Lsof is an extremely powerful unix diagnostic tool. Its name stands for LiSt Open Files, and it does just that. It lists information about any files that are open by processes currently running on the system. It easily pinpoints which process is using each network connection / open port. FAQ available here.
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Samhain (stable branch) is a file system integrity checker that can be used as a client/server application for centralized monitoring of networked hosts. Databases and configuration files can be stored on the server. In addition to forwarding reports to the log server via authenticated TCP/IP connections, several other logging facilities (e-mail, console, tamper-resistant log file, and syslog) are available. Tested on Linux, AIX 4.1, HP-UX 10.20, Unixware 7.1.0, and Solaris 2.6.
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The Openwall Linux kernel patch is a collection of security "hardening" features for the Linux kernel which can stop most 'cookbook' buffer overflow exploits. The patch can also add more privacy to the system by restricting access to parts of /proc so that users may not see what others are doing. Also tightens down file descriptors 0, 1, and 2, implements process limits and shared memory destruction.
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