The private key is the most important part of the public key infrastructure. For the Root Certification Authority (CA) the private key is the "root anchor" of trust. If there is only one tier to a PKI hierarchy, everything depends on this private key being kept safe. The risk of having just one tier, is that the one private key needs to be available to sign the certificates used by the various endpoints verified by the PKI.
If a certificate is "self signed" or the private key of a single tier infrastructure, and the private key is ever compromised, all trust is lost. A new trusted certificate must be issued and all entities that depend on the compromised must must be updated to trust the new private key. This can be a very expensive and time consuming process.
Now what if we have a multi-tier PKI, where the root CA is offline and the intermediate and issuing CAs are online, and one of the online CAs is compromised?
Each of the online tiers is configured to provide information on how to access a Certificate Revocation List (CRL), and this information is included in the certificates they issue. Entities regularly check the certificates presented to them against the CRL, and reject any certificate that is on the CRL. In the case of a CA, the certificate-issuing-certificate is invalidated, along with all the certificates under it. A new CA is created, its certificate signed, and the invalidated certificates are reissued.
When an endpoint encounters one of these new certificates the chain of trust is followed back to the still trusted root CA. The endpoint can present the new issuing CA certificate, which is then implicitly trusted by the endpoint.
The risks to the offline root CA private key can be divided into two categories:
The loss of trust in the private key integrity is important to understand. With the speed at which attackers are capable of moving, even one minute of unauthorized access to the private key can result in the loss of trust in the key. If it is possible the key data was accessed, then the key must be considered compromised.