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International Association for Cryptologic Research (IACR)
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
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