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Id like to create an application which trusts certificates issued from specific CAs.

My ideas is to have a list of thumbprints for CA certificates I trust. Then whenever my app receives a certificate for authentication, it checks its cert chain and makes sure the thumbprint of its issuing certificate is found in my "trusted thumbprints list".

However, what happens when a CA certificate expires? Will the CA generate a new certificate with a different thumbprint, forcing me to update my list of trusted thumbprints whenever this occurs?

Would trusting CA certs based on public key make a difference, or will these be rotated as well?

How about trusting CA SAN? Can a malicious party create issuing certificates with the same SAN as one of my trusted CAs?

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First, a thumbprint (also called fingerprint) of a CA certificate is not sufficient to verify the trust chain. In order to validate the trust chain you need to have the public key of the CA which is contained in the CA certificate but not in the thumbprint. Still, you can have a collection of CA certificates and then define using the thumbprint which to trust and which not.

Whenever a certificate gets renewed the certificate fingerprint will change because the fingerprint is computed based on the full certificate, which includes the (changed) expiration. A public key fingerprint is more stable in this regard since a renewal might reuse the previous public key and in this case the public key fingerprint will not change. But while this is at least possible it is far from guaranteed. A CA might decide to use a different public key, for example because the previous one was considered too weak and not sufficiently future proof.

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