CheekyBucket use the shopping cart produced by a company called Cartloom and all payments are made via the shopping cart and Paypal. No credit card information or account information goes through the CheekyBucket site, it is all handled by Paypal.
Cartloom does not hold any buyer information it is all handled through Paypal. For more information on the Secure gateways it uses for payment processes please see Security under the the features page here.
For general information on Payapl Security please click here.