Document Type
Article
Publication Date
6-14-2020
Department 1
Mathematics
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.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
DOI
10.1515/jmc-2015-0047
Version
Version of Record
Recommended Citation
Boneh, Dan, Darren Glass, Daniel Krashen, Kristin Lauter, Shahed Sharif, Alice Silverberg, Mehdi Tibouchi, and Mark Zhandry. "Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves." Journal of Mathematical Cryptology 14, no. 1 (2020): 5-14.
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