Table 3.

Notations.

Symbol	Description
$CA{N}^i$	The ith group under CAN bus.
$G{W}^i$	The gateway that manages the $CA{N}^i$ bus.
$MGW$	The main gateway that manages all gateways.
$EC{U}_j^i$	The jth ECU in the $CA{N}^i$ bus.
$S_j^i$	The pre-shared key between $EC{U}_j^i$ and $G{W}^i$.
$M\left(message\right)$	The sent frame.
${S_g}^i$	The pre-shared keys for all ECUs and the $G{W}^i$ in the $CA{N}^i$ bus.
$G{S}_{i,M}$	The key shared by $MGW$ and $G{W}^i$.
$s{k}^i$	The session key used by the ECUs in $CA{N}^i$ bus.
$Gsk$	The session key used in the GW group.