ssh public key authentication

[Markus Kovero]

Hi, I'm asking around is it possible to hijack clients rsa/dsa private key 
if ssh-daemon is modified by someone who has evil means. I thought this was 
good place to ask, so here it goes.

From what i've heard so far is that daemon sends signing request to the 
client and clients signs request using private key and sends answer back to 
the daemon which verifies authentication using public key.

Is this how it really happens, eg. there is no possibility whatsoever that 
client would ever send its private key to server that has possibly infected 
sshd running?

Yours
Markus Kovero