### From Laconic Zero-Knowledge to Public-Key Cryptography

Itay Berman, Akshay Degwekar, Ron D. Rothblum, and Prashant Nalini Vasudevan

##### Abstract

Since its inception, public-key encryption (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 the intersection of NP and SZK. 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 NP 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 NP 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 PKE which, in particular, captures many of the assumptions that were already known to yield 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 PKE, thereby giving a complexity-theoretic characterization of PKE. Second, a mild strengthening of our assumption also yields a (2-message) oblivious transfer protocol.

Available format(s)
Publication info
Published by the IACR in CRYPTO 2018
Keywords
Public Key Cryptographyzero knowledge
Contact author(s)
itayberm @ mit edu
akshayd @ mit edu
ronr @ mit edu
prashvas @ mit edu
History
Short URL
https://ia.cr/2018/548

CC BY

BibTeX

@misc{cryptoeprint:2018/548,
author = {Itay Berman and Akshay Degwekar and Ron D.  Rothblum and Prashant Nalini Vasudevan},
title = {From Laconic Zero-Knowledge to Public-Key Cryptography},
howpublished = {Cryptology ePrint Archive, Paper 2018/548},
year = {2018},
note = {\url{https://eprint.iacr.org/2018/548}},
url = {https://eprint.iacr.org/2018/548}
}

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