If you're interested in doing a PhD in computer security and cryptography, you should definitely apply to Cornell University's CS PhD program. We have one of the largest and most active research groups in the world. When measured by top-tier papers in security and cryptography over the last decade we are apparently number one, though that's certainly not the best way to measure our quality.

Despite having two locations (Ithaca, New York and New York City), Cornell has a single, unified PhD program. PhD students move to where their advisers are located. If you're interested in working with me, you should apply to the Cornell CS PhD program. Put me down in your application as a contact at Cornell (whether or not we've actually spoken, this helps us route applications during review) and mention me by name in your statement of purpose. Even if admitted, expressing interest in working with me is not going to be an obligation to do so: students are admitted to the program, not individual research groups, and given the freedom to explore working with multiple potential advisers regardless of what they put in their original application. Similarly, being accepted does not guarantee we will be able to work together, you should reach out to discuss with me your situation as you navigate the application and decision process.

Individual faculty can't unilaterally make acceptance decisions, rather all decisions are made by an admissions committee. Admissions are highly competitive.

Good luck!