Although this question was asked by an individual wanting to record his own sessions, an alternative use case might be a system administrator who wants to keep track of what various users are doing.
I fear running
script inside the system-wide
bashrc might not be suitable in the case when users of the machine are reluctant to have recordings made of their sessions.
Users who wish to remain incognito could bypass the logging by asking sshd to open a different shell (e.g.
zsh) or run
bash --rcfile ___ to prevent
/etc/bash.bashrc from being loaded.
This guide from 2008 uses a different method to force
script to be run when a user logs in with ssh, which requires users to log in with a public/private key.
This is done by adding a script to the user's
.ssh/authorized_keys file, in front of the key:
command="/usr/local/sbin/log-session" ssh-dss AAAAB3NzaC1kc3MAAAEBAMKr1HxJz.....
log-session script then decides whether or not to run
/usr/bin/script to log this user's session.
To prevent the user from removing the added command, the administrator will need to assume ownership of the user's
chown root:root ~user/.ssh/authorized_keys
Unfortunately, this means the user won't be able to add any additional keys him/herself, or more importantly revoke the existing key if it is compromised, which is far from ideal.
It is common for sshd's default configuration to allow users to perform SFTP over their ssh login. This offers a way for users to edit files without the changes being logged. If the administrator does not want users to be able to do that, then he should either enable some logging for SFTP, or disable the service. Although even then, users could still make unseen changes to files by running something like this in their terminal:
curl "http://users.home/server/new_data" > existing_file
It is unlikely that logging user sessions provides any real security for administrators. By default a user can only manipulate their own files, and cannot harm the system. If a malicious user did manage to escalate privileges, then he could disable logging and delete the logs (unless the administrator has configured logs to be stored on a separate machine, in an append-only fashion).
Administrators who do automatically log user sessions should probably inform the users that this is being done. In some jurisdictions, this form of data collection might violate data or privacy laws. And at the very least, it would be respectful to users to make them aware.
It is more likely that an administrator would be interested in logging the sessions of
sudo users. That could perhaps be tackled in a different answer, or indeed a different question.