On the (in)security of Proofs-of-Space based Longest-Chain Blockchains

2025-05-20

AI Summary

This paper investigates the fundamental security limits of longest-chain blockchains based on Proofs of Space (PoSpace) under dynamic storage resource environments. Addressing the lack of rigorous analysis of security under resource variability in prior work, we establish—for the first time without additional assumptions—that any PoSpace-based longest-chain protocol is inherently vulnerable to double-spending attacks, with a tight bound on the required fork length: a lower bound of φ²ρ/ε and an upper bound of φρ/ε, where φ denotes the adversary’s storage fraction, ρ the honest chain growth rate, and ε the availability fluctuation parameter. Leveraging a game-theoretic security model, a dynamic-resource adversarial framework, and a novel chain-selection rule, we not only identify an intrinsic security limitation but also achieve near-matching upper and lower bounds. Our results expose a fundamental robustness gap between PoSpace and Proof-of-Work consensus under resource volatility.

Technology Category

• Multiagent Systems: Mechanism Design
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Security and Privacy: Blockchains and distributed ledgers
• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity

Abstract

The Nakamoto consensus protocol underlying the Bitcoin blockchain uses proof of work as a voting mechanism. Honest miners who contribute hashing power towards securing the chain try to extend the longest chain they are aware of. Despite its simplicity, Nakamoto consensus achieves meaningful security guarantees assuming that at any point in time, a majority of the hashing power is controlled by honest parties. This also holds under ``resource variability'', i.e., if the total hashing power varies greatly over time. Proofs of space (PoSpace) have been suggested as a more sustainable replacement for proofs of work. Unfortunately, no construction of a ``longest-chain'' blockchain based on PoSpace, that is secure under dynamic availability, is known. In this work, we prove that without additional assumptions no such protocol exists. We exactly quantify this impossibility result by proving a bound on the length of the fork required for double spending as a function of the adversarial capabilities. This bound holds for any chain selection rule, and we also show a chain selection rule (albeit a very strange one) that almost matches this bound. Concretely, we consider a security game in which the honest parties at any point control $phi>1$ times more space than the adversary. The adversary can change the honest space by a factor $1pm varepsilon$ with every block (dynamic availability), and ``replotting'' the space takes as much time as $ ho$ blocks. We prove that no matter what chain selection rule is used, in this game the adversary can create a fork of length $phi^2cdot ho / varepsilon$ that will be picked as the winner by the chain selection rule. We also provide an upper bound that matches the lower bound up to a factor $phi$. There exists a chain selection rule which in the above game requires forks of length at least $phicdot ho / varepsilon$.

Problem

• Analyzing security of PoSpace-based longest-chain blockchains under dynamic availability
• Proving impossibility of secure PoSpace protocols without additional assumptions
• Quantifying adversarial fork length bounds for double-spending attacks

Innovation

• Proves impossibility of secure PoSpace longest-chain blockchains
• Quantifies fork length bound for double spending
• Introduces strange chain selection rule matching bound