Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves
Authors: D. Boneh, D. Glass, D. Krashen, K. Lauter, S. Sharif, A. Silverberg, M. Tibouchi, and M. 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.
Reference:
In proceedings of MathCrypt 2018
Full paper: pdf