Paper 2026/2176

Budgeted Threshold Signatures: Protocol-Native Spending Limits with Zero On-Chain Footprint

Abstract

Spending limits are the workhorse of custody policy, yet in every deployed threshold-signing stack they live outside the signing protocol—in centralized policy engines, on-chain covenants, or hardware co-signers—where they leak budget state, bind to a single chain, or add a trusted bypass surface. The workload is compounding: agent payments passed one hundred million transfers on a single chain in under a year. We initiate the study of protocol-native spending limits: per-epoch budgets secret-shared among the signers and enforced inside the signing session, with unchanged on-chain verification. We first show that the natural approach fails: gating a threshold signature with a passively secure MPC comparison admits a deterministic bypass. For the class of linear gatein-combination protocols we prove that every member signs over-budget transactions with probability one, disguised against any transcript auditor up to the statistical masking bound. We then construct BTS, a budgeted threshold Schnorr scheme with a formal budget-soundness definition for honest-majority configurations. The gap is closed with an authenticated gate: in implementation, every attack attempt is caught before a signature is produced, at a measured cost of 3.4–3.7× multiplications and five extra rounds. Batched over k=20 payments, enforcement amortizes to about one network round trip per payment in our WANmodeled prototype.