Constant-round interactive proofs for delegating computation

On Doubly-Efficient Interactive Proof Systems

“…6 Hence, Theorem 1.1 is incomparable to the following Theorem 1.2 (doubly-efficient interactive proof systems for SC [42]). Every set that is decidable by an algorithm that runs in polynomial time and has space complexity s such that s(n) < √ n, has a doublyefficient interactive proof system.…”

“…Seeking to make interactive proof systems available for a wider range of applications, Goldwasser, Kalai and Rothblum put forward a notion of doubly-efficient interactive proof systems (also called interactive proofs for muggles [27] and interactive proofs for delegating computation [42]). In these proof systems the prescribed prover strategy can be implemented in polynomial-time and the verifier's strategy can be implemented in almost-linear-time.…”

“…A recent work of Reingold, Rothblum, and Rothblum [42] provided doubly-efficient (constant-round) proof systems for any set that can be decided in polynomial-time and small amount of space (e.g., for all sets in SC). These two results are actually incomparable.…”

“…This interpretation is suitable for Chapter 3 and most of Chapter 2 (i.e., for the results of [27] and [24,25], resp). In contrast, Chapter 4 (following [42]) uses a much more liberal interpretation by which a sequence of functions of the form f : N → N (representing the complexities of a sequence of constructions) is almost linear if f (n) = O(n 1+ ) for every > 0. We mention that these interpretations have been used in the past also in other settings (see discussion in [20,Sec.…”

“…As noted in [42], Theorem 1.2 can be extended to randomized algorithms by first reducing their randomness complexity to linear (using adequate pseudorandom generators), and then letting the verifier toss coins for the derived algorithm and send the outcomes to the prover (asking it to prove membership in the corresponding residual set). 7 A begging open problem is whether the upper bound of s(n) 2 can be replaced by s(n); that is, Problem 1.3 (a possible quantitative improvement of Theorem 1.2).…”