We created the new keys and certificates.
After replacing the files in /var/lib/puppet/ssl/private_keys/server.pem and /var/lib/puppet/ssl/certs/server.pem
The web interface is fine.
However, the node.rb failed with the error:
SSL_connect returned=1 errno=0 state=SSLv3 read server session ticket A: sslv3 alert unsupported certificate