The aim of CryptoBook is to have a consolidated space for all of the mathematics required to properly learn and enjoy cryptography. The focus of any topic should be to introduce a reader to a subject in a way that is fun, engaging and with an attempt to frame it as an applied resource.
The second focus should be to cleanly implement the various topics using SageMath, so that there is a clear resource for a new reader to gain insight on how SageMath might be used to create the objects needed.
Write about what you love and this book will be a success.
Descriptions of attacks against cryptosystems are strongly encouraged, however full SageMath implementations should not be included, as this has the potential for destroying CryptoHack challenges, or making all attacks known by so many people that CTFs become a total nightmare!!
This list is not complete so please add to it as you see fit.
Gauss' Lemma and its ten thousand corollaries
Morphisms et al.
Mainly thinking things like
Prime decomposition and distribution
Legendre / Jacobi symbol
Mainly thinking things like:
Groups, Rings, Fields, etc.
Abelian groups and their relationship to key-exchange