I have some problems to understand the storage of my private key when a CA generates my key pair. Let's assume the CA creates my key pair, issues the certificate with my public key and signs it with the corresponding private key. So MY private key is first stored at the CA and after issuing of my certificate I will get my private key? Is that right?
Typically you send a Certificate Signing Request (CSR) to the CA. The CSR contains everything you want to be inside your certificate, including your public key. The CA takes a look, and if it likes it, creates a certificate and signs it and sends it back to you. The CA never has to see your private key.