Verifiable Delay Function Based on Non-linear Hybrid Cellular Automata

A Verifiable Delay Function (VDF) is a function that takes a specified (typically long) sequential time to be evaluated but can be efficiently verified. VDFs are useful in several applications ranging from randomness beacons to sustainable blockchains. However, VDFs are really rare in practice as they need computational problems that are inherently sequential. At present, we are aware of only two such problems, a group of unknown orders [16, 18] and isogenies over super-singular curves [8]. In this paper, we show that nonlinear hybrid cellular automata (NHCA) also turns out to be another option to derive VDF. The sequentiality comes from the fact that a state in an NHCA can be reached from another state only sequentially. As the key reason behind this sequentiality, we prove that NHCA produces a sequence of random unbiased bit-strings that cannot be accessed arbitrarily. Therefore, the only way to reach a state from another state is to enumerate all the intermediate states sequentially. We also establish that our VDF is appropriately sound.