Theoretical foundations of cryptosystems based on isogenies of supersingular elliptic curves
| Thesis title in Czech: | Teoretické základy kryptosystémů využívajících isogenie supersingulárních eliptických křivek |
|---|---|
| Thesis title in English: | Theoretical foundations of cryptosystems based on isogenies of supersingular elliptic curves |
| Key words: | funkční těleso|eliptická křivka|supersingulární eliptická křivka|isogenie|kryptografie založená na eliptických křivkách|CSIDH |
| English key words: | function field|elliptic curve|supersingular elliptic curve|isogeny|elliptic curve cryptography|CSIDH |
| Academic year of topic announcement: | 2021/2022 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Department of Algebra (32-KA) |
| Supervisor: | prof. RNDr. Aleš Drápal, CSc., DSc. |
| Author: | Mgr. Jan Oupický - assigned and confirmed by the Study Dept. |
| Date of registration: | 11.12.2021 |
| Date of assignment: | 11.12.2021 |
| Confirmed by Study dept. on: | 17.12.2021 |
| Date and time of defence: | 11.02.2022 09:00 |
| Date of electronic submission: | 06.01.2022 |
| Date of submission of printed version: | 10.01.2022 |
| Date of proceeded defence: | 11.02.2022 |
| Opponents: | doc. Mgr. et Mgr. Jan Žemlička, Ph.D. |
| Guidelines |
| Student se seznámí s teorií potřebnou pro porozumění kryptosystému CSIDH a tuto reprodukuje v kontextu algebraických funkčních těles. V přiměřené míře uvede potřebné důkazy a text vybaví příklady. |
| References |
| Washington, L.C., Elliptic Curves: Number Theory and Cryptography, Second Edition, CRC Press, 2008
Silverman, J.H., The Arithmetic of Elliptic Curves, Second Edition, Springer, 2010 Silverman, J.H., Advanced Topics in the Arithmetic of Elliptic Curves, Corrected second printing, Springer, 1999 Galbraith, S.D., Mathematics of Public Key Cryptography, Cambridge University Press, 2012 Cox, D.A., Primes of the Form x2+ny2: Fermat, Class Field Theory, and Complex Multiplication, Second Edition, Wiley, 2013 https://csidh.isogeny.org/csidh-20181118.pdf, Wouter Castryck, Tanja Lange, Chloe Martindale, Lorenz Panny, Joost Renes. "CSIDH: An Efficient Post-Quantum Commutative Group Action". Date: 2018.11.18. ASIACRYPT 2018, LNCS 11274, pages 395–427. https://arxiv.org/abs/1208.5370, Andrew V. Sutherland. Isogeny volcanoes. In ANTS X, volume 1 of The Open Book Series, pages 507–530. Mathematical Sciences Publishers, 2012 https://ia.cr/2011/506, Luca De Feo, David Jao, and Jérôme Plût. Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. Journal of Mathematical https://arxiv.org/abs/1310.7789, Cryptology, 8(3):209–247, 2014, Christina Delfs and Steven D. Galbraith. Computing isogenies between supersingular elliptic curves over Fp. Des. Codes Cryptography, 78(2):425–440, 2016 |