> I would like to write a program that could deycrypt ssh communication
> by using the private key of the server computer. This should be

possable right?

I don't believe that is the case. SSH uses its private key only to
certify its identity to the client. So knowing the private key lets
you do a monkey in the middle attack, but not to decrypt a captured
stream.

Keying material is derived using the Diffie-Hellman algorithm, which
uses randomly generated secrets at both ends. You'd have to know the
transient Diffie-Hellman secret used by either the server or client.

Regards
Mark