# Resources for mathematics of cryptology

I am an undergraduate student looking for resources (books or lectures) explaining mathematics involved in cryptography, such as number theory, elliptic curves etc. I found the book 'A Course in Number Theory and Cryptography by Neal Koblitz' hard to follow.

• It is a graduate book. Ideal, varieties, and algorithm by Cox at al. has some nice part for Elliptic curves, Elliptic tales by Ash and Gross. Any good number theory book should be enough. It is hard to say that any elementary number theory is not used in Cryptography. – kelalaka Jul 1 at 8:34
• Does it need to be a book? There are quite a few ECC primers on the internet that are worth looking at, e.g. the one from Certicom: An Elliptic Curve Cryptography (ECC) Primer. You can read those first and then look up more advanced mathematical books / papers. – Maarten Bodewes Jul 1 at 10:32
• No it doesn't necessarily have to be a book. – Aiytan Jul 2 at 4:43
• Not a book reference, but as you are an undergraduate student, probably, you've access to multiple resources that are otherwise under a paywall, these are for example: Springer(Link), Elsevier, IEEE and journals on information security and cryptography. There you can find multiple schemes based on multiple branches of mathematics like: group theory, (group) algebras over a field, linear algebra and modules, number theory and a large etc. Some provide the reader with a background in the theory, so my recommendation is to let yourself go. Arxiv and IACR's eprint are good sources to browse too. – kub0x Jul 2 at 12:48

I think

Johannes Buchmann, Introduction To Cryptography, Springer, 2nd Ed, 2004

is very nice and pitched squarely at undergraduates. You can see a preview here

Its contents are:

Integers Congruences and Residue Class Rings Encryption Probability and Perfect Secrecy DES AES Prime Number Generation Public Key Encryption Factoring Discrete Logarithms Cryptographic Hash Functions Digital Signatures Other Systems Identification Secret Sharing Public Key Infrastructures

It is broad, as opposed to very deep, but really well written.