STAKE: Preventing a colluding majority from double spending

2026-10-01

AI Summary

This study addresses the vulnerability of traditional blockchain consensus mechanisms to collusive double-spending attacks in poorly synchronized networks, which typically rely on a supermajority of honest nodes. This work proposes the STAKE protocol, introducing a game-theoretic staking mechanism that reduces the required proportion of honest nodes for security to n/3+1. By establishing a (k,t)-robust equilibrium framework, we demonstrate that rational players have no incentive to collude with Byzantine nodes. Furthermore, integrating a probabilistic defense model, we prove that the success probability of double-spending attacks decays polynomially with the number of attempts. Our analysis shows that the proposed protocol maintains a stable equilibrium even under lower staking ratios, significantly enhancing the system's fault tolerance and overall security.

Abstract

Blockchains typically operate in open networks where it is hard to control the delay of messages. While classic blockchain protocols assumed synchrony, newer protocols try to remain secure despite unexpected network delays. Unfortunately, in the traditional model where $n$ participants can either be honest or Byzantine, we need a supermajority, or $\lfloor 2n/3\rfloor + 1$, of them to be honest. Recent work have explored the question of reducing the number of needed honest nodes in a game theory model to a majority sometimes by introducing $k$ rational players and $t$ Byzantine players. Yet, to our knowledge, no blockchain protocol managed to reduce it further. In this paper, we offer a blockchain protocol called Secure and Tolerant Algorithm through ($k,t$)-robust Equilibrium (STAKE) that works with only $\lfloor n/3\rfloor + 1$ honest players. STAKE requires each consensus participant to stake a sufficiently large amount $s$ compared to their liquidity $\ell$. We show that the probability that a coalition manages to execute $ζ$ double spending attacks (we call them a $ζ$-uple attack) drops polynomially fast with $ζ$. This allows us to demonstrate that STAKE reaches a ($k,t$)-robust equilibrium, or that rational players do not collude with Byzantine, even with a relatively low $s/\ell$ ratio.

Problem

• blockchain
• double spending
• Byzantine fault tolerance
• game theory
• collusion

Innovation

• Blockchain consensus
• (k,t)-robust equilibrium
• Double spending prevention
• Staking mechanism
• Game theory