Partial Selfish Mining for More Profits

TL;DR

This paper introduces Partial Selfish Mining (PSM), a novel block-sharing attack that reveals only parts of a discovered block to attract rational miners to the attacker's private chain, thereby increasing the attacker’s revenue relative to both honest and traditional selfish mining under certain conditions. It further extends to Advanced PSM (A-PSM), which leverages timely knowledge of the public chain height to enhance profits, ensuring attacker revenue is no less than selfish mining and often higher. The authors formalize a detailed mining model with attacker, rational, attracted, and public-miner roles, provide mathematical expressions for attacker and rational-miner rewards, and validate the results with simulations. They also propose practical mechanisms to prove block possession and to deter PSM-DoS, including zero-knowledge proofs and smart-contract-based collateral protections. The work highlights a new, profit-driven collaboration paradigm in PoW mining and discusses countermeasures and optimal strategies under various network conditions, underscoring implications for blockchain security and consensus design.

Abstract

Mining attacks aim to gain an unfair share of extra rewards in the blockchain mining. Selfish mining can preserve discovered blocks and strategically release them, wasting honest miners' computing resources and getting higher profits. Previous mining attacks either conceal the mined whole blocks (hiding or discarding), or release them completely in a particular time slot (e.g., causing a fork). In this paper, we extend the mining attack's strategy space to partial block sharing, and propose a new and feasible Partial Selfish Mining (PSM) attack. We show that by releasing partial block data publicly and attracting rational miners to work on attacker's private branch, attackers and these attracted miners can gain an unfair share of mining rewards. We then propose Advanced PSM (A-PSM) attack that can further improve attackers' profits to be no less than the selfish mining. Both theoretical and experimental results show that PSM attackers can be more profitable than selfish miners under a certain range of mining power and network conditions. A-PSM attackers can gain even higher profits than both selfish mining and honest mining with attracted rational miners.

Figures (16)

• Figure 1: (a) Selfish mining withholds discovered blocks in its private chain; (b) Partial selfish mining can firstly withhold a discovered block, then share partial block data, and finally broadcast the whole block.
• Figure 2: Miners' roles in PSM scenario.
• Figure 3: Workflow of PSM strategy. Instead of publishing a new block, the attacker shares partial block data with other miners to attract them to join its private branch.Three possible cases of finding another new block after the announcement of the partial block. Case 1: By public miners; Case 2: By the attacker; Case 3: By attracted miners.
• Figure 4: State machine of PSM when miners with overall $\alpha_i$ mining power working greedy.
• Figure 5: Four reward cases exist when a rational miner k follows the public mining strategy. Case A: Miner k finds two blocks on the public branch. Case B: Miner k finds one block on the public branch, and a public miner further extends the block on the public branch. Case C: Another public miner finds a new block on the public branch, and miner k further extends the block on the public branch. Case D: Another public miner finds a new block on the public branch, then miner k finds a new block on the attacker's branch. Please note that once a public miner finds a block, the attacker will surely release the full block and start a race.

Theorems & Definitions (9)

• Theorem 1
• Theorem 2
• Proof 1
• Theorem 3
• Theorem 4
• Proof 2
• Theorem 5
• Theorem 6
• Theorem 7