Properties of the product like security, reliability, and quality are the job of the entire team, not just one department.
I was recently reading Lessons Learned in Software Testing and would like to highlight three lessons from chapter 1.
Lesson 4: "Your group's mission includes (or should include) informing clients about anything that threatens the value of the product, according to your clients' definition of value." (Emphasis in original).
Lesson 11: You don't assure quality by testing. "It's all too easy to think of yourself as the guardian of quality. But you don't create quality, and you don't take it away... you can't [do your job] well if you give the impression that you think you're the only one on the product who cares about shipping a good product."
Lesson 13: Beware of the not-my-job theory of testing. "All other things being equal, your mission should be to inform the team, to the best of your ability, about any problems that could adversely impact the value of the product."
Security holes are certainly a "problem that could adversely impact the value of the product." That being said, security testing is absolutely part of the QA process. Obviously, you won't actually be able to find all potential security problems (and it's very dangerous to assume that you will), but don't take such a limited view of QA that you think that this kind of testing is entirely outside of your job.