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Majority is not Needed: A Counterstrategy to Selfish Mining

Jonathan Gal, Maytal B Szabo, Ori Rottenstreich

TL;DR

The paper addresses selfish mining by proposing piggyback mining as a counterstrategy in which a large pool leverages an opposing selfish pool to gain control of the main blockchain and even perform double spending. It develops a formal framework, including a threshold condition for success and a Markov-chain-inspired slowdown analysis, and extends the approach to general deviant strategies with an optimal reveal-time analysis. Key contributions include enabling 51% capabilities with less than half the computing power, deriving the optimal waiting time to reveal the piggybacked branch, and proving applicability to arbitrary deviant strategies, along with a resilience-based deterrence mechanism. The findings provide a theoretical basis for the observed resilience of blockchain ecosystems against selfish mining, highlighting slowdown as a robust countermeasure that shifts incentives away from deviant behavior.

Abstract

In the last few years several papers investigated selfish mine attacks, most of which assumed that every miner that is not part of the selfish mine pool will continue to mine honestly. However, in reality, remaining honest is not always incentivized, particularly when another pool is employing selfish mining or other deviant strategies. In this work we explore the scenario in which a large enough pool capitalises on another selfish pool to gain 100\% of the profit and commit double spending attacks. We show that this counterstrategy can effectively counter any deviant strategy, and that even the possibility of it discourages other pools from implementing deviant strategies.

Majority is not Needed: A Counterstrategy to Selfish Mining

TL;DR

The paper addresses selfish mining by proposing piggyback mining as a counterstrategy in which a large pool leverages an opposing selfish pool to gain control of the main blockchain and even perform double spending. It develops a formal framework, including a threshold condition for success and a Markov-chain-inspired slowdown analysis, and extends the approach to general deviant strategies with an optimal reveal-time analysis. Key contributions include enabling 51% capabilities with less than half the computing power, deriving the optimal waiting time to reveal the piggybacked branch, and proving applicability to arbitrary deviant strategies, along with a resilience-based deterrence mechanism. The findings provide a theoretical basis for the observed resilience of blockchain ecosystems against selfish mining, highlighting slowdown as a robust countermeasure that shifts incentives away from deviant behavior.

Abstract

In the last few years several papers investigated selfish mine attacks, most of which assumed that every miner that is not part of the selfish mine pool will continue to mine honestly. However, in reality, remaining honest is not always incentivized, particularly when another pool is employing selfish mining or other deviant strategies. In this work we explore the scenario in which a large enough pool capitalises on another selfish pool to gain 100\% of the profit and commit double spending attacks. We show that this counterstrategy can effectively counter any deviant strategy, and that even the possibility of it discourages other pools from implementing deviant strategies.
Paper Structure (10 sections, 4 theorems, 5 equations, 4 figures)

This paper contains 10 sections, 4 theorems, 5 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Piggyback Mining - Utilizing an Opposing Selfish Pool
  4. The Piggyback Strategy
  5. $|P| > |P_s| > |P_h|$
  6. $|P| > |P_h| \ge |P_s|$
  7. Extending Piggyback Mining to Any Deviant Strategy
  8. Optimal Waiting Time for Piggybackers to Reveal Their Branch
  9. Responding to a Piggybacking Strategy
  10. Conclusions

Key Result

Theorem 1

Every deviant strategy causes a slowdown.

Figures (4)

  • Figure 1: The Markov chain as envisioned by Eyal and Sirer main. States represent the lead of a secret branch over the public-main branch, $\alpha$ represents the selfish pool's relative mining power, and $\gamma$ represents the portion of honest miners who will mine on top of the selfish branch in case of a competition.
  • Figure 2: Relative selfish pool size compared to the slowdown caused by it. Simulation and theoretical analysis show that selfish mining always causes a slowdown, where the most significant slowdown is when the selfish pool is the same size as the honest miners.
  • Figure 3: For a given relative size of the selfish pool, the black line shows the maximal size of honest miners for which a piggyback attack is possible. Colored areas are where piggybacking is possible, and each colored area represents one of the cases described in this section.
  • Figure 4: The probability of maintaining the longest blockchain branch as a function of the relative computing power of a piggybacking pool, given a fixed number of total mined blocks.

Theorems & Definitions (8)

  • Definition 1: Protocol-Legitimate and Deviant Strategies
  • Definition 2: Slowdown
  • Theorem 1
  • Corollary 1
  • proof
  • Corollary 2
  • Definition 3: Resilience
  • Corollary 3