Paper 2026/2001

The Price of Time: Deterrence as the Third Pillar of Payment Channel Security

Abstract

Safety and liveness are the two classical pillars of payment channel security. Both price attacks that merely occupy channel resources, such as jamming, at zero. We propose a third pillar, deterrence: harm carries a provable price. We give its theory for occupied shared-state resources. Within a holding-cost framework, we characterize occupation pricing for lock-resolve channels. Time-dependence in the occupier's liability is necessary for any deterrence: today's time-independent pricing admits unbounded griefing, with damage-to-cost ratios above 10^7. Linear time-proportional liability achieves the tight rate. Its two faces, deadline-proportional upfront fees and hold-proportional penalty bonds, differ exactly in what they charge honest traffic. Our main theorem maps the landscape of four desiderata: deterrence against colluding sinks, penalty-only honesty, zero intermediary lockup, and path privacy. Three of them are jointly unachievable, and every remaining combination is achieved by a matching construction; onion-message fee-swallowing gives a second enforcement instance. Single-channel enforcement is characterized exactly: penalty-only pricing is unilaterally enforceable if and only if scripts expose time. The proof is a three-case exhaustion, and it explains why pre-BIP65 Bitcoin could not support trustless occupation pricing. Our flagship fused-bond construction runs on Bitcoin today, with no covenants, oracles, or miner assumptions; it improves slot-jamming deterrence by eight orders of magnitude at zero net cost to punctual honest payments. For multi-hop payments we prove the forwarding trilemma, settling a 2020 conjecture of the Lightning engineering community, and we quantify the price of privacy, including a new O(1/n) extreme-value side channel on the sender's path length.