Formal Security Analysis of SPV Clients Versus Home-Based Full Nodes in Bitcoin-Derived Systems

TL;DR

This paper provides a formal analysis comparing SPV clients and home-based full nodes in Bitcoin, showing SPV clients are cryptographically sufficient and more resilient to attacks under honest-majority assumptions.

Contribution

It introduces a formal framework and axioms to analyze the security of SPV clients versus full nodes, demonstrating SPV's sufficiency and robustness.

Findings

SPV clients are cryptographically sufficient under honest-majority assumptions.

Home-based full nodes increase systemic entropy without improving consensus security.

SPV clients are the rational equilibrium for non-mining participants.

Abstract

This paper presents a mathematically rigorous formal analysis of Simplified Payment Verification (SPV) clients, as specified in Section 8 of the original Bitcoin white paper, versus non-mining full nodes operated by home users. It defines security as resistance to divergence from global consensus and models transaction acceptance, enforcement capability, and divergence probability under adversarial conditions. The results demonstrate that SPV clients, despite omitting script verification, are cryptographically sufficient under honest-majority assumptions and topologically less vulnerable to attack than structurally passive, non-enforcing full nodes. The paper introduces new axioms on behavioral divergence and communication topology, proving that home-based full nodes increase systemic entropy without contributing to consensus integrity. Using a series of formally defined lemmas, propositions, and Monte Carlo simulation results, it is shown that SPV clients represent the rational equilibrium strategy for non-mining participants. This challenges the prevailing narrative that home validators enhance network security, providing formal and operational justifications for the sufficiency of SPV models.