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We study the problem of building a verifiable delay function (VDF). A requires a specified number of sequential steps to evaluate, yet produces a unique output that can be efficiently and publicly verified. s have many applications in decentralized systems, including public randomness beacons, leader election in consensus protocols, and proofs of replication. We formalize the requirements for s and present new candidate constructions that are the first to achieve an exponential gap between evaluation and verification time.