English
An efficient break of the supersingular isogeny Diffie-Hellman protocol
Multi angle
Auteurs : Castryck, Wouter (Auteur de la conférence)
CIRM (Editeur )
14G15 - Finite ground fields
14G50 - Applications to coding theory and cryptography - application à la théorie de codes et à la cryptographie
14H40 - Jacobians, Prym varieties
14H52 - Elliptic curves
14K02 - Isogeny
CIRM (Editeur )
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Résumé :
Finding an explicit isogeny between two given isogenous elliptic curves over a finite field is considered a hard problem, even for quantum computers. In 2011 this led Jao and De Feo to propose a key exchange protocol that became known as SIDH, shorthand for Supersingular Isogeny Diÿe-Hellman. The security of SIDH does not rely on a pure isogeny problem, due to certain 'auxiliary' elliptic curve points that are exchanged during the protocol (for constructive reasons). In this talk I will discuss a break of SIDH that was discovered in collaboration with Thomas Decru. The attack uses isogenies between abelian surfaces and exploits the aforementioned auxiliary points, so it does not break the pure isogeny problem. I will also discuss improvements of this attack due to Maino et al. and Robert, as well as a countermeasure by Fouotsa et al., along with breaks of this countermeasure in some special cases.
Mots-Clés : elliptic curves; isogenies; abelian surfaces; cryptography
Codes MSC : Mots-Clés : elliptic curves; isogenies; abelian surfaces; cryptography
14G15 - Finite ground fields
14G50 - Applications to coding theory and cryptography - application à la théorie de codes et à la cryptographie
14H40 - Jacobians, Prym varieties
14H52 - Elliptic curves
14K02 - Isogeny
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 28/06/2023 Date de Captation : 05/06/2023 Sous Collection : Research talks Catégorie arXiv : Number Theory ; Algebraic Geometry ; Cryptography and Security Domaine(s) : Informatique ; Géométrie Complexe & géométrie Algébrique ; Théorie des Nombres Format : MP4 (.mp4) - HD Durée : 00:54:58 Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-06-08_Castryck.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : AGCT - Arithmetic, Geometry, Cryptography and Coding Theory / AGCT - Arithmétique, géométrie, cryptographie et théorie des codesOrganisateurs de la Rencontre : Anni, Samuele ; Bruin, Nils ; Kohel, David ; Martindale, Chloe Dates : 05/06/2023 - 09/06/2023 Année de la rencontre : 2023 URL de la Rencontre : https://conferences.cirm-math.fr/2889.html
Données de citation
DOI : 10.24350/CIRM.V.20055403Citer cette vidéo: Castryck, Wouter (2023). An efficient break of the supersingular isogeny Diffie-Hellman protocol. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20055403 URI : http://dx.doi.org/10.24350/CIRM.V.20055403 |
Voir Aussi
- [Multi angle] Probabilistic approaches to rational points on algebraic surfaces / Auteur de la conférence Várilly-Alvarado, Anthony.
- [Multi angle] Isogeny-based cryptography on the (abelian) surface / Auteur de la conférence Ti, Yan Bo.
- [Multi angle] The geometry of stable lattices in Bruhat-Tits buildings / Auteur de la conférence Stanojkovski, Mima.
- [Multi angle] Computing Ceresa classes of curves / Auteur de la conférence Srinivasan, Padmavathi.
- [Multi angle] Counting S4 and S5 extensions satisfying the Hasse norm principle / Auteur de la conférence Newton, Rachel.
Bibliographie
- CASTRYCK, Wouter et DECRU, Thomas. An efficient key recovery attack on SIDH. In : Annual International Conference on the Theory and Applications of Cryptographic Techniques. Cham : Springer Nature Switzerland, 2023. p. 423-447. - http://dx.doi.org/10.1007/978-3-031-30589-4_15
- MAINO, Luciano, MARTINDALE, Chloe, PANNY, Lorenz, et al. A direct key recovery attack on SIDH. In : Annual International Conference on the Theory and Applications of Cryptographic Techniques. Cham : Springer Nature Switzerland, 2023. p. 448-471. - http://dx.doi.org/10.1007/978-3-031-30589-4_16
- ROBERT, Damien. Breaking SIDH in polynomial time. In : Annual International Conference on the Theory and Applications of Cryptographic Techniques. Cham : Springer Nature Switzerland, 2023. p. 472-503. - http://dx.doi.org/10.1007/978-3-031-30589-4_17
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