What are the ways of keeping a shared LAMP server secure, assuming SSH access is available for every user?
Edit: I am mainly thinking of securing the server from the users themselves and between themselves.
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It’s probably impossible, but you can make it harder for an attacker to succeed.
Strengthen your defenses:
Security harden the system (maybe referencing one of the following checklists)
http://iase.disa.mil/stigs/checklist/ (look for UNIX Security Checklist)
A decent comparison of the above tools is described here: http://www.lifelinux.com/selinux-vs-apparmor-vs-grsecurity-345.html
Keep up to date on security patches.
Deploy a HIDS (e.g. OSSEC) to help you detect when users are behaving bad.
All of the above will require continual effort. That is security.
In addition to the other answers:
The permissions of programs (cgi, php, etc.) executed by the webserver is an issue:
If they run with the permissions of the webserver, a malicious user can access the files provided by others users. I am thinking of configuration files with database credentials here.
If those programs run with the permission of the individual users, they may modify program files themselves. This might make it easier to exploit security issues in the applications, for example a .php script might not properly validate file names when it saves files. And the users needs write permissions in the web directory, so the php program has write permissions there, too.
SourceForge has released an apache module and a fuse file system that allows for finer grained permissions:
Permissions bits are in a standard trio of "rwx" (read/write/execute) sets, but the normal "user" (owner), "group", and "other" categories are replaced by the trio of "project member", "project-initiated apache access", and "everyone".
Basically there's nothing you can do to really make things secure as things such as wordpress always end up with massive security problems, as well as PHP itself etc.
The only way (I think) to be quite sure is to run each site in a separate virtual machine. This (almost) totally isolates one site from another, but it of course has the overhead of having to administer every VM, has more memory usage, more CPU cycles etc.
Oh and each VM needs all of the software patching continually.
It's certainly worth considering though as it's far more secure than trying to keep on top of all those sites.