Finding top Pure Math colleges

OP: I get the impression from what you’ve said in this thread that you’ve kind of turned things around from your high school days, are excelling at your CC, and have specific interests and experience in math and cryptography that you’d like to take further. And also that you’ve been told – perhaps by faculty at your CC? – that you have a good chance to transfer into some top schools and continue your studies there.

If that’s the case, I suggest you talk further with these faculty, get recommendations from them, suggestions about schools to consider, and ask them for contacts at these schools. They’d very likely know people there, perhaps faculty in the math departments. Then talk to those contacts and, if you can impress them, it might increase your chances of getting into some of those schools. It sounds like you have a somewhat unusual situation, and maybe something like this can benefit you.

In addition, I’d listen to the caution that many other responses are giving you, that it’s very difficult to transfer into many of these top schools. That doesn’t mean you shouldn’t try, but try to get more information on what your chances are, how many transfers each schools generally accept, and consider a variety of schools, not just top ones.