On the doubly-efficient interactive proof systems of GKR

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We present a somewhat simpler variant of the doubly-efficient interactive proof systems of Goldwasser, Kalai, and Rothblum (JACM, 2015). Recall that these proof systems apply to log-space uniform sets in NC (or, more generally, to inputs that are acceptable by log-space uniform bounded-depth circuits, where the number of rounds in the proof system is linearly related to the depth of the circuit). Our simplification is in the handling of the log-space uniformity condition. Rather than having the prover provide the verifier with bits of the encoding of the circuit and establish their correctness, we employ the proof system to a highly regular universal circuit that constructs and evaluates the log-space uniform circuit in question.

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