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you may want to consider creating a new administrator account as your current User account is being denied from writing to not only the registry but also the C:\Program Files (x86)\Adobe\Adobe Creative Cloud\.
Please see Error "Exit 6" or "Exit 7" | Install log | Read, write, system file errors | CS5, CS5.5 -http://helpx.adobe.com/creative-suite/kb/error-exit-6-exit-7.html for information on how to adjust your file permissions. This may not resolve the registry permission error though.
You can contact Adobe Support via http://adobe.ly/yxj0t6.