What books do you recommend on mathematics behind cryptography? I am currently reading the Book Understanding Cryptography from Cristof Paar. I am enjoying the book but i don't like to scratch the surface when it comes to cryptography. I would like do dig a little deeper on the mathematics behind it. I read on:
https://www.schneier.com/crypto-gram/archives/1999/1015.html
that cryptography demands an understanding of multiple fields of mathematics, such as:
-Number theory
-Complexity theory
-Algorithms
-Statistics
-Abstract algebra
I have a masters on Telecommunications and Informatics, so i have an understanding of mathematics, calculus, statistics, algebra and complex calculus. I am no pro, but i think i am good. Could you advise me on books i should buy? I would like books that explain theorems and demonstrate those theorems. Do you think i am doing the right thing? Should i read only applied cryptography books, or should go deeper on the subject? I would like to go beyond the basic understanding. I would like to develop algorithms and break other algorithms. If you know books that talk about all these subjects, they are more than welcome.
Thank you
Kind regards
 A: I would recommend a series of books, specifications, libraries and CAS programs.
Books


*

*A Course in Number Theory and Cryptography, Neal Koblitz (very dense, but an amazing book)

*An Introduction to Mathematical Cryptography, Jeffrey Hoffstein, Jill Pipher, J.H. Silverman (very readable and excellent book, which is more up-to-date)

*An Introduction to Cryptography, Second Edition (Discrete Mathematics and Its Applications), Richard A. Mollin (easier on the math)

*Handbook of Applied Cryptography, Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone (note, there is also a variant for Elliptic Curve Cryptography and both are just an excellent way to describe and detail cryptographic algorithms)

*As a side note, these should be supplemented with books on Number Theory, Abstract Algebra, Algebraic Geometry and the like, but there are many excellent posts for such books on MSE


Specifications


*

*NIST Digital Signature Standard - you can see what a real-world specification looks like.

*Many other NIST specifications

*IETF's Request For Comments (RFCs)


Software Libraries


*

*Libtomcrypt and Libtommath

*Crypto ++
Computer Algebra Systems


*

*Mathematica, Maple, ... (not free, professional packages with large integer math)

*SAGE, Pari/Gp, ..., Python (free)

*Here is a list of CAS programs, which is very helpful for experimenting with number theory topics and quickly coding things up (enormously helpful)


There are many others, but these are the ones I go back to often.
