Cryptology ePrint Archive: Report 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.

Category / Keywords: public-key cryptography / Multilinear maps, Non-Interactive Key Exchange, Isogenies, Witness Encryption, Abelian Varieties

Original Publication (with major differences): MATHCRYPT 2018

Date: received 9 Jul 2018, last revised 9 Jul 2018

Contact author: mehdi tibouchi at normalesup org

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Version: 20180710:114640 (All versions of this report)

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