Why Nonces and timestamps are used in Public key authority?
To understand how nonces and timestamps are used to prevent a replay attack, you must understand generally what a replay attack is. A replay attack is a network attack in which a data transmission (that is valid) is repeated or delayed. An attack like this is usually done by an adversary who happens to intercept this data and re-transmits it. 

If Alice (Initiator A) and Bob (Responder B) are conversing, Alice can send over a nonce with a MAC which can be checked by Bob to verify that it is Alice and not an adversary sending it. 

Timestamping also is important because if Alice sends a message with one, Bob can choose to only accept messages with reasonable timestamps. 

So for 'Certificate-Based Key exchanges', Alice provides nonce, or a timestamp along with her certificate. This will help preventing Replay Attacks!