This is from Stripe's website:
All card numbers are encrypted on disk with AES-256. Decryption keys are stored on separate machines. None of Stripe's internal servers and daemons are able to obtain plaintext card numbers; instead, they can just request that cards be sent to a service provider on a static whitelist. Stripe's infrastructure for storing, decrypting, and transmitting card numbers runs in separate hosting infrastructure, and doesn't share any credentials with Stripe's primary services (API, website, etc.).
You can read more about the security features of Stripe here: https://stripe.com/help/security
Let us know if you have any additional questions.