On the supersingular GPST attack

The main attack against static-key supersingular isogeny Diffie–Hellman (SIDH) is the Galbraith–Petit–Shani–Ti (GPST) attack, which also prevents the application of SIDH to other constructions such as non-interactive key-exchange. In this paper, we identify and study a specific assumption on which t...

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Bibliographic Details
Main Authors:	Basso Andrea, Pazuki Fabien
Format:	Article
Language:	English
Published:	De Gruyter 2021-09-01
Series:	Journal of Mathematical Cryptology
Subjects:	isogenies supersingular elliptic curves modular invariants 14h52 14k02 11t71 94a60 81p94 65p25
Online Access:	https://doi.org/10.1515/jmc-2021-0020

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spelling	doaj-6cd44119188b496ea8c3e6a069561d3e2021-10-03T07:42:35ZengDe GruyterJournal of Mathematical Cryptology1862-29842021-09-01161141910.1515/jmc-2021-0020On the supersingular GPST attackBasso Andrea0Pazuki Fabien1Centre for Cyber Security and Privacy, School of Computer Science, University of Birmingham, Birmingham, UKDepartment of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, DenmarkThe main attack against static-key supersingular isogeny Diffie–Hellman (SIDH) is the Galbraith–Petit–Shani–Ti (GPST) attack, which also prevents the application of SIDH to other constructions such as non-interactive key-exchange. In this paper, we identify and study a specific assumption on which the GPST attack relies that does not necessarily hold in all circumstances. We show that in some circumstances the attack fails to recover part of the secret key. We also characterize the conditions necessary for the attack to fail and show that it rarely happens in real cases. We give a link with collisions in the Charles-Goren-Lauter (CGL) hash function.https://doi.org/10.1515/jmc-2021-0020isogeniessupersingular elliptic curvesmodular invariants14h5214k0211t7194a6081p9465p25
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Basso Andrea Pazuki Fabien
spellingShingle	Basso Andrea Pazuki Fabien On the supersingular GPST attack Journal of Mathematical Cryptology isogenies supersingular elliptic curves modular invariants 14h52 14k02 11t71 94a60 81p94 65p25
author_facet	Basso Andrea Pazuki Fabien
author_sort	Basso Andrea
title	On the supersingular GPST attack
title_short	On the supersingular GPST attack
title_full	On the supersingular GPST attack
title_fullStr	On the supersingular GPST attack
title_full_unstemmed	On the supersingular GPST attack
title_sort	on the supersingular gpst attack
publisher	De Gruyter
series	Journal of Mathematical Cryptology
issn	1862-2984
publishDate	2021-09-01
description	The main attack against static-key supersingular isogeny Diffie–Hellman (SIDH) is the Galbraith–Petit–Shani–Ti (GPST) attack, which also prevents the application of SIDH to other constructions such as non-interactive key-exchange. In this paper, we identify and study a specific assumption on which the GPST attack relies that does not necessarily hold in all circumstances. We show that in some circumstances the attack fails to recover part of the secret key. We also characterize the conditions necessary for the attack to fail and show that it rarely happens in real cases. We give a link with collisions in the Charles-Goren-Lauter (CGL) hash function.
topic	isogenies supersingular elliptic curves modular invariants 14h52 14k02 11t71 94a60 81p94 65p25
url	https://doi.org/10.1515/jmc-2021-0020
work_keys_str_mv	AT bassoandrea onthesupersingulargpstattack AT pazukifabien onthesupersingulargpstattack
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On the supersingular GPST attack

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