Number Theory for Cryptography (Lecture Notes)

In these lectures (8 hours taught in November 2020), we mention some topics from (algebraic) number theory as well as some related concepts from (algebraic) geometry that can be useful in cryptography.
We cannot go deeply into any of the topics and most results will be presented without any proofs.

One of the things that one encounters are `ideal lattices'. In the examples I saw, this was nothing but (an ideal in) an order in a number field, which is one of the concepts that we present here in its mathematical context (i.e. embedded in a conceptual setting).
It has been noted long ago (already in the 19th century) that number fields and function fields of curves have many properties in common. Accordingly, we shall also present some basic topics on affine plane curves and their function fields. This leads us to mention elliptic curves, however, only in an affine version (instead of the better projective one); we cannot go deeply into that topic at all.

The material presented here is classical and very well known.