Cryptography and Coding Theory

Cryptography: Here is the essence of cryptography (both sides of the story). I have some information, and it's encoded in a text file. You really want to know what it says, but I can't let you do that. So what happens is I'm going to try to translate it into my own secret language that I can share with my pals, but not with you. Now, you want to do whatever you can to obtain and read my message. Once you have the message you have some different things. You can try to work backwards through my encoding scheme (if you know it), or you could try every possible decoding scheme until you find one that makes sense. What you're doing here is called cryptanalysis.

Coding Theory: I have some information, in the form of a binary string (a sequence of 0's and 1's) that I want to store for a long time on my hard drive. It's, like, a really long string. But I'm pretty sure my hard drive is a safe place to store it, so we can take away some of the redundancy. This compresses the file, and makes it easier to store.

Now, I want to take that file, and send it over the internet, but the connection isn't too good - it's a noisy channel. How can I make sure that you receive the correct file? I can do this by adding redundancy - finding an efficient way to send my message with the following property: If some percentage of the bits get "flipped" (some 0's turn into 1's and vice versa) when I send the message, you'll still be able to recognize what I said.

There are many other excellent (both theoretical and applied in both these areas and there are combined books too), but these should get you started.

Cryptography Books

A Course in Number Theory and Cryptography, Neal Koblitz

Algebraic Aspects of Cryptography, Neal Koblitz

The mathematics of ciphers: number theory and RSA cryptography, Coutinho S C, Severino Collier Coutinho

An Introduction to Cryptography, Richard A. Mollin

Introduction to Cryptography with Coding Theory (2nd Edition) by Wade Trappe and Lawrence C. Washington (Jul 25, 2005)

Coding Theory

Introduction to Coding Theory (Graduate Texts in Mathematics), J.H. van Lint (Author)

Information and Coding Theory (Springer Undergraduate Mathematics Series), Gareth A. Jones (Author), J.Mary Jones (Author)

Coding Theory and Cryptography: The Essentials, Second Edition (Chapman & Hall/CRC Pure and Applied Mathematics) by D.C. Hankerson, Gary Hoffman, D.A. Leonard and Charles C. Lindner (Aug 4, 2000)

I can add more applied books to each list and there are many, so just ask.

Regards -A