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Update 22.10.2017: updated use-case recommendations based on best practices.
Update 27.06.2018: added commands
In this article I will discuss about Root CA certificate renewal with new and existing key pair. At first we discuss about CA certificate renewal with existing key pair.
When you renew CA certificate with existing key pair, nothing important in certificate is changed. The certificate will contain the same public and private key. As the result all previously issued certificates will chain up to new CA cert without any changes. You just replace old CRT file in AIA download locations. In addition, new CA cert ValidFrom (NotBefore) field will contain the value when existing CA key pair was generated. For example, old CA cert has ValidFrom (NotBefore) = 08.10.2000 and ValidTo (NotAfter) 08.10.2010. When you renew CA cert with existing key pair new certificate will have following values: ValidFrom (NotBefore) 08.10.2000 and ValidTo (NotAfter) 08.10.2020. In other words this renewal just increases current CA certificate validity period. In addition new CA cert introduces one new extension: Preious CA certificate hash that will contains preious certificate Thumbprint extension value. And changes another extension: CA Version. Let's take a look to a CA Version extension.
Recently I decided to perform little changes on my OCSP Responder. I'm using offline CA (root) and have configured to include OCSP URL to all issued certificates. But some time I haven't OCSP configuration for my root CA. And today I have completed all changes and now Root CA issues OCSP signing certs for appropriate OCSP configuration.
You can find required info about the subject on TechNet: Online Responder Installation, Configuration, and Troubleshooting Guide or in AskDS blog: Implementing an OCSP responder: Part IV - Configuring OCSP for use with Standalone CAs. However both links contains incorrect settings, therefore I'll post correct steps.