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These considerations are not at all true in an EAP authentication context, such as an eduroam login. Here, the end user device is pre-provisioned with the entire set of information it needs to verify this specific TLS connection: the IdP has a certificate from exactly one CA, and needs to communicate both that CA and the name of his authentication server to the end user. A trust store list from the web browser is thus insignificant in this context; certificates from a commercial CA are as valid for EAP conversation authentications as are self-made certificates or certificates from a small, special-purpose CA. For a commercial CA, the installation of the actual CA file may be superfluous in some client operating systems (particularly those who make their "web browser" trust store also accessible for EAP purposes), but marking that particular CA as trusted for this specific EAP authentication setup still needs to be done.
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