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Paper 2018/665

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

Dan Boneh and Darren Glass and Daniel Krashen and Kristin Lauter and Shahed Sharif and Alice Silverberg and 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.

Metadata
Available format(s)
PDF
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
2018-07-10: received
See all versions
Short URL
https://ia.cr/2018/665
License
Creative Commons Attribution
CC BY
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