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Client certificates are, by default, optional; however, the server configuration might require that the client present a valid certificate as part of the initial connection negotiation.
The Framework caches SSL sessions as they are created and attempts to reuse a cached session for a new request, if possible. When attempting to reuse an SSL session, the Framework uses the first element of SmtpClient.ClientCertificates (if there is one), or tries to reuse an anonymous sessions if SmtpClient.ClientCertificates is empty.