As the device complexity keeps increasing, the blockchain networks have been celebrated as the cornerstone of numerous prominent platforms owing to their ability to provide distributed and immutable ledgers and data-driven autonomous organizations. The distributed consensus algorithm is the core component that directly dictates the performance and properties of blockchain networks. However, the inherent characteristics of the shared wireless medium, such as fading, interference, and openness, pose significant challenges to achieving consensus within these networks, especially in the presence of malicious jamming attacks. To cope with the severe consensus problem, in this paper, we present a distributed jamming-resilient consensus algorithm for blockchain networks in wireless environments, where the adversary can jam the communication channel by injecting jamming signals. Based on a non-binary slight jamming model, we propose a distributed four-stage algorithm to achieve consensus in the wireless blockchain network, including leader election, leader broadcast, leader aggregation, and leader announcement stages. With high probability, we prove that our jamming-resilient algorithm can ensure the validity, agreement, termination, and total order properties of consensus with the time complexity of $O(n)$. Both theoretical analyses and empirical simulations are conducted to verify the consistency and efficiency of our algorithm.

In recent years, due to the wide implementation of mobile agents, the Internet-of-Things (IoT) networks have been applied in several real-life scenarios, servicing applications in the areas of public safety, proximity-based services, and fog computing. Meanwhile, when more complex tasks are processed in IoT networks, demands on identity authentication, certifiable traceability, and privacy protection for services in IoT networks increase. Building a blockchain system in IoT networks can greatly satisfy such demands. However, the blockchain building in IoT brings about new challenges compared with that in the traditional full-blown Internet with reliable transmissions, especially in terms of achieving consensus on each block in complex wireless environments, which directly motivates our work. In this study, we fully considered the challenges of achieving a consensus in a blockchain system in IoT networks, including the negative impacts caused by contention and interference in wireless channel, and the lack of reliable transmissions and prior network organizations. By proposing a distributed consensus algorithm for blockchains on multi-hop IoT networks, we showed that it is possible to directly reach a consensus for blockchains in IoT networks, without relying on any additional network layers or protocols to provide reliable and ordered communications. In our theoretical analysis, we showed that our consensus algorithm is asymptotically optimal on time complexity and is energy saving. The extensive simulation results also validate our conclusions in the theoretical analysis.