On the post-quantum future of Elliptic Curve Cryptography - Lucaroni, Rayen (My University, 2023)
This thesis is a literature study on current published quantum-resistant isogeny-based key exchange protocols. Here we cover the topic from foundations. Chapters 1 and 2 discuss classical computation models, algorithm complexity, and how these concepts support the security of modern elliptic curve cryptography methods, such as ECDH and ECDSA. Next, in Chapters 3 to 5, we present quantum computation models, and how Shor's algorithm on quantum computers presents a threat to the future security of classical asymmetric cryptography. We explore the foundations of isogeny-based cryptography, and two key exchange protocols of this kind: SIDH and CSIDH. Appendices A and B are provided for readers wanting more in-depth background explanations on the algebraic geometry of elliptic curves, and quantum mechanics respectively.
Keywords: cryptography, isogeny-based cryptography, elliptic curves, ECDH, ECDSA, quantum computing, Shor's algorithm, key exchange SIDH, CSIDH