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If a root certificate has a 2048 bit key is it correct to assume that if a certificate request signs a request made by a 4096 bit key and generates a certificate that the security has been weakened to some degree.

For example if a client application is encrypting the data (HTTPS) then, since the issued certificate has a 4096 bit private key / cert that the strength of the encryption / confidentiality of the HTTPs connections aren't weakened, only the trust associated with the CA?

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The strength of the key in the CA certificate is only relevant for the strength of the signature on the issued certificate. A weak enough CA key means that somebody could find the matching private key and would then be able to create arbitrary certificates which look like they were issued by the CA.

Thus a weak CA key does not affect the strength of the encryption or the strength of the key exchange but it weakens the authentication part of the TLS handshake. This means that the client more likely considers a server as the correct one even though it is an attacker which was able to create a fake certificate which essentially means a possible man in the middle attack.

Still, the 2048 bit RSA key in your example is still considered strong enough at the moment so it is not actually considered a practically relevant weakness currently.

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