### Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves

Dan Boneh, Darren Glass, Daniel Krashen, Kristin Lauter, Shahed Sharif, Alice Silverberg, Mehdi Tibouchi, and Mark Zhandry

##### Abstract

We describe a framework for constructing an efficient non-interactive key exchange (NIKE) protocol for n parties for any n >= 2. Our approach is based on the problem of computing isogenies between isogenous elliptic curves, which is believed to be difficult. We do not obtain a working protocol because of a missing step that is currently an open problem. What we need to complete our protocol is an efficient algorithm that takes as input an abelian variety presented as a product of isogenous elliptic curves, and outputs an isomorphism invariant of the abelian variety. Our framework builds a cryptographic invariant map, which is a new primitive closely related to a cryptographic multilinear map, but whose range does not necessarily have a group structure. Nevertheless, we show that a cryptographic invariant map can be used to build several cryptographic primitives, including NIKE, that were previously constructed from multilinear maps and indistinguishability obfuscation.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. MAJOR revision.MATHCRYPT 2018
Keywords
Multilinear mapsNon-Interactive Key ExchangeIsogeniesWitness EncryptionAbelian Varieties
Contact author(s)
mehdi tibouchi @ normalesup org
History
2018-08-31: last of 2 revisions
See all versions
Short URL
https://ia.cr/2018/665

CC BY

BibTeX

@misc{cryptoeprint:2018/665,
author = {Dan Boneh and Darren Glass and Daniel Krashen and Kristin Lauter and Shahed Sharif and Alice Silverberg and Mehdi Tibouchi and Mark Zhandry},
title = {Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves},
howpublished = {Cryptology ePrint Archive, Paper 2018/665},
year = {2018},
note = {\url{https://eprint.iacr.org/2018/665}},
url = {https://eprint.iacr.org/2018/665}
}

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