Transaction Capacity, Security and Latency in Blockchains

TL;DR

This paper analyzes the security-latency trade-off in Nakamoto consensus under an exponential network delay, deriving an upper bound on safety-violation probability as a function of confirmation depth $k$, honest fraction $\alpha$, block size $b$, and delay/mining rates $\mu_1,\mu_2$. It then connects these results to a GI/M/1-type batch-service queue to express the sustainable transaction rate in terms of $b$, fork rate $\kappa=\mu_2/\mu_1$, and network conditions. The authors introduce a rigged jumper attack to bound safety and derive the steady-state lead distribution via Ramaswami's formula, quantify the distribution of adversarial blocks during confirmation and the post-confirmation race, and demonstrate substantial throughput gains when increasing $k$ (e.g., from $k=6$ to $k=7$) with adjusted mining rates. They also analyze two queue-attacks (queue-service and selfish-mining) and provide conservative bounds on throughput under attack, offering a design framework for balancing throughput, latency, and security in blockchain systems.

Abstract

We analyze how secure a block is after the block becomes $k$-deep, i.e., security-latency, for Nakamoto consensus under an exponential network delay model. We provide the fault tolerance and extensive bounds on safety violation probabilities given mining rate, delay rate and confirmation rules. Next, modeling the blockchain system as a batch service queue with exponential network delay, we connect the security-latency analysis to sustainable transaction rate of the queue system. As our model assumes exponential network delay, batch service queue models give a meaningful trade-off between transaction capacity, security and latency. Our results indicate that, by simply picking $k=7$-block confirmation rule in Bitcoin instead of the convention of $k=6$, mining rate, latency and throughput can be increased sixfold with the same safety guarantees. We further consider adversarial attacks on the queue service to hamper the service process. In an extreme scenario, we consider the selfish-mining attack for this purpose and provide the maximum adversarial block ratio in the longest chain under the exponential delay model. The ratio in turn reflects the maximum rate of decrease in the sustainable transaction rate of the queue.

Figures (5)

• Figure 1: Queue model.
• Figure 2: State transition relation.
• Figure 3: Safety violation for exponential and bounded delay, $\alpha=0.90$.
• Figure 4: Safety violation for exponential and bounded delay, $\alpha=0.75$.
• Figure 5: Safety violation probability effect on different parameters, $\alpha=0.9$.

Theorems & Definitions (13)

• Theorem 1
• Lemma 1
• Lemma 2
• Corollary 1
• Lemma 3
• Theorem 2
• Corollary 2
• Proposition 1
• Remark 1
• Theorem 3