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.

Most blockchain systems currently adopt resource-consuming protocols to achieve consensus between miners; for example, the Proof-of-Work (PoW) and Practical Byzantine Fault Tolerant (PBFT) schemes, which have a high consumption of computing/communication resources and usually require reliable communications with bounded delay. However, these protocols may be unsuitable for Internet of Things (IoT) networks because the IoT devices are usually lightweight, battery-operated, and deployed in an unreliable wireless environment. Therefore, this paper studies an efficient consensus protocol for blockchain in IoT networks via reinforcement learning. Specifically, the consensus protocol in this work is designed on the basis of the Proof-of-Communication (PoC) scheme directly in a single-hop wireless network with unreliable communications. A distributed MultiAgent Reinforcement Learning (MARL) algorithm is proposed to improve the efficiency and fairness of consensus for miners in the blockchain system. In this algorithm, each agent uses a matrix to depict the efficiency and fairness of the recent consensus and tunes its actions and rewards carefully in an actor-critic framework to seek effective performance. Empirical results from the simulation show that the fairness of consensus in the proposed algorithm is guaranteed, and the efficiency nearly reaches a centralized optimal solution.

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.

In the past decades, with the widespread implementation of wireless networks, such as the Internet of Things, an enormous demand for designing relative algorithms for various realistic scenarios has arisen. However, with the widening of scales and deepening of network layers, it has become increasingly challenging to design such algorithms when the issues of message dissemination at high levels and the contention management at the physical layer are considered. Accordingly, the abstract medium access control (absMAC) layer, which was proposed in 2009, is designed to solve this problem. Specifically, the absMAC layer consists of two basic operations for network agents: the acknowledgement operation to broadcast messages to all neighbors and the progress operation to receive messages from neighbors. The absMAC layer divides the wireless algorithm design into two independent and manageable components, i.e., to implement the absMAC layer over a physical network and to solve higher-level problems based on the acknowledgement and progress operations provided by the absMAC layer, which makes the algorithm design easier and simpler. In this study, we consider the implementation of the absMAC layer under jamming. An efficient algorithm is proposed to implement the absMAC layer, attached with rigorous theoretical analyses and extensive simulation results. Based on the implemented absMAC layer, many high-level algorithms in non-jamming cases can be executed in a jamming network.