PoW Security-Latency under Random Delays and the Effect of Transaction Fees
Mustafa Doger, Sennur Ulukus, Nail Akar
TL;DR
The paper addresses the security-latency problem for Proof-of-Work blockchains under general random delays, deriving tight, explicit bounds on the safety of a transaction after it becomes $k$-deep. It introduces a general bounding framework based on three phases (pre-mining gain, confirmation interval, post-confirmation race) and expresses the safety probability as $p \le \bar{p}=P(\bar{L}+\bar{S}_k+\bar{M}\ge k)$, with the lead and race dynamics captured by Lindley-type processes and delay-dependent random variables. The analysis distinguishes the case $b_0=0$ and $b_0>0$, using constructs like the pacer/jumper model and establishing bounds via $Z=C_{\alpha}+C_{\Delta}-1$ (or $Z^{(b_0)}$ when $b_0>0$), under the requirement $1>\mathbb{E}[C_{\alpha}+C_{\Delta}]$. A complementary lower bound is derived through a similar Lindley-process framework, and numerical results demonstrate tight bounds under realistic, right-skewed delay distributions and BTC-like parameters, including the impact of halving via transaction-fee dynamics. The framework applies to arbitrary delay distributions, providing a practical tool to assess safety, transaction-fee effects, and maintenance-cost sustainability in PoW systems.
Abstract
Safety guarantees and security-latency problem of Nakamoto consensus have been extensively studied in the last decade with a bounded delay model. Recent studies have shown that PoW protocol is secure under random delay models as well. In this paper, we analyze the security-latency problem, i.e., how secure a block is, after it becomes k-deep in the blockchain, under general random delay distributions. We provide tight and explicit bounds which only require determining the distribution of the number of Poisson arrivals during the random delay. We further consider potential effects of recent Bitcoin halving on the security-latency problem by extending our results.