Catfish Effect Between Internal and External Attackers: Semi-honest Mining Strategy Analysis

Table of Contents

1. Introduction

Blockchain technology has revolutionized decentralized systems, with Proof of Work (PoW) consensus mechanisms dominating the cryptocurrency market. However, mining attacks like selfish mining threaten blockchain security by allowing attackers to gain disproportionate rewards. This paper introduces a novel multi-attacker model that reveals the catfish effect between internal and external attackers, demonstrating how semi-honest strategies can be beneficial in competitive mining environments.

2. Background and Related Work

2.1 Proof of Work Consensus

Proof of Work requires miners to solve cryptographic puzzles to validate transactions and create new blocks. The mathematical foundation involves finding a nonce $n$ such that:

$H(block\_header, n) < target$

where $H$ is the cryptographic hash function and $target$ determines the mining difficulty.

2.2 Mining Attacks Overview

Selfish mining, introduced by Eyal and Sirer (2014), allows attackers to withhold discovered blocks strategically. The relative revenue (RR) for an attacker with computational power $\alpha$ can be modeled as:

$RR = \frac{\alpha(1-\alpha)^2(4\alpha+\gamma(1-2\alpha))-\alpha^3}{1-\alpha(1+(2-\alpha)\alpha)}$

3. Multi-Attacker Mining Model

3.1 System Architecture

The model transitions from original system to multi-attacker system with two phases. Internal attackers operate within existing mining pools, while external attackers join from outside the system.

3.2 Attack Scenarios

Three main causes of revenue reduction:

• Unexpected competitions between attackers
• Auction scenarios in block propagation
• Overestimation of influence factors

4. Catfish Effect Analysis

4.1 Internal vs External Attackers

The catfish effect describes how introducing external competition changes the behavior and revenue of internal attackers. This phenomenon mirrors competitive dynamics observed in traditional markets when new entrants disrupt established players.

4.2 Revenue Impact

Experimental results show significant RR reductions:

• Internal attacker: 31.9% drop in RR
• External attacker: 44.6% overestimation of RR

5. Partial Initiative Release Strategy

5.1 Algorithm Design

PIR is a semi-honest strategy that optimizes block release timing. The algorithm balances between honest mining and strategic withholding:

function PartialInitiativeRelease(block_chain, attacker_blocks):
    if len(attacker_blocks) >= 2:
        release_blocks = select_optimal_subset(attacker_blocks)
        broadcast(release_blocks)
        update_chain(block_chain, release_blocks)
    else:
        continue_mining()
    return updated_chain

5.2 Implementation Details

The strategy involves calculating the optimal release threshold $\theta$ based on network conditions and competitor behavior:

$\theta = f(\alpha, \beta, network\_latency, competitor\_strategy)$

6. Experimental Results

6.1 Performance Metrics

The experiments measured relative revenue under varying computational power distributions. Key findings include:

• PIR outperforms pure selfish mining in multi-attacker scenarios
• Revenue optimization occurs at specific computational power ratios
• Network latency significantly impacts strategy effectiveness

6.2 Comparative Analysis

The following diagram illustrates the revenue comparison between different strategies:

7. Future Applications

The research opens several directions for future work:

• Application to Proof of Stake and other consensus mechanisms
• Integration with machine learning for adaptive attack detection
• Cross-chain security implications in interoperable blockchain networks
• Real-time monitoring systems for multi-attacker scenarios

8. References

1. Nakamoto, S. (2008). Bitcoin: A Peer-to-Peer Electronic Cash System
2. Eyal, I., & Sirer, E. G. (2014). Majority is not Enough: Bitcoin Mining is Vulnerable
3. Liu, H., Ruan, N., & Liu, J. K. (2023). Catfish Effect Between Internal and External Attackers
4. Zhu, J., et al. (2017). Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks
5. Gervais, A., et al. (2016). On the Security and Performance of Proof of Work Blockchains