Computational two-party correlation: A dichotomy for key-agreement protocols

Iftach Haitner, Kobbi Nissim, Eran Omri, Ronen Shaltiel, Jad Silbak

Research output: Contribution to journalArticlepeer-review

Abstract

Let π be an efficient two-party protocol that, given security parameter κ, both parties output single bits Xκ and Yκ, respectively. We are interested in how (Xκ, Yκ) “appears” to an efficient adversary that only views the transcript Tκ. We make the following contributions: (a) We develop new tools to argue about this loose notion and show (modulo some caveats) that for every such protocol π, there exists an efficient simulator such that the following holds: on input Tκ, the simulator outputs a pair (Xκ0, Yκ0) such that (Xκ0, Yκ0, Tκ) is (somewhat) computationally indistinguishable from (Xκ, Yκ, Tκ). (b) We use these tools to prove the following dichotomy theorem: every such protocol π is either uncorrelated-it is (somewhat) indistinguishable from an efficient protocol whose parties interact to produce Tκ, but then choose their outputs independently from some product distribution (that is determined in poly-time from Tκ), or the protocol implies a key-agreement protocol (for infinitely many κ's). Uncorrelated protocols are uninteresting from a cryptographic viewpoint, as the correlation between outputs is (computationally) trivial. Our dichotomy shows that every protocol is either completely uninteresting or implies key-agreement. (c) We use the above dichotomy to make progress on open problems on minimal cryptographic assumptions required for differentially private mechanisms for the XOR function. (d) A subsequent work [I. Haitner, N. Makriyannis, and E. Omri, in Theory of Cryptography Conference, Springer, Cham, Switzerland, 2018, pp. 539-562] uses the above dichotomy to makes progress on a long-standing open question regarding the complexity of fair two-party coin-flipping protocols. We also highlight the following two ideas regarding our technique: (a) The simulator algorithm is obtained by a carefully designed “competition” between efficient algorithms attempting to forecast (Xκ, Yκ)|=t. The winner is used to simulate the outputs of the protocol. (b) Our key-agreement protocol uses the simulation to reduce to an information theoretic setup and is, in some sense, a non-black-box.

Original languageEnglish
Pages (from-to)1041-1082
Number of pages42
JournalSIAM Journal on Computing
Volume49
Issue number6
DOIs
StatePublished - 2020

Bibliographical note

Funding Information:
∗Received by the editors January 4, 2019; accepted for publication (in revised form) July 30, 2020; published electronically November 3, 2020. https://doi.org/10.1137/19M1236837 Funding: The first and fifth authors were supported by ERC starting grant 638121. The second author was supported by NSF grant CNS-1565387. The third author was supported by ISF grants 544/13 and 152/17. The fourth and fifth authors were supported by ISF grant 1628/17. †Department of Computer Science, Tel Aviv University, Tel Aviv, 69978 (iftachh@cs.tau.ac.il, jadsilbak@mail.tau.ac.il). ‡Department of Computer Science, Georgetown University, Washington D.C. 20057 USA (kobbi. nissim@georgetown.edu). §Department of Computer Science and Mathematics, Ariel University, Ariel, 40700 (omrier@ariel. ac.il). ¶Department of Computer Science, University of Haifa, Haifa, 31905 (ronen@cs.haifa.ac.il).

Publisher Copyright:
© 2020 Society for Industrial and Applied Mathematics

Keywords

  • Cryptography
  • Differential privacy
  • Key-agreement
  • Simulation

ASJC Scopus subject areas

  • Computer Science (all)
  • Mathematics (all)

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