A Gaussian Reputation-Based Hybrid BFT Consensus With a Formal Security Framework

Blockchain systems have evolved over decades, addressing the inefficiencies and high costs associated with centralized architectures. Among various consensus mechanisms, committee-based hybrid Byzantine Fault Tolerant (BFT) protocols are a fundamental approach to blockchain consensus. However, designing a hybrid BFT consensus protocol that ensures fairness, responsiveness, and formal security remains challenging. In this paper, we propose GRBFT: a Gaussian reputation-based hybrid BFT blockchain consensus protocol with a formal security framework. Our proposed protocol integrates a multilateral Gaussian reputation evaluation to incentivize trusted nodes' participation in the consensus. We use threshold signatures and verifiable random functions (VRFs) to randomly select committee members and leaders, ensuring fair reconfiguration and unbiased sortition. A formal security framework is utilized to design and analyze the blockchain consensus system. Additionally, we design a speculative GRBFT (S-GRBFT) protocol to circumvent the traditional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(n^{2})$</tex-math></inline-formula> leader sortition complexity and reduce the communication to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(n)$</tex-math></inline-formula> within a single round. Moreover, we present a secure candidate committee reconfiguration method that efficiently updates members based on their reputation and a Proof-of-Stake (PoS) mechanism. The proposed GRBFT protocol is proven to achieve consistency and liveness under the corruption and liveness parameters.