# Proof-of-Stake Longest Chain Protocols: Security vs Predictability

arXiv: https://arxiv.org/abs/1910.02218 · HTML: https://mlsanity.com/paper/1910.02218/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2019.

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

- [Proof-of-Learning with Incentive Security](https://mlsanity.com/paper/2404.09005/) (2024)
- [Game of Trust: How Trustworthy Does Your Blockchain Think You Are?](https://mlsanity.com/paper/2505.14551/) (2025)

## Abstract (arXiv)

The Nakamoto longest chain protocol is remarkably simple and has been proven to provide security against any adversary with less than 50% of the total hashing power. Proof-of-stake (PoS) protocols are an energy efficient alternative; however existing protocols adopting Nakamoto's longest chain design achieve provable security only by allowing long-term predictability (which have serious security implications). In this paper, we prove that a natural longest chain PoS protocol with similar predictability as Nakamoto's PoW protocol can achieve security against any adversary with less than 1/(1+e) fraction of the total stake. Moreover we propose a new family of longest chain PoS protocols that achieve security against a 50% adversary, while only requiring short-term predictability. Our proofs present a new approach to analyzing the formal security of blockchains, based on a notion of adversary-proof convergence.