Challenge Response Authentication - Client Generating Challenge Let's say we have a client (the not trusted party) and the server(wants to verify that the client is who he claims to be.

The client has access to both the private key and the public key, whereas the server only knows the public key.

Question
Instead of the server being responsible for generating the challenge, would it be as safe if the the client himself generated a random challenge and later signed it (so that the server could later verify this). Is there a weakness in RSA that would make this scenario bad?

NOTE
The public/private key pair will only be used once, and will be re-generated each time.
The attacker can use replay attack, i.e, he/she can replay a challenge that is signed by the user in the past(which is used as a challenge to server) and can send this as a nonce to the server. To avoid this, server generates and sends the challenge.The idea works if server maintains a list of previous nonce used but this has its limitations on practical implementation.

Hope this helps.