Abstract
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.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Arora, S., Lund, C., Motwani, R., Sudan, M., Szegedy, M.: Proof verification and the hardness of approximation problems. Journal of the ACM 45(3), 501–555 (1998)
Arora, S., Safra, S.: Probabilistic checking of proofs: A new characterization of NP. Journal of the ACM 45(1), 70–122 (1998)
Babai, L., Fortnow, L., Lund, C.: Non-deterministic exponential time has two-prover interactive protocols. Computational Complexity 1, 3–40 (1991)
Barak, B., Goldreich, O.: Universal Arguments. In: Proc. Complexity (CCC) (2002)
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)
Blum, M., De Santis, A., Micali, S., Persiano, G.: Noninteractive Zero-Knowledge. SIAM J. Comput. 20(6), 1084–1118 (1991)
Blum, M., Feldman, P., Micali, S.: Non-Interactive Zero-Knowledge and Its Applications (Extended Abstract). In: STOC 1988, pp. 103–112 (1988)
Canetti, R., Goldreich, O., Halevi, S.: The Random Oracle Methodology, Revisited. In: STOC 1998, pp. 209–218 (1998)
Fischlin, M.: Communication-efficient non-interactive proofs of knowledge with online extractors. Advances in Cryptology (2005)
Goldreich, O., Sudan, M.: Locally testable codes and PCPs of almost-linear length. In: FOCS 2002 (2002)
Goldwasser, S., Micali, S., Rackoff, C.: The Knowledge Complexity of Interactive Proof Systems. SIAM J. on Computing 18(1), 186–208 (1989)
Kilian, J.: A note on efficient zero-knowledge proofs and arguments. In: STOC, pp. 723–732 (1992)
Micali, S.: Computationally Sound Proofs. SIAM J. Computing 30(4), 1253–1298 (2000)
Pass, R.: On deniability in the common reference string and random oracle model. In: Advances in Cryptology, pp. 316–337 (2003)
Shamir, A.: IP = PSPACE. Journal of the ACM 39(4), 869–877 (1992)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Valiant, P. (2008). Incrementally Verifiable Computation or Proofs of Knowledge Imply Time/Space Efficiency. In: Canetti, R. (eds) Theory of Cryptography. TCC 2008. Lecture Notes in Computer Science, vol 4948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78524-8_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-78524-8_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78523-1
Online ISBN: 978-3-540-78524-8
eBook Packages: Computer ScienceComputer Science (R0)