Vortrag von Marc Newman
Datum: 26.08.20 Zeit: 15.00 - 16.00 Raum: Online
(**This eSeminar will take place on Zoom, using the same meeting details as previous seminars. If you do not have meeting details, please contact firstname.lastname@example.org **)
In this thesis, we consider two different supersingular isogeny-based Diffie- Hellman schemes: SIDH and CSIDH. We review the fundamental definitions underpinning isogeny-based cryptography including Diffie-Hellman key exchange, elliptic curves, algebraic number theory, and graph theory providing various examples supported by SageMath. We cover the mathematical bases, protocols, and hardness assumptions of SIDH and CSIDH as well as surveying some numerical analysis of the practical uses of the schemes from the literature. We review additional cryptographic schemes and applications which also utilize isogenies and offer a brief direct comparison between SIDH and CSIDH. Finally, we state certain open questions pertaining to approaches to better understanding isogeny-based cryptography using related branches of mathematics.