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Zero Knowledge LTCs and Their Applications

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2013, RANDOM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8096))

Abstract

Locally testable codes (LTCs) are error-correcting codes for which membership in the code can be tested by probing few symbols of a purported codeword. Motivated by applications in cryptography, we initiate the study of zero knowledge locally testable codes (ZK-LTCs). ZK-LTCs are LTCs which admit a randomized encoding function, such that even a malicious tester which reads a large number of codeword symbols learns essentially nothing about the encoded message.

We obtain ZK-LTCs with good parameters by applying general transformations to standard LTCs. We also obtain LTCs and ZK-LTCs which are stable in the sense that they limit the influence of adaptively corrupted symbols on the output of the testing procedure.

Finally, we apply stable ZK-LTCs for obtaining protocols for verifiable secret sharing (VSS) in which the communication complexity required for verifying a shared secret is sublinear in the secrecy threshold. We also obtain the first statistically secure VSS protocols and distributed coin-flipping protocols which use n servers, tolerate a constant fraction of corrupted servers, and have error that vanishes almost exponentially with n using only O(n) bits of communication. These improve over previous VSS and coin-flipping protocols from the literature, which require nearly quadratic communication to achieve similar guarantees.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Technion, Haifa, Israel

    Yuval Ishai, Michael Viderman & Mor Weiss

  2. Computer Science Department, UCLA, USA

    Amit Sahai

Authors
  1. Yuval Ishai
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  2. Amit Sahai
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  3. Michael Viderman
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  4. Mor Weiss
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Editor information

Editors and Affiliations

  1. University of California, Berkeley, CA, USA

    Prasad Raghavendra

  2. Dept. of computer Science and Engineering, Pennsylvania State University, University Park, PA, USA

    Sofya Raskhodnikova

  3. Institute of Computer Science, University of Kiel, 24118, Kiel, Germany

    Klaus Jansen

  4. University of Geneva, Centre Universitaire d’Informatique, 1227, Carouge, Switzerland

    José D. P. Rolim

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Ishai, Y., Sahai, A., Viderman, M., Weiss, M. (2013). Zero Knowledge LTCs and Their Applications. In: Raghavendra, P., Raskhodnikova, S., Jansen, K., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2013 2013. Lecture Notes in Computer Science, vol 8096. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40328-6_42

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  • DOI: https://doi.org/10.1007/978-3-642-40328-6_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40327-9

  • Online ISBN: 978-3-642-40328-6

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