ′ ) t ) (17)

where I m ′ ~ I n ′ is the travel preferences of vehicle V i corresponding to the preference attributes selected by passenger P i , the number is M, corresponding to the updated trust value is T V V i ( I m ′ ) t + 1 ~ T V V i ( I n ′ ) t + 1 , and the total weight is w s ; I p ′ ~ I q ′ is the travel preferences of vehicle V i not selected by the passenger,

the number is N, corresponding to the historical trust value is T V V i ( I p ′ ) t ~ T V V i ( I q ′ ) t , the total weight is w t , where w t = 1 − w s .

For the TPCM scheme, the TA assigns a pseudonym P I D V i to the vehicle when the vehicle is registered, and the vehicle uses the pseudonym identity to broadcast the carpooling information. Since the number v in P I D V i is a random number, which is kept secretly by the TA. Therefore, the adversary cannot reveal the identity of the vehicle from the pseudonym P I D V i to obtain private data. Only the TA can reveal the identity of the vehicle by using R I D V i = P I D V i ⊕ H 1 ( v | | P K T | | P K R i ) and punish the malicious vehicle. Therefore, the TPCM scheme not only protects the user’s identity privacy, but also tracks the real identity of malicious users and realizes the conditional privacy protection of users’ identities.

When the carpooling information is generated, this paper uses ElGamal encryption algorithm to encrypt it. That is, the vehicles or passengers use the public key of the RSU to encrypt the carpooling information, and the RSU decrypts the encrypted carpooling information by using its private key to verify the identity of the vehicles or passengers. Since a random number needs to be selected when the ElGamal encryption algorithm is used to encrypt a carpooling message and the private key of the RSU is used to decrypt the message. The private key of the RSU is a random number and is kept secretly by the RSU. The adversary cannot initiate an attack to get the plaintext information after the carpooling information is encrypted. Therefore, the TPCM scheme protects the privacy of carpooling data. In addition, the encrypted ciphertext of the same carpooling message is also different within the communication range of different RSUs by using the ElGamal encryption algorithm. Moreover, the carpooling matching method in this paper introduces travel preferences, which uses BF-PSI technology to match passengers and vehicles to meet the individual needs of passengers. The carpooling matching method by using the BF-PSI not only protects the preference privacy of vehicles and passengers, but also prevents mismatch between vehicles and passengers caused by ignoring the passenger’s individual needs.

The attackers may modify the carpooling message by launching a message modification attack to disrupt the carpooling network. However, for the TPCM scheme in this paper, the passenger P i will calculate a signature δ Q M P i for the carpooling request Q M P i when he issues it. After the RSU within the communication range of P i receives Q M P i , which uses Equation (7) to verify the validity of the passenger’s carpooling request signature. If it holds, then the carpooling request Q M P i has not been modified. Otherwise, the carpooling message will be discarded. Therefore, the TPCM scheme can resist the message modification attack.

Passengers or vehicles may initiate message cheating attacks and use false certificates to deceive each other. However, for the TPCM scheme in this paper, the reputation certificate of carpooling users has a validity period. When the reputation certificate expires, the TA will issue a new reputation certificate to the user. Although the internal attacker has a reputation certificate issued by the TA, the malicious user cannot repeatedly initiate a reputation certificate request to cover up his malicious behavior before the certificate expires. TA can reveal the identity of the internal attacker, who will reduce the trust value of a certain travel preference when the vehicle has malicious behavior. And TA will revoke the malicious vehicle when a certain trust value is lower than the score threshold. If an external attacker uses a fake reputation certificate to broadcast carpooling messages, who cannot pass the reputation certificate verification from RSU. Therefore, for the TPCM scheme in this paper, the reputation certificate with validity period can not only resist message cheating attacks and ensure the legitimacy of the carpooling user identity, but also avoid the communication delay of requesting the certificate every time for carpooling.

The computational cost of TPCM scheme mainly comes from ElGamal encryption and signature verification. We let T m be the time to perform the maptopoint function operation, T e be the time to perform the exponentiation operation, T b be the time to perform bilinear pairing, and T u be the time to perform multiplication. In the Intel i3-4170 3.7 GHz processor, 8 GB RAM and Windows 10 platform, the times of these operations are: T m = 3 . 7   ms , T e = 3 . 9   ms , T b = 4.5   ms , T u = 0.6   ms [30].

In order to compare the TPCM scheme with the FICA scheme [13] and SRSCB scheme [31], this paper considers the computation overhead of three stages of passenger carpooling request, information verification and vehicle carpooling response in Table 4. We let PCRG be the carpooling request generation stage,

RMV be the information verification stage, and VCRG be the carpooling response generation stage.

The computation cost comparison of different carpooling schemes is shown in Table 4. In the FICA scheme, the time consumption of passenger carpooling request generation, RSU information verification, and carpooling response is 55.1 ms, 66.8 ms, and 55.1 ms, respectively. In the SRSCB scheme (assuming the number of attributes is 1), the time consumption for the passenger generates an encrypted carpooling request, RSU information verification, and driver generates a carpooling response is 59.5 ms, 34.2 ms, and 20.3 ms, respectively. For the TPCM scheme, the time consumption of carpooling request generation, RSU information verification and carpooling response is 16 ms, 29.9 ms, and 16 ms, respectively.

