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Theory of Cryptography Conference

TCC 2006: Theory of Cryptography pp 1–20Cite as

Concurrent Zero Knowledge Without Complexity Assumptions

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Part of the Lecture Notes in Computer Science book series (LNSC,volume 3876)

Abstract

We provide unconditional constructions of concurrent statistical zero-knowledge proofs for a variety of non-trivial problems (not known to have probabilistic polynomial-time algorithms). The problems include Graph Isomorphism, Graph Nonisomorphism, Quadratic Residuosity, Quadratic Nonresiduosity, a restricted version of Statistical Difference, and approximate versions of the (coNP forms of the) Shortest Vector Problem and Closest Vector Problem in lattices.

For some of the problems, such as Graph Isomorphism and Quadratic Residuosity, the proof systems have provers that can be implemented in polynomial time (given an NP witness) and have Õ(log n) rounds, which is known to be essentially optimal for black-box simulation.

To the best of our knowledge, these are the first constructions of concurrent zero-knowledge proofs in the plain, asynchronous model (i.e., without setup or timing assumptions) that do not require complexity assumptions (such as the existence of one-way functions).

Keywords

  • Proof System
  • Graph Isomorphism
  • Commitment Scheme
  • Complexity Assumption
  • Zero Knowledge

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.

A full version of this paper is available [1].

The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-540-32732-5_32

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Author information

Authors and Affiliations

  1. University of California, San Diego, La Jolla, CA, 92093, USA

    Daniele Micciancio

  2. Harvard University, Cambridge, MA, 02138, USA

    Shien Jin Ong & Salil Vadhan

  3. University of California, Los Angeles, CA, 90095, USA

    Amit Sahai

Authors
  1. Daniele Micciancio
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  2. Shien Jin Ong
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  3. Amit Sahai
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  4. Salil Vadhan
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Editor information

Editors and Affiliations

  1. IBM Research, Hawthorne, NY, USA

    Shai Halevi

  2. IBM T.J.Watson Research Center, Hawthorne, NY, USA

    Tal Rabin

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Micciancio, D., Ong, S.J., Sahai, A., Vadhan, S. (2006). Concurrent Zero Knowledge Without Complexity Assumptions. In: Halevi, S., Rabin, T. (eds) Theory of Cryptography. TCC 2006. Lecture Notes in Computer Science, vol 3876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11681878_1

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  • DOI: https://doi.org/10.1007/11681878_1

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