Skip to main content
SpringerLink
Log in
Book cover

Conference on Computability in Europe

CiE 2008: Logic and Theory of Algorithms pp 175–185Cite as

Succinct NP Proofs from an Extractability Assumption

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5028))

Abstract

We prove, using a non-standard complexity assumption, that any language in has a 1-round (that is, the verifier sends a message to the prover, and the prover sends a message to the verifier) argument system (that is, a proof system where soundness holds against polynomial-time provers) with communication complexity only polylogarithmic in the size of the instance. We also show formal evidence that the nature of the non-standard complexity assumption we use is analogous to previous assumptions proposed in the cryptographic literature. The question of whether complexity assumptions of this nature can be considered acceptable or not remains of independent interest in complexity-theoretic cryptography as well as complexity theory.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aiello, W., Bhatt, S.N., Ostrovsky, R., Rajagopalan, S.R.: Fast Verification of Remote procedure Calls: Short Witness-Indistinguishable One-Round Proofs for . In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  2. Arora, S., Safra, S.: Probabilistic Checking of Proofs: A New Characterization of NP. Journal of the ACM 45(1), 70–122 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  3. 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)

    Article  MATH  MathSciNet  Google Scholar 

  4. Babai, L., Moran, S.: Arthur-Merlin Games: a Randomized Proof System, and a Hierarchy of Complexity Classes. Journal of Computer and System Sciences 36, 254–276 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  5. Barak, B., Goldreich, O.: Universal Arguments and Their Applications. In: Proc. of IEEE Conference on Computational Complexity (2002)

    Google Scholar 

  6. Biehl, I., Meyer, B., Wetzel, S.: Ensuring the Integrity of Agent-Based Computation by Short Proofs. In: Proc. of Mobile Agents 1998. LNCS. Springer, Heidelberg (1998)

    Google Scholar 

  7. Brassard, G., Chaum, D., Crépeau, C.: Minimum Disclosure Proofs of Knowledge. Journal of Computer and System Sciences 37(2), 156–189 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  8. Cachin, C., Micali, S., Stadler, M.: Computationally Private Information Retrieval with Polylogarithmic Communication. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592. Springer, Heidelberg (1999)

    Google Scholar 

  9. Damgård, I.: Towards Practical Public-key Systems Secure against Chosen Ciphertext Attack. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576. Springer, Heidelberg (1992)

    Google Scholar 

  10. Di Crescenzo, G.: Extractability Complexity Assumptions (August 2006) (unpublished manuscript)

    Google Scholar 

  11. Dwork, C., Langberg, M., Naor, M., Nissim, K., Reingold, O.: Succinct NP Proofs and Spooky Interactions (December 2004) (unpublished manuscript)

    Google Scholar 

  12. Goldwasser, S., Micali, S., Rackoff, C.: The Knowledge Complexity of Interactive Proof-Systems. SIAM Journal on Computing 18(1) (1989)

    Google Scholar 

  13. Gentry, C., Ramzan, Z.: Single-Database Private Information Retrieval with Constant Communication Rate. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580. Springer, Heidelberg (2005)

    Google Scholar 

  14. Hada, S., Tanaka, T.: On the existence of 3-round Zero-Knowledge Protocols. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462. Springer, Heidelberg (1998)

    Google Scholar 

  15. Kilian, J.: A note on Efficient Zero-knowledge Priifs and Arguments. In: Proc. of ACM STOC 1991 (1991)

    Google Scholar 

  16. Kushilevitz, E., Ostrovsky, R.: Replication is not needed: Single Database, computationally-private information retrieval. In: Proc. of 38th IEEE FOCS 1997 (1997)

    Google Scholar 

  17. Laur, S., Lipmaa, H.: Consistent Adaptive Two-Party Computations, Cryptology ePrint Archive, Report 2006/088 (2006)

    Google Scholar 

  18. Lipmaa, H.: An Oblivious Transfer Protocol with Log-Squared Communication. In: Zhou, J., López, J., Deng, R.H., Bao, F. (eds.) ISC 2005. LNCS, vol. 3650. Springer, Heidelberg (2005)

    Google Scholar 

  19. Merkle, R.: A Certified Digital Signature. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435. Springer, Heidelberg (1990)

    Google Scholar 

  20. Micali, S.: CS proofs. In: Proc. of 35th IEEE FOCS 1994 (1994)

    Google Scholar 

  21. Russell, A.: Necessary and Sufficient Conditions for Collision-Free Hashing. J. Cryptology 8(2), 87–100 (1995)

    MATH  MathSciNet  Google Scholar 

  22. Samorodnitsky, A., Trevisan, L.: A PCP characterization of NP with Optimal Amortized Query Complexity. In: Proc. of the 32nd ACM STOC 2000 (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Telcordia Technologies, Piscataway, NJ, USA

    Giovanni Di Crescenzo

  2. University College London, London, UK

    Helger Lipmaa

Authors
  1. Giovanni Di Crescenzo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Helger Lipmaa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Arnold Beckmann Costas Dimitracopoulos Benedikt Löwe

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Di Crescenzo, G., Lipmaa, H. (2008). Succinct NP Proofs from an Extractability Assumption. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-69407-6_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69405-2

  • Online ISBN: 978-3-540-69407-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation