modular mathmatics

[Agent Johnson]

modulo arithmetic does indeed play an important role in many cryptosystems, but simply having a good understanding of modulus arithmetic (and generators, and fields (Abelian field, anyone???), or how about elliptic curve crypto?!?, etc) will not enable you to go out and whip up the next big cryptosystem overnight. Read plenty of books, (Avis187 named some good ones), go to a university (they dont' teach this stuff at the community college level, i've been there), and keep visiting AO, one of the premier sites for security info and discussions.

[loughp]

I would also say that if you're working on building a "new" encryption system without the knowledge that can be gained from working with existing ones, you're likely to make a lot of mistakes that have been made before.

I would suggest instead of trying to build one of your own at this point, pick up one of the books Avis187 suggested (I highly rate Applied Cryptography for a good introduction.) Try to make your own implementation of some of the more simple algorithms in there and understand why they do what they do. This will help you better understand what to look for in speed, security and complexity. They're all trade-offs.

Good luck with it.

[AviS187]

Agent Johnson: You're right about certain things not being taught at community colleges, but only in the sense that they don't usually have courses for which they are part of the curriculum. However, as a person who has gone to a community college in the past, I assure you that if you are lucky enough to have a really good professor they will be able to help you accelerate you learning process to extend far beyond what is normally taught in a particular class, regardless of whether it is officially in the course outline.