Can computer science student do PhD under supervisor in mathematics?
The answer is Maybe...

I know quite a lot of person, which are currently involved in a PhD. Since it is about cloud security, it might be useful to have a supervisor knowing algebra, since cryptography is more in the domain of mathematics than of computer science.

Since you seem not to know what you should expect from your supervisor, you might want this person what she thinks about this.
Ask her something related to the following :


What is the role of a supervisor in this PhD ?
What do you expect from me ?
In which area would you think your expertise will help me in this PhD ? Will I not struggle on the computer science's side ?


It might help you understand what you will do, what she will help you with, etc...

Hope it helps.