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.