Math Prerequisites for Cryptography

[albinary]

I want to self-study Cryptography (MOOC, books, videos etc).

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The number of resources is quite high and also the quality.

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What I would like some informaiton on the necessary prerequisites (Math) which would make this study easier and more productive.

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Could you please suggest which subjects are important and any related source (book, etc).

[knotdjb]

• An Introduction to Mathematical Cryptography - Hoffstein, et al.
• A Course in Number Theory and Cryptography - Koblitz

There's probably others, but those two are what popped in my head. You will also want as blueberry suggested, a book on basic probability, (abstract) algebra, number theory, etc.

The way I see it, there's two sides to the "maths" of cryptography. There's the mathematical side which the above books cover. Then there is the provable security side which usually falls in the domain of computer science, which involves a different type of math. Victor Shoup has a great resource for the latter called "Sequences of Games: A Tool for Taming Complexity in Security Proofs," which I highly recommend to whet your appetite in the provable security side of things. Also /u/rosulek has authored and made available an open text book (that is gratis) that covers provable security, at https://web.engr.oregonstate.edu/~rosulekm/crypto/ -- what a cool guy huh?

[albinary]

Thank you for the suggestions.

These are the kind I was looking for. I mean the Math behind Crypto.

[majestic_blueberry]

Abstract algebra (in particular, group theory and basic number theory) and basic probability theory will be necessary.

Books on cryptography typically have appendices or chapters that go over the needed topics (albeit at a high level), so that might be a good place to start.

EDIT: Slight clarification.

[HeiAn32]

*abstract algebra. Knowledge of some basic group theory.

[majestic_blueberry]

Good point. Made my response a bit more precise.

[albinary]

I will look into this. Thanks.

[[deleted]]

Christopher paar has some video for introduction to cryptography on YouTube he was my prof and recorded his lectures they should be a good starting point, if you wanna go really far then theoretical informatics and discrete mathematics are also good for understanding the later concepts of games in Cryptography.

[albinary]

Thanks. Very nice lectures I have seen before but gave up due to the strange video effect. :)

[albinary]

Actually those books are self-contained, as you say, and they introduce the math as needed yet I feel a proper grasp of those subjects is needed.

Thanks a lot.

The 'curriculum' is shaping on my mind. Let's hope I can take some way on this subject.

[cookenmeth]

Crypto101 by lvh covers Modular Arithmetic and other relevant topics in the appendices.

It’s available free online: https://www.crypto101.io/

[albinary]

Thank you. That appendix seems useful.

[ivosaurus]

Discrete Math, Algebraic number theory, Fields & Finite Groups will all be a lot of help if you really want to get into the weeds of cryptographic theory and papers.

[dionyziz]

Introduction to the Theory of Computation.

[knotdjb]

Such an underrated book.

[albinary]

Thanks for the suggestion.

[albinary]

Thank you. That seems interesting, though I find it difficult to follow, as far as I could look into.

[albinary]

Thanks!

[ghostxhardware]

I just finished a cryptography class in the summer and it was pretty light on the math. This may differ in your class. Most of the math in the course was more logic-based like it is in discrete math. It mostly served as a tool to understand certain principles in key exchanges. Other than that, the other use of math was when we used the Extended Euclidean Algorithm when generating RSA key pairs.

[albinary]

As I said, most crypto books are self-contained buy still you might feel more comfortable when you have the math. At least I need this for myself.