Daniel Jones shows how to use backup encryption in SQL Server:
The backup encryption in SQL server is needed due to following reasons:
Way to Keep Database File Secure: Users need to encrypt SQL server database backup files because this procedure provides complete security to copy of SQL server data. This security measure will keep transaction logs, tables, and other server data safe from any person, who wants to make use of these data in wrong manner.
Accessed Only By Authorized Person: It is impossible to restore an encrypted backup file, if a person is not having certificate or asymmetric key for decryption. Therefore, it means that only authorized persons who are knowing credentials of encrypted backup file can restore data with its full access.
Encrypting backups (and storing the encryption key somewhere independent of the backups themselves) can help prevent a very bad day.