Table 1.

The proposed protocol contributions over the basic Shamir secret protocol.

Security Properties	Basic Shamir Secret Sharing Issues	The Proposed Protocol Contributions
Misleading members	Assume all members of the group are honest. Individual members can mislead or ignore other participants’ contributions.	This assumption cannot be held in an untrustworthy and decentralized network. Members are not involved in the key reconstruction.
Decentralizing	Group members must communicate to exchange their secret parts required for key recovery. Require $t$ participants to share their secret pieces to recover the original key.	Support centralized implantation where the base stations work as trusted group managers for vehicles. No need for the existence of t participants. The group manager broadcast $t-1$ public shares that are very important for only registered vehicles to recover the key.
High dynamic networks	It is impractical in V2X communication with high dynamic nature as many vehicles can join or leave the group frequently. At least $t$ members must exist in the network.	Adding or removing group members does not affect the generated secret shares and the original key reconstruction. The group manager provides any required shares to reconstruct the key.
High communication overhead	Substantial overhead owing to high communication among participants.	No need for communication between participants to share their secret parts. Vehicles depend on the received information from the group manager.
Requirement of a secure channel	The communications between group members require secure channels.	No need for secure channels between participants. We are reducing the overhead of establishing secure channels between vehicles.
Key recovery attacks	Vulnerable to key recovery attacks since each participant’s secret part is broadcasted in a broadcast channel.	Resistance to key recovery attacks by reducing the communication between vehicles at the initialization phase.
The misbehaving dealer	If the dealer is a bad actor, the private key can be stolen or abused.	The dealer in the proposed protocol is trusted and authenticates itself via HMAC authentication protocol.
The key authentication and confidentiality	It’s a security issue since the private key must first be produced and divided into parts.	The proposed protocol supports the key authentication using HMAC signatures.
Verification of secret shares	Requires the verification of secret shares to ensure the correctness of shared secret parts.	Only authorized and registered vehicles can join the network. No need for secret shares verification process. Vehicles are not required to broadcast their secret parts to other vehicles.