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From Laconic Zero-Knowledge to Public-Key Cryptography

Extended Abstract
  • Itay Berman
  • Akshay Degwekar
  • Ron D. Rothblum
  • Prashant Nalini Vasudevan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10993)

Abstract

Since its inception, public-key encryption (\(\mathsf {PKE}\)) has been one of the main cornerstones of cryptography. A central goal in cryptographic research is to understand the foundations of public-key encryption and in particular, base its existence on a natural and generic complexity-theoretic assumption. An intriguing candidate for such an assumption is the existence of a cryptographically hard language Open image in new window .

In this work we prove that public-key encryption can be based on the foregoing assumption, as long as the (honest) prover in the zero-knowledge protocol is efficient and laconic. That is, messages that the prover sends should be efficiently computable (given the Open image in new window witness) and short (i.e., of sufficiently sub-logarithmic length). Actually, our result is stronger and only requires the protocol to be zero-knowledge for an honest-verifier and sound against computationally bounded cheating provers.

Languages in Open image in new window with such laconic zero-knowledge protocols are known from a variety of computational assumptions (e.g., Quadratic Residuocity, Decisional Diffie-Hellman, Learning with Errors, etc.). Thus, our main result can also be viewed as giving a unifying framework for constructing \(\mathsf {PKE}\) which, in particular, captures many of the assumptions that were already known to yield \(\mathsf {PKE}\).

We also show several extensions of our result. First, that a certain weakening of our assumption on laconic zero-knowledge is actually equivalent to \(\mathsf {PKE}\), thereby giving a complexity-theoretic characterization of \(\mathsf {PKE}\). Second, a mild strengthening of our assumption also yields a (2-message) oblivious transfer protocol.

Notes

Acknowledgments

We thank Vinod Vaikuntanathan for his encouragement and for helpful discussions. We thank the anonymous reviewers for very useful comments and in particular for suggesting the abstraction of trapdoor pseudoentropy generator.

Research supported in part by NSF Grants CNS-1413920 and CNS-1350619, and by the Defense Advanced Research Projects Agency (DARPA) and the U.S. Army Research Office under contracts W911NF-15-C-0226 and W911NF-15-C-0236. The third author was also supported by the SIMONS Investigator award agreement dated 6-5-12 and the Cybersecurity and Privacy Institute at Northeastern University.

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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  • Itay Berman
    • 1
  • Akshay Degwekar
    • 1
  • Ron D. Rothblum
    • 1
    • 2
  • Prashant Nalini Vasudevan
    • 1
  1. 1.MITCambridgeUSA
  2. 2.Northeastern UniversityBostonUSA

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