# Everything is a Race and Nakamoto Always Wins

arXiv: https://arxiv.org/abs/2005.10484 · HTML: https://mlsanity.com/paper/2005.10484/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2020.

## Built on by (most cited first, 2 of 2)

- [FEDSTR: Money-In AI-Out | A Decentralized Marketplace for Federated Learning and LLM Training on the NOSTR Protocol](https://mlsanity.com/paper/2404.15834/) (2024)
- [Deep Reinforcement Learning-based Rebalancing Policies for Profit Maximization of Relay Nodes in Payment Channel Networks](https://mlsanity.com/paper/2210.07302/) (2022)

## Abstract (arXiv)

Nakamoto invented the longest chain protocol, and claimed its security by analyzing the private double-spend attack, a race between the adversary and the honest nodes to grow a longer chain. But is it the worst attack? We answer the question in the affirmative for three classes of longest chain protocols, designed for different consensus models: 1) Nakamoto's original Proof-of-Work protocol; 2) Ouroboros and SnowWhite Proof-of-Stake protocols; 3) Chia Proof-of-Space protocol. As a consequence, exact characterization of the maximum tolerable adversary power is obtained for each protocol as a function of the average block time normalized by the network delay. The security analysis of these protocols is performed in a unified manner by a novel method of reducing all attacks to a race between the adversary and the honest nodes.