Incrementally Verifiable Computation or Proofs of Knowledge Imply Time/Space Efficiency
- 1.8k Downloads
A probabilistically checkable proof (PCP) system enables proofs to be verified in time polylogarithmic in the length of a classical proof. Computationally sound (CS) proofs improve upon PCPs by additionally shortening the length of the transmitted proof to be polylogarithmic in the length of the classical proof.
In this paper we explore the ultimate limits of non-interactive proof systems with respect to time and space efficiency. We present a proof system where the prover uses space polynomial in the space of a classical prover and time essentially linear in the time of a classical prover, while the verifier uses time and space that are essentially constant. Further, this proof system is composable: there is an algorithm for merging two proofs of length k into a proof of the conjunction of the original two theorems in time polynomial in k, yielding a proof of length exactly k.
We deduce the existence of our proposed proof system by way of a natural new assumption about proofs of knowledge. In fact, a main contribution of our result is showing that knowledge can be “traded” for time and space efficiency in noninteractive proof systems. We motivate this result with an explicit construction of noninteractive CS proofs of knowledge in the random oracle model.
KeywordsTuring Machine Proof System Random Oracle Random String Random Oracle Model
- 4.Barak, B., Goldreich, O.: Universal Arguments. In: Proc. Complexity (CCC) (2002)Google Scholar
- 5.Ben-Sasson, E., Goldreich, O., Harsha, P., Sudan, M., Vadhan, S.: Robust PCPs of proximity, shorter PCPs and applications to coding. In: STOC 2004, pp. 1–10 (2004)Google Scholar
- 7.Blum, M., Feldman, P., Micali, S.: Non-Interactive Zero-Knowledge and Its Applications (Extended Abstract). In: STOC 1988, pp. 103–112 (1988)Google Scholar
- 8.Canetti, R., Goldreich, O., Halevi, S.: The Random Oracle Methodology, Revisited. In: STOC 1998, pp. 209–218 (1998)Google Scholar
- 9.Fischlin, M.: Communication-efficient non-interactive proofs of knowledge with online extractors. Advances in Cryptology (2005)Google Scholar
- 10.Goldreich, O., Sudan, M.: Locally testable codes and PCPs of almost-linear length. In: FOCS 2002 (2002)Google Scholar
- 12.Kilian, J.: A note on efficient zero-knowledge proofs and arguments. In: STOC, pp. 723–732 (1992)Google Scholar
- 14.Pass, R.: On deniability in the common reference string and random oracle model. In: Advances in Cryptology, pp. 316–337 (2003)Google Scholar