To eliminate efficacy errors in ID-based 2PAKA protocols with couplings, all types of ID-based 2PAKA protocols have been introduced over the past ten years, without bilineares functions. In 2007, the first ID-based 2PAKA protocol was presented without bileic operations by Zhu et al.  on the basis of an ID-based signature scheme. Nevertheless, their protocol was still ineffective and required three exchanges of messages. To reduce communication traffic, Fiore and Gennaro  used an exporation process in 2010 to create an ID-based 2PAKA protocol. In addition, the safety of this protocol has been demonstrated by them in the CK model. But this weak security model could not properly describe the ability of a real adversary. In the same year, Cao et al.  proposed a new 2PAKA protocol based on the ID, which does not contain pairs to reduce message exchange.
Unfortunately, cao et al.s protocol was vulnerable to the attack of the volatile keys discovered. After the work of Cao et al., many 2PAKA protocols based on ID have been proposed without bilineares functions, but these protocols have still not been effective in solving the efficiency and safety problem. Typically, the duration of an AKA protocol consists of approximately a computational time and a transfer time. We can only consider airtime here, since we already know the corresponding calculation time of each protocol. In terms of transmission time, we believe that transmission time is mainly related to message size and hardware power. We assume that these hardware devices have similar performance. So if the message size is longer, it will take longer to transfer it. Fortunately, we analyzed the size of the messages in these protocols in the analysis of computational costs. (ii) Requests. As before, S contains four empty tables, and to deal with the corresponding queries. S responds to these C queries as follows. (1) Challenger S has a blank list in the form of .
i) If the list already has matching input, S returns to C. (ii) Otherwise S checks the entire table. If the item is found, S will enter the new entry into the list. If this is not the case, it is randomly selected by S and the corresponding data are written in. (2) StaticKeyReveal (). is revealed by S an C.(3)MasterPrivateKeyReveal. Challenger S responds to this request with . (4) EphemeralKeyReveal (). If so, stop. Otherwise, S returns the volatile key of C.
(5) Send (, M). S manages a blank list in the form of . i) If , S X returns to C. (ii) Si , S Y returns to C. Then looks for the corresponding entry in . When the item is obtained by S, the challenger sits down and the board is added with this new entry. Conversely, the selection is taken at random from S and the corresponding item is inserted into the table. iii) Under other conditions, S responds to C in accordance with protocol specifications.
In VANETs, communication channels between vehicles and nearby road infrastructure are generally implemented through special DSRC protocols . Using these channels, a vehicle can send messages, such as information or traffic conditions, to nearby vehicles and road infrastructure for a uniform period.