VDF

a verifiable delay function is a function that requires a specified number of sequential steps to compute, cannot be parallelized, and produces a proof that can be verified in much less time than the computation itself

VDFs prove minimum elapsed time without trusted clocks. the output is deterministic — given the same input and delay parameter, every evaluator produces the same result. the proof convinces any verifier that the evaluator performed the sequential work

construction

a typical VDF consists of three algorithms:

• setup(T) — produces public parameters for delay parameter T
• eval(x, T) — computes output y and proof π after T sequential steps
• verify(x, y, π) — checks the proof in O(log T) or O(1) time

the sequential nature comes from iterated squaring in groups of unknown order, or from iterated hashing in a hash chain. the key property: no amount of parallelism reduces the wall-clock time below T steps

role in cyber

cyber uses VDFs for rate limiting and temporal ordering. a neuron attaches a VDF proof to its signal to demonstrate that real time has elapsed between consecutive emissions. this prevents burst flooding without requiring synchronized clocks or a central rate limiter

foculus leverages VDF proofs as one input to the timing model — they provide a lower bound on the real time between events, anchoring the asynchronous gossip protocol to physical time

see hash chain for the iterated hash construction. see signal for the emission mechanism. see foculus for how VDF proofs integrate with consensus