Revision #1 Authors: Omer Reingold, Ron Rothblum, Guy Rothblum

Accepted on: 3rd May 2016 14:37

Downloads: 705

Keywords:

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

polynomial number of communication rounds and an exponential-time

(polynomial-space complete) prover. In this paper, we study the

power of more efficient interactive proof systems.

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 (rather than arguments). This

result represents significant progress on the round complexity of

interactive proofs (even if we ignore the running time of the

honest prover), and on the expressive power of interactive proofs

with polynomial-time honest prover (even if we ignore the round

complexity). This result has several applications, and in

particular it can be used for verifiable delegation of

computation.

Our construction leverages several new notions of interactive

proofs, which may be of independent interest. One of these

notions is that of unambiguous interactive proofs where the

prover has a unique successful strategy. Another notion is that

of probabilistically checkable interactive proofs (PCIPs) where

the verifier only reads a few bits of the transcript in checking

the proof (this could be viewed as an interactive extension of

PCPs).

Minor changes

TR16-061 Authors: Omer Reingold, Ron Rothblum, Guy Rothblum

Publication: 17th April 2016 19:40

Downloads: 876

Keywords:

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 polynomial number of communication rounds and an exponential-time (polynomial-space complete) prover. In this paper, we study the power of more efficient interactive proof systems.

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. This result represents significant progress on the round complexity of interactive proofs (even if we ignore the running time of the honest prover), and on the expressive power of interactive proofs with polynomial-time honest prover (even if we ignore the round complexity). This result has several applications, and in particular it can be used for verifiable delegation of computation.

Our construction leverages several new notions of interactive proofs, which may be of independent interest. One of these notions is that of unambiguous interactive proofs where the prover has a unique successful strategy. Another notion is that of probabilistically checkable interactive proofs (PCIPs) where the verifier only reads a few bits of the transcript in checking the proof (this could be viewed as an interactive extension of PCPs).