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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Autores principales:	Basso Andrea, Pazuki Fabien
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	isogenies supersingular elliptic curves modular invariants 14h52 14k02 11t71 94a60 81p94 65p25 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/6cd44119188b496ea8c3e6a069561d3e
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spelling	oai:doaj.org-article:6cd44119188b496ea8c3e6a069561d3e2021-12-05T14:10:52ZOn the supersingular GPST attack1862-298410.1515/jmc-2021-0020https://doaj.org/article/6cd44119188b496ea8c3e6a069561d3e2021-09-01T00:00:00Zhttps://doi.org/10.1515/jmc-2021-0020https://doaj.org/toc/1862-2984The 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.Basso AndreaPazuki FabienDe Gruyterarticleisogeniessupersingular elliptic curvesmodular invariants14h5214k0211t7194a6081p9465p25MathematicsQA1-939ENJournal of Mathematical Cryptology, Vol 16, Iss 1, Pp 14-19 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	isogenies supersingular elliptic curves modular invariants 14h52 14k02 11t71 94a60 81p94 65p25 Mathematics QA1-939
spellingShingle	isogenies supersingular elliptic curves modular invariants 14h52 14k02 11t71 94a60 81p94 65p25 Mathematics QA1-939 Basso Andrea Pazuki Fabien On the supersingular GPST attack
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.
format	article
author	Basso Andrea Pazuki Fabien
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
publishDate	2021
url	https://doaj.org/article/6cd44119188b496ea8c3e6a069561d3e
work_keys_str_mv	AT bassoandrea onthesupersingulargpstattack AT pazukifabien onthesupersingulargpstattack
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On the supersingular GPST attack

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