VdF

A verifiable delay function (VDF) is a cryptographic primitive designed to produce a result that becomes available only after a predetermined amount of time, while allowing anyone to verify the result quickly and efficiently. A VDF must be easy to compute in a sequential manner, meaning that parallel processing does not substantially shorten the required time. In addition to the output, a short, non-interactive proof accompanies the result to enable fast verification that the computation was performed correctly.

A VDF is typically specified by a time parameter t, a computation function F, and a verification procedure. To evaluate a VDF on input x, the evaluator applies F for t sequential steps to obtain an output y, together with a proof π. A verifier can then check, using x, t, y, and π, that y = F_t(x) and that the prescribed sequential process was followed. The key properties are correctness (the output is what the sequential computation yields), sequentiality (speedups from parallelization are limited), and verifiability (the proof can be checked quickly).

Common constructions rely on cryptographic groups or rings where the evaluation requires a long sequence of operations. A widely discussed approach uses sequential squaring in a group of unknown order, with two prominent proof systems—Pietrzak and Wesolowski—to produce succinct proofs of correct computation. These designs aim to provide practical, publicly verifiable delay while maintaining security under standard cryptographic assumptions.

Applications include generating public randomness beacons, improving time-stamped data integrity, enabling delay-based consensus and leader election in distributed systems, and reducing the predictability of certain on-chain activities. Limitations involve reliance on specific mathematical structures, potential setup assumptions, and the need for robust, quantum-resistant developments as cryptographic research advances.