Four implications follow:
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Because the certificate contains the subjects's public key, the certificate and the private key together are all that is needed to encrypt and decrypt.
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To verify certificates, you need the certificates of all CAs you trust.
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The simplest form of a dummy-certificate is one that is signed by the subject.
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A CA is needed. The client can't simply issue local certificates for servers it trusts because the server determines which certificate it presents.