ROR Model. In this section, we use the universally-accepted real-or-random (ROR) model [25] in order to prove the security of the session key in our proposed protocol.We provide the similar proof as adopted in [26,27]. Short Discussion about ROR Model In the ROR model [25], the malicious attacker A is modeled using the DY model, which interacts with the instance of the participants in the protocol. In our proposed protocol, vi, RSUj and TA are considered as participants. Additionally, Pt1 , Pt2 , and Pt3 , which are called oracles denoting the vi RSUj TA instances t1, t2, and t3 of vi, RSUj, and TA, respectively. Table 2 shows various queries that simulate attacks, such as eavesdropping, modifying, and deleting or inserting the transmitted messages among the entities. h(·) and Collision-resistant one-way hash function Hash are modeled as a random oracle and they can be used by all participants including X. Xxxx et al. [28] showed that the password chosen by the user follows the Xxxx’x law, which is quite different from the uniform distribution. They also found that the size of password dictionary is quite limited in the sense that users do not generally use the entire space of the passwords; instead, they use a small space of the allowed characters space. We apply the Xxxx’x law in order to prove the session key security of our proposed protocol.
Theorem 1. If AdvP is the advantage function of an attacker A in breaking the session key SK security of the proposed protocol P, respectively, qh, qsend, and |Hash| are the number of Hash queries, Send queries, and the range space of the hash function, respectively. Subsequently, q2 h + |Hash| 2max where C′ and s′ are the Xxxx’x parameters [28].
Table 2. Various queries and their meanings. Execute(Pt1 , Pt2 , Pt3 ) This query means that the model of the eavesdropping attack between the vi RSUj TA entities vi , RSUj and TA via an insecure channels. vi CorruptOBU(Pt1 ) Under this corrupt on-board-unit (OBU) query, A can fetch all sensitive credentials stored in the OBU of vi . This is modeled as an active attack. Send(Pt ) Under this query, can transmits a message to Pt, and in response, it also receives a message from Pt. This is also modeled as an active attack. Reveal(Pt ) The query means that A reveals session key SK created by Pt and its partner to Test(Pt ) Before the game begins, under this query, an unbiased coin c is flipped. Depending on the output, the following decisions are made. At executes this query and if the...
