Most research is sponsored by DARPA or the government (I suppose requires security clearance)
Some specific research projects in cybersecurity may require security clearance, or are restricted to US citizens. The vast majority are not restricted in this way. You can see this for yourself by looking at the author lists of papers published in conferences like S&P. Specifically look at those papers coming from US institutions and note the many papers with at least one author who is an international student.
US graduate programs in cybersecurity routinely admit large numbers of international students, who for the most part have access to the same research opportunities as students that are US citizens. If you want to be sure that the program you are applying to conducts research in which non-citizens may participate, check the authors of publications coming out of that lab - look up the authors online, and see if there are many international students among them. Some labs might also have a web page where they list current graduate students involved in their research.
(You obviously can't determine citizenship of an author accurately with a Google search, but if there are a large number of international students involved, it's almost certain that there are also non-citizens involved.)
One difference is that you will not be eligible for certain federal fellowships specifically for US citizen students involved in cybersecurity research, such as the Scholarship for Service program.