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Brief Announcement
Brief Announcement: Zero-Knowledge Protocols for Search Problems

Authors: Ben Berger and Zvika Brakerski

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)


Abstract
We consider natural ways to extend the notion of Zero-Knowledge (ZK) Proofs beyond decision problems. Specifically, we consider search problems, and define zero-knowledge proofs in this context as interactive protocols in which the prover can establish the correctness of a solution to a given instance without the verifier learning anything beyond the intended solution, even if it deviates from the protocol. The goal of this work is to initiate a study of Search Zero-Knowledge (search-ZK), the class of search problems for which such systems exist. This class trivially contains search problems where the validity of a solution can be efficiently verified (using a single message proof containing only the solution). A slightly less obvious, but still straightforward, way to obtain zero-knowledge proofs for search problems is to let the prover send a solution and prove in zero-knowledge that the instance-solution pair is valid. However, there may be other ways to obtain such zero-knowledge proofs, and they may be more advantageous. In fact, we prove that there are search problems for which the aforementioned approach fails, but still search zero-knowledge protocols exist. On the other hand, we show sufficient conditions for search problems under which some form of zero-knowledge can be obtained using the straightforward way.

Cite as

Ben Berger and Zvika Brakerski. Brief Announcement: Zero-Knowledge Protocols for Search Problems. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 105:1-105:5, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{berger_et_al:LIPIcs.ICALP.2018.105,
  author =	{Berger, Ben and Brakerski, Zvika},
  title =	{{Brief Announcement: Zero-Knowledge Protocols for Search Problems}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{105:1--105:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.105},
  URN =		{urn:nbn:de:0030-drops-91099},
  doi =		{10.4230/LIPIcs.ICALP.2018.105},
  annote =	{Keywords: Zero-Knowledge, Search Problems, Interactive Proofs}
}
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