Single-Query Verifiable Proof-of-Sequential-Work (2202.10295v2)

Abstract: We propose a proof-of-sequential-work (PoSW) that can be verified with only a single query to the random oracle for each random challenge. Proofs-of-sequential-work are protocols that facilitate a verifier to efficiently verify if a prover has executed a specified number of computations sequentially. Denoting this number of sequential computations with N , the prover with poly(N) parallelism must take $\Omega(N)$-sequential time while the verifier verifies the computation in O(log N)-sequential time using upto O(log N) parallelism. We propose a PoSW that allows any verifier, even the one with no parallelism, to verify using just a single sequential computation on a single challenge. All the existing PoSWs [10, 5, 2, 6] mandate a prover to compute a sequence of responses from a random oracle against N-rounds of queries. Then the prover commits this sequence using a commitment scheme (e.g., Merkle root (like) commitment) predefined in the PoSWs. Now the verifier asks the prover to provide a set of proofs against t randomly chosen checkpoints, called challenges, in the computed sequence. The verifier finds out the commitment from each of these proofs spending O(log N) rounds of queries to the oracle. It can be reduced to a single round of queries only if the verifier owns O(log N) parallelism [6]. The verifier in our PoSW demands no parallelism but uses a single query to the random oracle in order to verify each of the t challenges. The key observation is that the commitment schemes themselves in the prior works demand O(log N ) oracle queries to verify.