Byzantine Fault Tolerant Consensus in Open Wireless Networks via an Abstract MAC Layer

The openness of wireless networks opens the door to Byzantine attacks on the physical channels, making the communications unreliable and resulting in more challenges in achieving consensus among mobile devices. To address this issue, this paper studies the Byzantine-fault-tolerant (BFT) consensus problem based on an unreliable Byzantine communication model. Different from the previous works requiring stable communications between the honest nodes, considering the unreliable communication makes our problem more realistic but also harder. Based on the unreliable communication model, we first implement a BFT abstract MAC (absMAC) layer with a distributed and randomized multi-channel communication algorithm. In the implemented absMAC layer, its acknowledgement and progress operations can be completed within <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O\left ({{\frac {kn}{k-f}\log n}}\right)$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O\left ({{\frac {k}{k-f}\log n}}\right)$ </tex-math></inline-formula> rounds, respectively. n, f, and k are the numbers of nodes, Byzantine nodes, and channels, respectively. With the implemented absMAC layer, an efficient and elegant BFT consensus algorithm is designed, which can solve the binary consensus problem within <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O\left ({{\frac {kn}{k-f}\log n}}\right) ^{^{^{^{}}}}$ </tex-math></inline-formula> rounds in expectation. Even though a series of works have discussed how to achieve consensus with a specific absMAC layer provided, to the best of our knowledge, this paper is the first one that implements a BFT absMAC layer.