Round Optimal Black-Box “Commit-and-Prove”

Dakshita Khurana, Rafail Ostrovsky, and Akshayaram Srinivasan

Abstract

Motivatedbytheoreticalandpracticalconsiderations,anim- portant line of research is to design secure computation protocols that only make black-box use of cryptography. An important component in nearly all the black-box secure computation constructions is a black- box commit-and-prove protocol. A commit-and-prove protocol allows a prover to commit to a value and prove a statement about this value while guaranteeing that the committed value remains hidden. A black- box commit-and-prove protocol implements this functionality while only making black-box use of cryptography. In this paper, we build several tools that enable constructions of round- optimal, black-box commit and prove protocols. In particular, assuming injective one-way functions, we design the first round-optimal, black- box commit-and-prove arguments of knowledge satisfying strong privacy against malicious verifiers, namely: – Zero-knowledge in four rounds and, – Witness indistinguishability in three rounds. Prior to our work, the best known black-box protocols achieving commit- and-prove required more rounds. We additionally ensure that our protocols can be used, if needed, in the delayed-input setting, where the statement to be proven is decided only towards the end of the interaction. We also observe simple applications of our protocols towards achieving black-box four-round constructions of extractable and equivocal commitments. We believe that our protocols will provide a useful tool enabling several new constructions and easy round-efficient conversions from non-black- box to black-box protocols in the future.

Available format(s)
Category
Foundations
Publication info
A minor revision of an IACR publication in TCC 2018
Contact author(s)
akshayaram @ berkeley edu
History
Short URL
https://ia.cr/2018/921

CC BY

BibTeX

@misc{cryptoeprint:2018/921,
author = {Dakshita Khurana and Rafail Ostrovsky and Akshayaram Srinivasan},
title = {Round Optimal Black-Box “Commit-and-Prove”},
howpublished = {Cryptology ePrint Archive, Paper 2018/921},
year = {2018},
note = {\url{https://eprint.iacr.org/2018/921}},
url = {https://eprint.iacr.org/2018/921}
}

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