Probably not the right place - Number Theory

[Stark]

For a cryptanalysis subject I'm doing this semester, I'd really like some more sources for the fundamentals of number theory. I can understand everything they go through in the lectures, but the functions themselves are meaningless to me (I just identify which theorem or problem it is and work it out from there) so I need to work through some computations to familiarise myself. Its been 10 years since I did advanced maths, and I'm feeling it a little bit. Any ideas on sites or articles?

[Lagmonster]

Moved somewhere more receptive to the discussion of mathematics.

[Stark]

LOL well I SAID it was probably the right place

I've determined that I understand all the theories required. My problem is that I can't read the notation: the functions themselves don't mean anything to me, although I can recognise them, apply them, discuss their implications etc. So I need a semesters-worth of advanced mathematics familiarity in about four weeks. Any takers?

[Kuroneko]

If you are asking for particularly good books on number theory, I can readily recommend Hardy and Wright's An Introduction to the Theory of Numbers. It is rather broad in scope, which is a good thing if you are trying to get a feel for number theory in general rather than any specialized subfield like cryptography. Despite its title, this book is somewhat demanding as a first course, so mastering it in a month may be a bit unrealistic unless you commit a very large fraction of your time into it--however, it also doubles as a very good reference book, meaning it will probably come handy while you are taking the class itself. If you are looking for very simple things, I'm not certain what advice to give other than simply going to the local university library and seeing which book looks most appealing, but if you are willing to seriously study number theory, Hardy and Wright should set you straight. On the other hand, if all you want is to familiarize yourself with the kinds of ideas and computations done in your upcoming cryptanalysis class, perhaps you should find out what the textbook is beforehand and study it. The best person to know what you need if you lack background knowledge is the professor that is to teach this class, so seeking his or her advice on this matter would be best. All those alternatives need not be mutually exclusive, and if you have any specific questions, go ahead and ask.

[Antares]

The first things to understand when talking about cryptography are the concepts of big-integer arithmetics.

I have written one with the most common algorithms myself (i had some help from "Knuth").

Another thing is calculating prime numbers for asymetric encryption with only a certain propability rather than absolute.

Well... of course there are a lot of other things, like hash algorithms, the principal of (a)symetric cryptography in general, cipher-block-chaining just to name a few.

Then there are some famous cryptographic algortihms/mechanims like RSA, DES3 and Diffie-Hellmann.

[Kuroneko]

Hm... that reminds me. Knuth's The Art of Computer Programming is actually a fairly good resource for elementary number theory and its the implementation of big-number arithmetic in computers, particularly volume 2. Number theory is not the book's primary focus, so gaining more than basic familiarity with it alone would be impossible, but if your cryptanalysis course is programming-oriented (rather than purely theoretical), as it probably would be, then Knuth would be worthwhile regardless. It would depend on how much you are concerned with number theory itself and how much with cryptanalysis--I'm rather unclear on how one can understand everything in the lectures but have no understanding on the functions involved, so I don't know where you currently stand.