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Fundamentals

Number Theory

Abstract algebra

Elliptic Curves

Lattices

Asymmetric Cryptography

Symmetric Cryptography

Isogeny Based Cryptography

Appendices

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Isogeny and Ramanujan Graphs

Isogeny graph (general definition, degree, duals...).

Starting vertex (Bröker's algorithm).

Supersingular isogeny graphs

Size, everything is defined over GF(p^2). (*as long as the degree divides (p+1)^2 or (p-1)^2).

Random walks are probably the best motivation to define Ramanujanness, and are directly applicable to cryptography. A (perhaps too large) source is Hoory-Linial-Wigderson.

Consequence from Ramanujan + random walk convergence: O(log p) diameter.

Last modified 5mo ago

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