Economic Security of VDF-Based Randomness Beacons: Models, Thresholds, and Design Guidelines

Randomness beacons based on Verifiable Delay Functions (VDFs) are increasingly proposed for blockchains and distributed systems, promising publicly verifiable delay and bias resistance. Existing analyses, however, treat adversaries purely as cryptographic entities and overlook that real attackers are economically motivated. A VDF may be sequentially secure, yet still vulnerable if a rational adversary can profit by purchasing faster hardware and exploiting reward spikes such as MEV opportunities. We develop a formal framework for economic security of VDF-based randomness beacons. Modeling the attacker as a rational agent facing hardware speedup, operating costs, and stochastic rewards, we cast the attack decision as an optimal-stopping problem and prove that optimal behavior has a monotone threshold structure. This yields tight necessary and sufficient conditions relating delay parameters to adversarial cost and reward distributions. We extend the analysis to grinding, selective abort, and multi-adversary competition, demonstrating how each amplifies effective rewards and increases required delays. Using realistic cloud costs, hardware benchmarks, and MEV data, we show that many proposed VDF delays, on the order of a few seconds, are economically insecure under plausible conditions. We conclude with deployable guidelines and introduce Economically Secure Delay Parameters (ESDPs) to support principled parameter selection in practical systems.