Relying on a PKI to provide trust has a number of disadvantages. For one, if a website loses control of its key, the certificate is no longer valid and must be revoked. Thus, in practice, TLS certificates contain instructions for determining whether or not they have been revoked, and clients can follow this to determine revocation status. The two main mechanisms for this are certificate revocation lists (CRLs) and OCSP. The problem with these online revocation checks is that [they don't work in practice](https://www.imperialviolet.org/2011/03/18/revocation.html). In short, online checks require being able to query a service (presumably run by the issuing CA) as to the revocation status of a certificate, but due to reluctance to have an availability requirement on these services, clients have generally accepted certificates when the online check times out. Soft-fail mechanisms are clearly vulnerable to active attacks, thereby limiting the effectiveness of certificate revocation schemes.
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