How Hard Are Verifiable Delay Functions?
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Verifiable delay functions (VDF) are functions that enable a verifier to verify if a prover has spent a specified number of sequential steps to execute the function. VDFs are useful in several applications ranging from non-interactive time-stamping to randomness beacons. A close resemble of VDFs are interactive proofs, however have the following difference. VDFs stand sequential against a prover using even poly(T ) parallelism to evaluate the function for T sequential steps. We know that the class of all interactive proofs IP = PSPACE. Then it seems natural to ask this question that how hard are VDFs? Equivalently does this sequentiality against parallel provers add more power to a Turing machine deciding larger class of languages than IP? In this paper, we show that the class of all the VDFs, VDF does not belong to IP. In particular, we construct a VDF from an EXP-complete language and reduce the EXP-complete language to the derived VDF. Thus if VDF belongs to PSPACE = IP then EXP belongs to PSPACE = IP which has no proof yet. So VDF does not belong to IP.
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