In this thesis, we aim to develop the theory of elliptic curves in order to understand the shape of isogeny graphs. This kind of graphs are used as a new cryptographic primitive to resist against quantum key-recovery attacks. We also prove that these graphs have some interesting properties, for example they are expanders. The last chapter is devoted to the study of the cryptosystem CSIDH, which is a relatively new (conjectured) quantum-resistant proposal based on isogeny graphs.
In this thesis, we aim to develop the theory of elliptic curves in order to understand the shape of isogeny graphs. This kind of graphs are used as a new cryptographic primitive to resist against quantum key-recovery attacks. We also prove that these graphs have some interesting properties, for example they are expanders. The last chapter is devoted to the study of the cryptosystem CSIDH, which is a relatively new (conjectured) quantum-resistant proposal based on isogeny graphs.
Isogeny Graphs and Cryptographic Applications
OSTUZZI, MASSIMO
2022/2023
Abstract
In this thesis, we aim to develop the theory of elliptic curves in order to understand the shape of isogeny graphs. This kind of graphs are used as a new cryptographic primitive to resist against quantum key-recovery attacks. We also prove that these graphs have some interesting properties, for example they are expanders. The last chapter is devoted to the study of the cryptosystem CSIDH, which is a relatively new (conjectured) quantum-resistant proposal based on isogeny graphs.| File | Dimensione | Formato | |
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https://hdl.handle.net/20.500.12608/50189