Implementing the Castryck-Decru attack on SIDH with general primes

dc.contributor.authorLaflamme, Jeanne
dc.date.accessioned2024-01-09T16:54:22Z
dc.date.available2024-01-09T16:54:22Z
dc.date.issued2024-01-09
dc.date.submitted2024-01-05
dc.description.abstractWith the rapid progress of quantum computers in recent years, efforts have been made to standardize new public-key cryptographic protocols which would be secure against them. One of the schemes in contention was Supersingular Isogeny Diffie-Hellman (SIDH). This scheme relied on the assumed hardness of the isogeny problem on supersingular elliptic curves. However, in the SIDH protocol extra information on the secret isogenies is transmitted. In July 2022, Castryck and Decru found a way to exploit this information to completely break the scheme. They gave an implementation of their attack which allows to recover Bob’s secret key in a few seconds on a laptop. Usually, Alice and Bob’s secret isogenies are taken to have degree 2^a and 3^b respectively. This thesis gives a more general implementation of the attack in Magma which works even if Alice and Bob’s secret isogenies have degrees lA^a and lB^b for more general primes lA and lB.en
dc.identifier.urihttp://hdl.handle.net/10012/20220
dc.language.isoenen
dc.pendingfalse
dc.publisherUniversity of Waterlooen
dc.relation.urihttps://git.uwaterloo.ca/jmlaflam/sidh-attack/en
dc.subjectcryptographyen
dc.subjectCastryck-Decru attacken
dc.subjectpublic-keyen
dc.subjectisogeniesen
dc.subjectpost-quantumen
dc.subjectSIDHen
dc.titleImplementing the Castryck-Decru attack on SIDH with general primesen
dc.typeMaster Thesisen
uws-etd.degreeMaster of Mathematicsen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws-etd.degree.disciplineCombinatorics and Optimizationen
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.embargo.terms0en
uws.contributor.advisorJao, David
uws.contributor.affiliation1Faculty of Mathematicsen
uws.peerReviewStatusUnrevieweden
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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