Books for pure cryptography. I am trying to find a"good" book (or a series of "good" books) which covers the following parts in cryptography:


*

*Some background (such as Number Theory, Finite Fields, )

*Classical cryptography (I would say private key cryptography)

*Public key cryptography

*The security models (In particlar, the constructions of protocols with security)

*Pairing-based cryptography (the inclusion of elliptic curves in cryptography, as an example)

*Lattice-based cryptography (I am really interested in this part)

*Fully-homomorphic encryption


I recommend you this book: A course of criptography that you can find here https://bookstore.ams.org/amstext-40. I think it's very good and covers (some in details some not as much) all your arguments. 
I recommend you also this site (https://bookauthority.org/books/new-cryptography-books) which gives you some good references (about 13 new books on criptography).
