Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves
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 mathematical 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.
Keywords
Cite
@article{arxiv.1807.03038,
title = {Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves},
author = {Dan Boneh and Darren Glass and Daniel Krashen and Kristin Lauter and Shahed Sharif and Alice Silverberg and Mehdi Tibouchi and Mark Zhandry},
journal= {arXiv preprint arXiv:1807.03038},
year = {2018}
}