### An Algebraic Approach to Non-Malleability

Vipul Goyal, Silas Richelson, Alon Rosen, and Margarita Vald

##### Abstract

In their seminal work on non-malleable cryptography, Dolev, Dwork and Naor, showed how to construct a non-malleable commitment with logarithmically-many "rounds"/"slots", the idea being that any adversary may successfully maul in some slots but would fail in at least one. Since then new ideas have been introduced, ultimately resulting in constant-round protocols based on any one-way function. Yet, in spite of this remarkable progress, each of the known constructions of non-malleable commitments leaves something to be desired. In this paper we propose a new technique that allows us to construct a non-malleable protocol with only a single slot", and to improve in at least one aspect over each of the previously proposed protocols. Two direct byproducts of our new ideas are a four round non-malleable commitment and a four round non-malleable zero-knowledge argument, the latter matching the round complexity of the best known zero-knowledge argument (without the non-malleability requirement). The protocols are based on the existence of one-way functions and admit very efficient instantiations via standard homomorphic commitments and sigma protocols. Our analysis relies on algebraic reasoning, and makes use of error correcting codes in order to ensure that committers' tags differ in many coordinates. One way of viewing our construction is as a method for combining many atomic sub-protocols in a way that simultaneously amplifies soundness and non-malleability, thus requiring much weaker guarantees to begin with, and resulting in a protocol which is much trimmer in complexity compared to the existing ones.

Note: Revised version. The earlier version of this paper had claimed that our 4-round non-malleable commitment construction (see Section 6) extends to provide 4-round concurrent non-malleable commitments as well. This claim was incorrect and has been withdrawn. Getting 4-round concurrent non-malleable commitments is left as an open problem.

Available format(s)
Category
Cryptographic protocols
Publication info
Published elsewhere. MAJOR revision.FOCS 2014
Keywords
Non-MalleabilityCommitmentsZero-Knowledge
Contact author(s)
silas richelson @ gmail com
History
2016-09-15: last of 7 revisions
See all versions
Short URL
https://ia.cr/2014/586

CC BY

BibTeX

@misc{cryptoeprint:2014/586,
author = {Vipul Goyal and Silas Richelson and Alon Rosen and Margarita Vald},
title = {An Algebraic Approach to Non-Malleability},
howpublished = {Cryptology ePrint Archive, Paper 2014/586},
year = {2014},
note = {\url{https://eprint.iacr.org/2014/586}},
url = {https://eprint.iacr.org/2014/586}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.