Interactive proofs, introduced by Goldwasser, Micali and Rackoff, have had a dramatic impact on Complexity Theory and Cryptography. In particular, the celebrated IP=PSPACE Theorem [LFKN92,Shamir92] allows an all-powerful but untrusted prover to convince a polynomial-time verifier of the validity of extremely complicated statements (as long as they can be evaluated using polynomial space). The interactive proof system designed for this purpose requires a large number of communication rounds and heavy computation for generating the proof.
We introduce new interactive proofs that are very efficient in the number of rounds and computation time, that are particularly well suited for delegating bounded-space computations (e.g., in the context of cloud computing). Our main result is that for every statement that can be evaluated in polynomial time and bounded-polynomial space there exists an interactive proof that satisfies the following strict efficiency requirements:
(1) the honest prover runs in polynomial time, (2) the verifier is almost linear time (and under some conditions
even sub linear), and (3) the interaction consists of only a constant number of communication rounds. Prior to this work, very little was known about the power of efficient, constant-round interactive proofs.
Joint work with Omer Reingold and Guy Rothblum