New Impossibility Results for Concurrent Composition and a Non-interactive Completeness Theorem for Secure Computation

  • Shweta Agrawal
  • Vipul Goyal
  • Abhishek Jain
  • Manoj Prabhakaran
  • Amit Sahai
Conference paper

DOI: 10.1007/978-3-642-32009-5_26

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7417)
Cite this paper as:
Agrawal S., Goyal V., Jain A., Prabhakaran M., Sahai A. (2012) New Impossibility Results for Concurrent Composition and a Non-interactive Completeness Theorem for Secure Computation. In: Safavi-Naini R., Canetti R. (eds) Advances in Cryptology – CRYPTO 2012. Lecture Notes in Computer Science, vol 7417. Springer, Berlin, Heidelberg

Abstract

We consider the client-server setting for the concurrent composition of secure protocols: in this setting, a single server interacts with multiple clients concurrently, executing with each client a specified protocol where only the client should receive any nontrivial output. Such a setting is easily motivated from an application standpoint. There are important special cases for which positive results are known – such as concurrent zero knowledge protocols – and it has been an open question whether other natural functionalities such as Oblivious Transfer (OT) are possible in this setting.

In this work:
  • We resolve this open question by showing that unfortunately, even in this very limited concurrency setting, broad new impossibility results hold, ruling out not only OT, but in fact all nontrivial finite asymmetric functionalities. Our new negative results hold even if the inputs of all honest parties are fixed in advance, and the adversary receives no auxiliary information.

  • Along the way, we establish a new unconditional completeness result for asymmetric functionalities, where we characterize functionalities that are non-interactively complete secure against active adversaries. When we say that a functionality \(\mathcal {F}\) is non-interactively complete, we mean that every other asymmetric functionality can be realized by parallel invocations of several copies of \(\mathcal {F}\), with no other communication in any direction. Our result subsumes a completeness result of Kilian [STOC’00] that uses protocols which require additional interaction in both directions.

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Copyright information

© International Association for Cryptologic Research 2012 2012

Authors and Affiliations

  • Shweta Agrawal
    • 1
  • Vipul Goyal
    • 2
  • Abhishek Jain
    • 1
  • Manoj Prabhakaran
    • 3
  • Amit Sahai
    • 1
  1. 1.UCLALos AngelesUSA
  2. 2.Microsoft ResearchBangaloreIndia
  3. 3.UIUCChampaignUSA

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