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

TL;DR

This paper models double spending risks in Nakamoto consensus with time-varying mining rates using ruin theory, providing new analytical tools for dynamic network conditions and miner participation.

Contribution

It introduces a ruin-theoretical model for double spending in Nakamoto consensus accounting for arbitrary time-varying mining rates, extending prior fixed-rate analyses.

Findings

The model effectively estimates double spend probabilities under dynamic conditions.

Numerical examples validate the analytical approach.

The approach captures realistic network delays and miner behavior.

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.