Partial pre-image attack on Proof-of-Work based blockchains

Blockchain is a type of distributed ledger technology that consists of a growing list of records, called blocks, that are securely linked together using cryptography. Each blockchain-based solution deploys a specific consensus algorithm that guarantees the consistency of the ledger over time. The most famous, and yet claimed to be the most secure, is the Proof-of-Work (PoW) consensus algorithm. In this paper, we revisit the fundamental calculations and assumptions of this algorithm, originally presented in the Bitcoin white paper. We break down its claimed calculations in order to better understand the underlying assumptions of the proposal. We also propose a novel formalization model of the PoW mining problem using the Birthday paradox. We utilize this model to formalize and analyze partial pre-image attacks on PoW-based blockchains, with formal analysis that confirms the experimental results and the previously proposed implications. We build on those analyses and propose new concepts for benchmarking the security of PoW-based systems, including Critical Difficulty and Critical Difficulty per given portion. Our calculations result in several important findings, including the profitability of launching partial pre-image attacks on PoW-based blockchains, once the mining puzzle difficulty reaches a given threshold. Specifically, for any compromised portion of the network ($q<0.5$; honest majority assumption still holds), the attack is formally proven profitable once the PoW mining puzzle difficulty reaches 56 leading zeros.