Post-Quantum Cryptography and Blockchain Governance: A Comparative Risk Analysis of Bitcoin and Ethereum

Abstract

The advent of sufficiently powerful quantum computers poses an existential cryptographic threat to elliptic-curve-based public key infrastructure, upon which major blockchain networks depend for transaction security and identity. This paper conducts a rigorous comparative analysis of quantum risk exposure for Bitcoin and Ethereum, examining the structural, governance, and economic dimensions of post-quantum cryptographic (PQC) transition for each protocol. We analyze the mathematical incompatibility of leading NIST standardized PQC signature schemes with current blockchain scalability constraints, with particular attention to signature size inflation (30-100× current schemes), the loss of algebraic linearity preventing signature aggregation, and the resulting implications for block space, fee markets, node economics, and validator infrastructure. We subsequently contrast Ethereum's upgrade-oriented, stake-weighted governance model and its modular cryptographic architecture against Bitcoin's deliberately ossified, consensus-driven governance structure. Our findings indicate that while Ethereum possesses the structural and institutional prerequisites for a credible, phased transition to post-quantum cryptography, Bitcoin's governance model and architectural constraints render such a transition highly contested and potentially irresolvable without chain fragmentation. We conclude that Bitcoin's structural limitations, compounded by deep ideological fractures and the irreversible nature of PQC deployment, place it at significant risk of prolonged governance stagnation or chain split, undermining its position as a reliable store of value and 'digital gold' standard in the medium term.