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

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

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 becaus...

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Bibliographic Details
Main Authors: Boneh Dan, Glass Darren, Krashen Daniel, Lauter Kristin, Sharif Shahed, Silverberg Alice, Tibouchi Mehdi, Zhandry Mark
Format: Article
Language:English
Published: De Gruyter 2020-06-01
Series:Journal of Mathematical Cryptology
Subjects:
multilinear maps
non-interactive key exchange
isogenies
14k02
14q20
11y16
94a60
Online Access:https://doi.org/10.1515/jmc-2015-0047
Description
Summary: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.
ISSN:1862-2976
1862-2984

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