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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.\n                  <\/jats:p>\n                  <jats:p>\n                    Our framework builds a\n                    <jats:italic>cryptographic invariant map<\/jats:italic>\n                    , 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.\n                  <\/jats:p>","DOI":"10.1515\/jmc-2015-0047","type":"journal-article","created":{"date-parts":[[2020,6,15]],"date-time":"2020-06-15T13:48:20Z","timestamp":1592228900000},"page":"5-14","source":"Crossref","is-referenced-by-count":12,"title":["Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves"],"prefix":"10.1515","volume":"14","author":[{"given":"Dan","family":"Boneh","sequence":"first","affiliation":[{"name":"Stanford University , California , United States of America"}]},{"given":"Darren","family":"Glass","sequence":"additional","affiliation":[{"name":"Gettysburg College , Gettysburg , United States of America"}]},{"given":"Daniel","family":"Krashen","sequence":"additional","affiliation":[{"name":"Rutgers University , New Jersey , United States of America"}]},{"given":"Kristin","family":"Lauter","sequence":"additional","affiliation":[{"name":"Microsoft Research , Bellevue , United States of America"}]},{"given":"Shahed","family":"Sharif","sequence":"additional","affiliation":[{"name":"California State University San Marcos , California , United States of America"}]},{"given":"Alice","family":"Silverberg","sequence":"additional","affiliation":[{"name":"University of California , Irvine , United States of America"}]},{"given":"Mehdi","family":"Tibouchi","sequence":"additional","affiliation":[{"name":"NTT Corporation , Tokyo , Japan"}]},{"given":"Mark","family":"Zhandry","sequence":"additional","affiliation":[{"name":"Princeton University , Princeton , United States of America"}]}],"member":"374","published-online":{"date-parts":[[2020,6,14]]},"reference":[{"key":"2025120600161794365_j_jmc-2015-0047_ref_001_w2aab3b7ab1b6b1ab2b1b1Aa","doi-asserted-by":"crossref","unstructured":"Karim Belabas, Topics in computational algebraic number theory, J. 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