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

Author(s): Boneh, Dan; Glass, Darren; Krashen, Daniel; Lauter, Kristin; Sharif, Shahed; et al

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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 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. 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.
Publication Date: 2020
Citation: Boneh, Dan, Darren Glass, Daniel Krashen, Kristin Lauter, Shahed Sharif, Alice Silverberg, Mehdi Tibouchi, and Mark Zhandry. "Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves." Journal of Mathematical Cryptology 14, no. 1 (2020): 5-14. doi:10.1515/jmc-2015-0047
DOI: 10.1515/jmc-2015-0047
ISSN: 1862-2976
EISSN: 1862-2984
Pages: 5 - 14
Type of Material: Journal Article
Journal/Proceeding Title: Journal of Mathematical Cryptology
Version: Final published version. This is an open access article.

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