Figure 2 and Figure 3 show the computation cost of different carpooling schemes as the number of passengers and vehicles changes. We can see that the computation cost gradually increases as the number of passengers and vehicles increases, but the computation cost of our TPCM scheme increases more slowly compared with other schemes and is lower than the computation cost of other schemes.

We assume the pseudonym and key length are 16 bytes, the hash value length is 4 bytes, and the signature and homomorphic ciphertext length are 67 bytes and 512 bytes, respectively [30]. For our TPCM scheme, the length of passenger’s carpooling information ciphertext is 595 bytes totally. The message length in the carpooling response and RSU verification phases is 595 bytes and 16 bytes, respectively. Comparing the communication overhead of our TPCM scheme with the FICA scheme [13] and PRIS scheme [32], Figure 4 and Figure 5 show the communication overhead of different carpooling schemes as the number of passengers and vehicles change. We can see that when the number of changes of passengers and vehicles from 100 to 1000, the communication overhead of our TPCM scheme is lower than other schemes regardless of whether the number of changes of passengers or vehicles. And it has a smaller growth rate compared with other schemes.

We propose a carpooling matching method that introduces travel preferences,

which uses the BF-PSI technology to match the vehicle’s preference attribute secret value set with the preference secret value set selected by the passenger. Figure 6 shows the change process of the probability that the carpooling is successfully matched n times with the size of the Bloom filter. We can see that with the increase of the size of the Bloom filter, the single matching success rate of our TPCM scheme is close to 100%, and the probability of multiple matching is almost 0. Therefore, the proposed carpooling matching scheme based on BF-PSI not only has high matching accuracy, but also has fast matching speed.

1) Simulation settings

In this section, we evaluate the robustness of the proposed trust management model. We mainly evaluate the robustness of the proposed model based on the changes in the average reputation scores of different carpooling vehicles. The factors that affect the average reputation score of a vehicle mainly include the percentage of malicious passengers in carpooling and the weight of passenger’s feedback. The detailed simulation parameter setting is shown in Table 5.

In addition, we use Rh and Rm to evaluate the robustness of the proposed trust management model, where Rh denotes the average reputation score of honest carpooling vehicles; Rm denotes the average reputation score of malicious carpooling vehicles. The reputation score range of passengers is (0, 1], which is generated by random sampling and obeys a normal distribution, where μ = 0.5 , σ = 0.5 / 3 .

f ( x | μ , σ ) = 1 2 π σ ∗ exp ( − ( x − μ ) 2 2 σ 2 ) (18)

2) Robustness evaluation

We mainly evaluate the robustness of proposed trust management model, that is, malicious passengers deliberately provide false trust feedback after carpooling to reduce or increase the trust value of certain travel preferences of the vehicle, thereby affecting the average reputation score of the vehicle. In this paper, the percentage of malicious passengers in carpooling is set to 5% - 25%. Each carpooling vehicle is first initialized and then performed 5 - 25 carpooling tasks respectively. The number of travel preferences selected by passengers is 1 - 7. After the interval, TA updates the trust value of each travel preference and preference attribute set of the unrevoked vehicle in the local database, and then updates the average reputation score of the vehicle based on the trust value of each updated travel preference. In the process of reputation update, the trust value of the travel preference of the carpooling vehicle that is not selected is 0.5 by default.

Figure 7 shows how the average reputation score of honest vehicles changes with the percentage of malicious passengers and weight w_s. We can see that when the percentage of malicious passengers gradually increases from 5% - 20%, the average reputation score of honest vehicles decreases slowly, which indicates that the presence of malicious passengers can’t largely affect the average reputation score of honest vehicles. Therefore, our trust management model can resist attacks from malicious passengers. As w_s decreases, the average reputation score of honest carpooling vehicles decreases slightly, which is due to the fact that after the trust value of the travel preferences selected of honest vehicles are updated, the trust value of the corresponding travel preferences increases in a large extent

and is greater than the historical trust value of unselected travel preferences, reducing the weight w_s is equivalent to reduce the weight of the travel preference selected and updated by passengers, and the average reputation score of honest vehicles is reduced.

Figure 8 shows the changing process of the average reputation score of malicious vehicles with the percentage of malicious passengers and weight w_s. We can see that as the percentage of malicious passengers increases, the average reputation score of malicious vehicles increases very slowly, and the false feedback of malicious passengers can’t greatly increase the average reputation score of malicious vehicles. Therefore, the trust management model proposed in this paper shows robustness against malicious users’ attacks. With the weight w_s decreases, the average reputation score of malicious vehicles has increased slightly, which is due to that after the trust value of travel preferences of vehicle reputation set selected by passengers is updated, the trust value rapidly decreases and is lower than the historical trust value of unselected travel preferences. Decreasing the weight w_s is equivalent to increase w_t, and the average reputation score of malicious vehicles is increased to a certain extent.