What prerequisite knowledge is needed to understand "Multiplicative group of integers modulo n"

I want to self teach myself Multiplicative group of integers modulo n since it's a foundation in cryptography, IT Security, and Microsoft's UProve technology.

When I go to the Wikipedia page I am lost in a sea of symbols I don't understand, and terminology that overwhelms me. I don't know where to begin.

What is the simplest most effective way for me to learn this group property especially in how it relates to UProve and encryption (if possible).

I would be most appreciative if someone could guide me with a set of building blocks of knowledge (terms, links, etc) that will get me to the point of comprehension.

Please assist in tagging this question properly.

Solution 1:

Studying the group $(\mathbb{Z}/n\mathbb{Z})^\times$ is pretty basic group theory. Any intro book in abstract algebra would be appropriate (I suggest Gallian's Contemporary Abstract Algebra; it is very thorough in dealing with groups). It will also be very important to know the Euler totient function as this gives the order of the multiplicative group. Fermat's Little Theorem and Euler's Theorem will be critical parts of understanding RSA cryptography. As far as links, there are countless I could provide. It really depends on your style and "mathematics maturity" so to speak. You'll have no problem finding a wealth of resources online