Your cutting it VERY tight. What if there is a 10 minute delay to the train or there is a delay at the security point. Is there a way you can get an earlier train, or else I would suggest a later flight. If you miss, you would need to pay what ever change fee their is on your ticket.
Figure more like 15 minutes. The elevates walkway can be busy, slowing you down.
Plus, avoid the main elevators at the end of the elevated walkway, as they are waay too busy.
Head straight ahead into T1, turn left and head to the end of the check-in hall. Use the elevators there down to G/F. Still a few more steps from there to T3.
Alternative, but not recommended in busy morning traffic or minus daylight, could be to cut across roads from "The Station" to T3. But again, only viable if you know your way around.
Overall a very tight connection, but if it is the only option, might be worth taking the risk.
Carpe diem ! Life is too short to waste your time ! Keep in mind, that today is the first day of the rest of your life !