There are many issues, According to my research experience on Cloud,

1. Searching for the sensitive data ( which is in encrypted form ) is a challenging problem in the cloud storage. Though few companies are currently solving this issue using "Tokenization" algorithms. It still remains a challenge in a massive storage and not studied much.

2. Encrypting the Cloud database is an another major problem.

3.There are no practical solutions available till date to support distributed clients to connect directly to an encrypted cloud database and make insertions / deletions / updations etc.

There are many similar problems can be listed out related to the current cloud security.