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When a user initiates a SSH connection for example, keys are exchanged and a session is established with a new "passphrase" each time. If an attacker were to attempt to brute force this connection, their chances of cracking the "passphrase" would be much higher if the connection persisted for a long period of time right? If this is true, wouldn't it make sense for secure connections such as OpenVPN, SSH, and SSL/TLS to "reboot" the connection, thus generating a new "passphrase" between the two hosts and foil the brute force attack? If this is true, has it been implemented already?

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It is implemented. Look for 'session re-keying'.

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