On the concrete efficiency of probabilistically-checkable proofs
Eli Ben‐Sasson, Alessandro Chiesa, Daniel Genkin, Eran Tromer · 2013
Probabilistically-Checkable Proofs (PCPs) form the algorithmic core that enables fast verification of long computations in many cryptographic constructions. Yet, despite the wonderful asymptotic savings they bring, PCPs are also the infamous computational bottleneck preventing these powerful cryptographic constructions from being used in practice. To address this problem, we present several results about the computational efficiency of PCPs. We construct the first PCP where the prover and verifier time complexities are quasi-optimal (i.e., optimal up to poly-logarithmic factors). The prover and verifier are also higly-parallelizable, and these computational guarantees hold even when proving and verifying the correctness of random-access machine computations. Our construction is explicit and has the requisite properties for being used in the cryptographic applications mentioned above.