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An efficient break of the supersingular isogeny Diffie-Hellman protocol
Multi angle
Authors : Castryck, Wouter (Author of the conference)
CIRM (Publisher )
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 (Publisher )
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Abstract :
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.
Keywords : elliptic curves; isogenies; abelian surfaces; cryptography
MSC Codes : Keywords : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 28/06/2023 Conference Date : 05/06/2023 Subseries : Research talks arXiv category : Number Theory ; Algebraic Geometry ; Cryptography and Security Mathematical Area(s) : Computer Science ; Algebraic & Complex Geometry ; Number Theory Format : MP4 (.mp4) - HD Video Time : 00:54:58 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-06-08_Castryck.mp4 
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Information on the Event
Event Title : AGCT - Arithmetic, Geometry, Cryptography and Coding Theory / AGCT - Arithmétique, géométrie, cryptographie et théorie des codesEvent Organizers : Anni, Samuele ; Bruin, Nils ; Kohel, David ; Martindale, Chloe Dates : 05/06/2023 - 09/06/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2889.html
Citation Data
DOI : 10.24350/CIRM.V.20055403Cite this video as: 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 |
See Also
- [Multi angle] Probabilistic approaches to rational points on algebraic surfaces / Author of the conference Várilly-Alvarado, Anthony.
- [Multi angle] Isogeny-based cryptography on the (abelian) surface / Author of the conference Ti, Yan Bo.
- [Multi angle] The geometry of stable lattices in Bruhat-Tits buildings / Author of the conference Stanojkovski, Mima.
- [Multi angle] Computing Ceresa classes of curves / Author of the conference Srinivasan, Padmavathi.
- [Multi angle] Counting S4 and S5 extensions satisfying the Hasse norm principle / Author of the conference Newton, Rachel.
Bibliography
- 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
Imagette Video
