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

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

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 becaus...

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Main Authors: Boneh Dan, Glass Darren, Krashen Daniel, Lauter Kristin, Sharif Shahed, Silverberg Alice, Tibouchi Mehdi, Zhandry Mark
Format: Article
Language:English
Published: De Gruyter 2020-06-01
Series:Journal of Mathematical Cryptology
Subjects:
multilinear maps
non-interactive key exchange
isogenies
14k02
14q20
11y16
94a60
Online Access:https://doi.org/10.1515/jmc-2015-0047
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spelling doaj-2fd85fdf323943fe90b5e2ee90bba3c52021-09-06T19:40:44ZengDe GruyterJournal of Mathematical Cryptology1862-29761862-29842020-06-0114151410.1515/jmc-2015-0047jmc-2015-0047Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic CurvesBoneh Dan0Glass Darren1Krashen Daniel2Lauter Kristin3Sharif Shahed4Silverberg Alice5Tibouchi Mehdi6Zhandry Mark7Stanford University, California, United States of AmericaGettysburg College, Gettysburg, United States of AmericaRutgers University, New Jersey, United States of AmericaMicrosoft Research, Bellevue, United States of AmericaCalifornia State University San Marcos, California, United States of AmericaUniversity of California, Irvine, United States of AmericaNTT Corporation, Tokyo, JapanPrinceton University, Princeton, United States of AmericaWe 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.https://doi.org/10.1515/jmc-2015-0047multilinear mapsnon-interactive key exchangeisogenies14k0214q2011y1694a60
collection DOAJ
language English
format Article
sources DOAJ
author Boneh Dan
Glass Darren
Krashen Daniel
Lauter Kristin
Sharif Shahed
Silverberg Alice
Tibouchi Mehdi
Zhandry Mark
spellingShingle Boneh Dan
Glass Darren
Krashen Daniel
Lauter Kristin
Sharif Shahed
Silverberg Alice
Tibouchi Mehdi
Zhandry Mark
Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves
Journal of Mathematical Cryptology
multilinear maps
non-interactive key exchange
isogenies
14k02
14q20
11y16
94a60
author_facet Boneh Dan
Glass Darren
Krashen Daniel
Lauter Kristin
Sharif Shahed
Silverberg Alice
Tibouchi Mehdi
Zhandry Mark
author_sort Boneh Dan
title Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves
title_short Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves
title_full Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves
title_fullStr Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves
title_full_unstemmed Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves
title_sort multiparty non-interactive key exchange and more from isogenies on elliptic curves
publisher De Gruyter
series Journal of Mathematical Cryptology
issn 1862-2976
1862-2984
publishDate 2020-06-01
description 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.
topic multilinear maps
non-interactive key exchange
isogenies
14k02
14q20
11y16
94a60
url https://doi.org/10.1515/jmc-2015-0047
work_keys_str_mv AT bonehdan multipartynoninteractivekeyexchangeandmorefromisogeniesonellipticcurves
AT glassdarren multipartynoninteractivekeyexchangeandmorefromisogeniesonellipticcurves
AT krashendaniel multipartynoninteractivekeyexchangeandmorefromisogeniesonellipticcurves
AT lauterkristin multipartynoninteractivekeyexchangeandmorefromisogeniesonellipticcurves
AT sharifshahed multipartynoninteractivekeyexchangeandmorefromisogeniesonellipticcurves
AT silverbergalice multipartynoninteractivekeyexchangeandmorefromisogeniesonellipticcurves
AT tibouchimehdi multipartynoninteractivekeyexchangeandmorefromisogeniesonellipticcurves
AT zhandrymark multipartynoninteractivekeyexchangeandmorefromisogeniesonellipticcurves
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