Safe Low Bandwidth SPV: A Formal Treatment of Simplified Payment Verification Protocols and Security Bounds
Journal:
arXiv
Published Date:
Jul 1, 2025
Abstract
This paper presents a complete formal specification, protocol description,
and mathematical proof structure for Simplified Payment Verification (SPV) as
originally defined in the Bitcoin whitepaper \cite{nakamoto2008}. In stark
contrast to the misrepresentations proliferated by popular implementations, we
show that SPV is not only secure under bounded adversarial assumptions but
strictly optimal for digital cash systems requiring scalable and verifiable
transaction inclusion. We reconstruct the SPV protocol from first principles,
grounding its verification model in symbolic automata, Merkle membership
relations, and chain-of-proof dominance predicates. Through rigorous
probabilistic and game-theoretic analysis, we derive the economic bounds within
which the protocol operates securely and verify its liveness and safety
properties under partial connectivity, hostile relay networks, and adversarial
propagation delay. Our specification further introduces low-bandwidth
optimisations such as adaptive polling and compressed header synchronisation
while preserving correctness. This document serves both as a blueprint for
secure SPV implementation and a rebuttal of common misconceptions surrounding
non-validating clients.
