  Decentralized, tamper-proof blockchain is regarded as a solution to a
challenging authentication issue in the Internet of Vehicles (IoVs). However,
the consensus time and communication overhead of blockchain increase
significantly as the number of vehicles connected to the blockchain. To address
this issue, vehicular fog computing has been introduced to improve efficiency.
However, existing studies ignore several key factors such as the number of
vehicles in the fog computing system, which can impact the consensus
communication overhead. Meanwhile, there is no comprehensive study on the
stability of vehicular fog composition. The vehicle movement will lead to
dynamic changes in fog. If the composition of vehicular fog is unstable, the
blockchain formed by this fog computing system will be unstable, which can
affect the consensus efficiency. With the above considerations, we propose an
efficient and stable identity authentication (ESIA) empowered by hierarchical
blockchain and fog computing. By grouping vehicles efficiently, ESIA has low
communication complexity and achieves high stability. Moreover, to enhance the
consensus security of the hierarchical blockchain, the consensus process is
from the bottom layer to the up layer (bottom-up), which we call B2UHChain.
Through theoretical analysis and simulation verification, our scheme achieves
the design goals of high efficiency and stability while significantly improving
the IoV scalability to the power of 1.5 (^1.5) under similar security to a
single-layer blockchain. In addition, ESIA has less communication and
computation overhead, lower latency, and higher throughput than other baseline
authentication schemes.
