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Paper: From Laconic Zero-Knowledge to Public-Key Cryptography

Authors:
Itay Berman
Akshay Degwekar
Ron D. Rothblum
Prashant Nalini Vasudevan
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DOI: 10.1007/978-3-319-96878-0_23
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Presentation: Slides
Conference: CRYPTO 2018
Abstract: Since its inception, public-key encryption ( $$\mathsf {PKE}$$ 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 .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 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 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 $$\mathsf {PKE}$$ PKE which, in particular, captures many of the assumptions that were already known to yield $$\mathsf {PKE}$$ 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 $$\mathsf {PKE}$$ PKE, thereby giving a complexity-theoretic characterization of $$\mathsf {PKE}$$ PKE. Second, a mild strengthening of our assumption also yields a (2-message) oblivious transfer protocol.
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BibTeX
@inproceedings{crypto-2018-28803,
  title={From Laconic Zero-Knowledge to Public-Key Cryptography},
  booktitle={Advances in Cryptology – CRYPTO 2018},
  series={Lecture Notes in Computer Science},
  publisher={Springer},
  volume={10993},
  pages={674-697},
  doi={10.1007/978-3-319-96878-0_23},
  author={Itay Berman and Akshay Degwekar and Ron D. Rothblum and Prashant Nalini Vasudevan},
  year=2018
}