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

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Multilinear map Key exchange Invariant (physics) Cryptographic protocol Cryptography Isogeny Mathematics Computer science Cryptographic primitive Theoretical computer science Elliptic curve Discrete mathematics Public-key cryptography Pure mathematics Algorithm Encryption Computer security Mathematical physics

Dan Boneh , Darren Glass , Daniel Krashen , Kristin Lauter , Shahed Sharif , Alice Silverberg , Mehdi Tibouchi , Mark Zhandry ·

YOU? · · 2020 · Open Access · · DOI: https://doi.org/10.1515/jmc-2015-0047 · OA: W2951500071

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.