Considering the classic scenario of Eve trying to listen in to Alice and Bob's conversation, if Eve can intercept messages between Alice and Bob but with no access to their computers would Timing attacks be possible? Am I right in saying it isnt possible because say Alice sends a message to Bob how will Eve listen in to how long Bob's computer will take to decrypt the message?
Eve could not just listen to the communication. If you're talking about RSA I assume that Bob's public key is not secret and that even Eve might know it. Then Eve could try to act as Alice by sending messages encrypted with Bob's public key to Bob. If Bob always answers those messages Eve could use the delay until Eve receives the message to perform a timing attack.
Even if Eve can only listen to the communication and Bob sends a reply to Alice every time he receives a message Eve could measure the time between Alice's message and Bob's reply.
Only if Bob does not reply to Alice's messages a timing attack would not be possible. If Bob must reply to Alice's messages Bob must reply only after a fixed amount of time. For example, if it takes at most 100ms to decrypt a message and Bob decrypts some message in 78ms, Bob has to wait 22ms until he is allowed to send a response.