Math PhD careers

Question

I am an undergraduate pure mathematics major who would like to maybe go to graduate school and then do industry research, but I am first wondering what kind of industry research jobs are actually available and what to expect. I understand pure math research is unlikely in private industry, but what about applied? What can I expect, what focuses are there and how much do they pay? I am not even sure whether a PhD is necessary for the job positions that most math PhDs seem to go to. I personally have been thinking it may be cool to go into cryptography or algorithms or something, but I'm not sure if that's feasible or high paying or anything.