This is a bit of a snarky answer to your question but... did you try Googling "PhD in Computer Science Security"? Perhaps even more useful have you looked at the offerings of your own university to see what a Masters or PhD entails?
To be a bit less snarky in PhD programs, at least, it's less about what the degree is called and more about the research and lab you become involved with. If you are interested in focusing on security, which is a broad field, in Computer Science you will often get a degree in 'Computer Science' but you will work in a lab focused on security.
With that in mind my first recommendation to you is to do some research. Find out what folks are researching at your current institution, see if you find it interesting. If you can, get involved! This is probably the best way to find out what programs exist out there for your interests.
Even beyond your local school - do some digging. I was about to do a quick Google search and find that there are a couple of schools that are considered to have the 'best'(subjectively of course) Security Information programs. You should be able to find this out as well! Start looking into other schools, see what they offer and also what their researchers are researching. See if anything seems interesting. Start reading papers. Do some research into what you want to do.
So, in short, do:
- Figure out what research is happening at your school. Try to get involved.
- Figure out what are the 'best' programs for the topics you are interested in. Who is the 'big name' in the field? Read those papers!
- Find 1 person who you want to be when you 'grow up'. In other words find one person whose job you want to have one day. Research how they got there! See if you can build a road map to your own success based on how they got to where they are.
