A Fast Consensus for Permissioned Wireless Blockchains

Yifei Zou, Minghui Xu, Jiguo Yu, Feng Zhao, Xiuzhen Cheng

Abstract: With the wide deployment of Internet of Things (IoT), blockchain systems have been playing a crucial role to establish a trusted computing environment among potentially mistrusting agents without depending on a centralized server. Different from previous blockchain consensus protocols adopted in IoT, which rely on efficient and stable transmissions, in this article, we consider how to reach blockchain consensus in wireless networks without reliable network support. Specifically, a realistic signal to interference plus noise ratio (SINR) model is adopted to depict the unreliable transmissions in wireless channels. Based on the SINR model, a distributed and randomized consensus algorithm is proposed to reach <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -times consensus among <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> devices within <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(k+\log n)$ </tex-math></inline-formula> time steps with high probability. Note that the time complexity of our algorithm is asymptotically optimal since <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega (k+\log n)$ </tex-math></inline-formula> is a lower bound to achieve <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -times consensus in a distributed environment. We conduct both rigorous theoretical analysis and extensive simulations to validate our method. It is believed that our work can facilitate the implementation of blockchains in many wireless scenarios in which the reliable and fast transmissions cannot be guaranteed.