Paper 2018/665

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

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


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.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Major revision. MATHCRYPT 2018
Multilinear mapsNon-Interactive Key ExchangeIsogeniesWitness EncryptionAbelian Varieties
Contact author(s)
mehdi tibouchi @ normalesup org
2018-08-31: last of 2 revisions
2018-07-10: received
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Creative Commons Attribution


      author = {Dan Boneh and Darren Glass and Daniel Krashen and Kristin Lauter and Shahed Sharif and Alice Silverberg and Mehdi Tibouchi and Mark Zhandry},
      title = {Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves},
      howpublished = {Cryptology ePrint Archive, Paper 2018/665},
      year = {2018},
      note = {\url{}},
      url = {}
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