[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content

Zero Knowledge and Circuit Minimization

  • Conference paper
Mathematical Foundations of Computer Science 2014 (MFCS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8635))

Abstract

We show that every problem in the complexity class SZK (Statistical Zero Knowledge) is efficiently reducible to the Minimum Circuit Size Problem (MCSP). In particular Graph Isomorphism lies in RP MCSP.

This is the first theorem relating the computational power of Graph Isomorphism and MCSP, despite the long history these problems share, as candidate NP-intermediate problems.

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

Access this chapter

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
GBP 19.95
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
GBP 35.99
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
GBP 44.99
Price includes VAT (United Kingdom)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Allender, E., Buhrman, H., Koucký, M., van Melkebeek, D., Ronneburger, D.: Power from random strings. SIAM Journal on Computing 35, 1467–1493 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  2. Arvind, V., Das, B.: SZK proofs for black-box group problems. Theory Comput. Syst. 43(2), 100–117 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  3. Arvind, V., Torán, J.: Isomorphism testing: Perspective and open problems. Bulletin of the EATCS 86 (2005)

    Google Scholar 

  4. Boppana, R.B., Håstad, J., Zachos, S.: Does co-NP have short interactive proofs? Information Processing Letters 25(2), 127–132 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  5. Ben-Or, M., Gutfreund, D.: Trading help for interaction in statistical zero-knowledge proofs. J. Cryptology 16(2), 95–116 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chailloux, A., Ciocan, D.F., Kerenidis, I., Vadhan, S.P.: Interactive and noninteractive zero knowledge are equivalent in the help model. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 501–534. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  7. Cook, S.A.: The complexity of theorem-proving procedures. In: ACM Symposium on Theory of Computing (STOC), pp. 151–158 (1971)

    Google Scholar 

  8. Goldreich, O., Micali, S., Wigderson, A.: Proofs that yield nothing but their validity for all languages in NP have zero-knowledge proof systems. Journal of the ACM 38(3), 691–729 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  9. Håstad, J., Impagliazzo, R., Levin, L., Luby, M.: A pseudorandom generator from any one-way function. SIAM Journal on Computing 28, 1364–1396 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  10. Kabanets, V., Cai, J.-Y.: Circuit minimization problem. In: ACM Symposium on Theory of Computing (STOC), pp. 73–79 (2000)

    Google Scholar 

  11. Kapron, B., Malka, L., Srinivasan, V.: A characterization of non-interactive instance-dependent commitment-schemes (NIC). In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 328–339. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  12. Krajíček, J.: Forcing with Random Variables and Proof Complexity. Cambridge University Press (2011)

    Google Scholar 

  13. Köbler, J., Schöning, U., Torán, J.: The Graph Isomorphism Problem: Its Structural Complexity. Birkhauser Verlag, Basel (1993)

    Book  MATH  Google Scholar 

  14. Levin, L.A.: Universal sequential search problems. Problems of Information Transmission 9, 265–266 (1973)

    Google Scholar 

  15. Levin, L.: Personal communication (2003)

    Google Scholar 

  16. Pemmaraju, S., Skiena, S.: Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Cambridge University Press, New York (2003)

    Book  Google Scholar 

  17. Razborov, A., Rudich, S.: Natural proofs. Journal of Computer and System Sciences 55, 24–35 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  18. Trakhtenbrot, B.A.: A survey of Russian approaches to perebor (brute-force searches) algorithms. IEEE Annals of the History of Computing 6(4), 384–400 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  19. Variyam, V.N.: Nondeterministic circuit minimization problem and derandomizing Arthur-Merlin games. Int. J. Found. Comput. Sci. 16(6), 1297–1308 (2005)

    Article  Google Scholar 

  20. Wikipedia (2014), http://en.wikipedia.org/wiki/NP-intermediate

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Allender, E., Das, B. (2014). Zero Knowledge and Circuit Minimization. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44465-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-44465-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44464-1

  • Online ISBN: 978-3-662-44465-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics