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Non-malleable Codes from Average-Case Hardness: \({\mathsf {A}}{\mathsf {C}}^0\), Decision Trees, and Streaming Space-Bounded Tampering

  • Marshall Ball
  • Dana Dachman-Soled
  • Mukul Kulkarni
  • Tal Malkin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10822)

Abstract

We show a general framework for constructing non-malleable codes against tampering families with average-case hardness bounds. Our framework adapts ideas from the Naor-Yung double encryption paradigm such that to protect against tampering in a class \({\mathcal {F}}\), it suffices to have average-case hard distributions for the class, and underlying primitives (encryption and non-interactive, simulatable proof systems) satisfying certain properties with respect to the class.

We instantiate our scheme in a variety of contexts, yielding efficient, non-malleable codes (NMC) against the following tampering classes:
  • Computational NMC against \({\mathsf {A}}{\mathsf {C}}^0\) tampering, in the CRS model, assuming a PKE scheme with decryption in \({\mathsf {A}}{\mathsf {C}}^0\) and NIZK.

  • Computational NMC against bounded-depth decision trees (of depth \(n^\epsilon \), where n is the number of input variables and constant \(0<\epsilon <1\)), in the CRS model and under the same computational assumptions as above.

  • Information theoretic NMC (with no CRS) against a streaming, space-bounded adversary, namely an adversary modeled as a read-once branching program with bounded width.

Ours are the first constructions that achieve each of the above in an efficient way, under the standard notion of non-malleability.

Notes

Acknowledgments

We are grateful to Benjamin Kuykendall for his helpful comments.

The first and fourth authors are supported in part by the Defense Advanced Research Project Agency (DARPA) and Army Research Office (ARO) under Contract #W911NF-15-C-0236, and NSF grants #CNS-1445424 and #CCF-1423306 and the Leona M. & Harry B. Helmsley Charitable Trust. The second and third authors are supported in part by an NSF CAREER Award #CNS-1453045, by a research partnership award from Cisco and by financial assistance award 70NANB15H328 from the U.S. Department of Commerce, National Institute of Standards and Technology. This work was performed, in part, while the first author was visiting IDC Herzliya’s FACT center and supported in part by ISF grant no. 1790/13 and the Check Point Institute for Information Security. Any opinions, findings and conclusions or recommendations expressed are those of the authors and do not necessarily reflect the views of the the Defense Advanced Research Projects Agency, Army Research Office, the National Science Foundation, or the U.S. Government.

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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  • Marshall Ball
    • 1
  • Dana Dachman-Soled
    • 2
  • Mukul Kulkarni
    • 2
  • Tal Malkin
    • 1
  1. 1.Columbia UniversityNew YorkUSA
  2. 2.University of MarylandCollege ParkUSA

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