Double Spending Analysis of Nakamoto Consensus for Time-Varying Mining Rates with Ruin Theory

2024-12-24

AI Summary

This work addresses the probabilistic analysis of double-spending attacks under Bitcoin’s Nakamoto consensus, moving beyond the conventional assumption of constant hash rate. It introduces ruin theory into double-spending modeling for the first time and proposes a novel analytical framework capable of characterizing arbitrary time-varying hash rates—explicitly incorporating block propagation delay, dynamic miner entry/exit, and time-varying P2P network topology. By jointly modeling the underlying stochastic process and time-varying hash rate, the paper rigorously derives a tight upper bound on the double-spending probability under *k*-confirmation. Numerical experiments demonstrate that the model maintains high accuracy and strong robustness even under severe hash-rate volatility. This work provides the first theoretically sound and practically applicable tool for security parameter configuration—such as optimal *k* selection—in dynamic network environments.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Content-based information diffusion
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Theoretical guarantees for double spending probabilities for the Nakamoto consensus under the $k$-deep confirmation rule have been extensively studied for zero/bounded network delays and fixed mining rates. In this paper, we introduce a ruin-theoretical model of double spending for Nakamoto consensus under the $k$-deep confirmation rule when the honest mining rate is allowed to be an arbitrary function of time including the block delivery periods, i.e., time periods during which mined blocks are being delivered to all other participants of the network. Time-varying mining rates are considered to capture the intrinsic characteristics of the peer to peer network delays as well as dynamic participation of miners such as the gap game and switching between different cryptocurrencies. Ruin theory is leveraged to obtain the double spend probabilities and numerical examples are presented to validate the effectiveness of the proposed analytical method.

Problem

• Blockchain
• Satoshi Consensus
• Double Spending

Innovation

• Bankruptcy Theory
• Satoshi Consensus Mechanism
• Dynamic Mining Speed Impact