1. If a side channel attack in a noisy environment is the best attack, you're way ahead of most of the computing world
2. This is why cloud providers offer the option of dedicated provisioning where you can use the cloud APIs but ensure that your VMs run on hosts dedicated to your organization.
WRT #1, a much simpler attack is to either become an employee or subvert an employee of the VM hosting company, pause the victim VM, and read the keys out of RAM.
2. This is why cloud providers offer the option of dedicated provisioning where you can use the cloud APIs but ensure that your VMs run on hosts dedicated to your organization.