For ssh they both have private and public keys. The server could be at risk of having it’s own private key compromised if somebody breaks in, and vice versa a compromised client can lose its private key. The original wording made it sound like a compromised server would steal client keys.
That server’s root access is now vulnerable to a compromise of the systems that have the private key.
Only the server should have the private key. Why would other systems have the private key?
The client has the private key, the server has the corresponding public key in its authorized keys file.
The server is vulnerable to the private key getting stolen from the client.
For ssh they both have private and public keys. The server could be at risk of having it’s own private key compromised if somebody breaks in, and vice versa a compromised client can lose its private key. The original wording made it sound like a compromised server would steal client keys.
Also passworded keys are recommended
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Finding an exploit in ssh is worth more than whatever your server has to offer though.
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