The Berkeley Packet Filter (BPF) started (article 1992) as a special-purpose virtual machine (register based filter evaluator) for filtering network packets, best known for its use in tcpdump. It is documented in the kernel tree, in the first part of: Documentation/networking/filter.txt
The extended BPF (eBPF) variant has become a universal in-kernel virtual machine, that has hooks all over the kernel. The eBPF instruction set is quite different, see description in section “BPF kernel internals” of Documentation/networking/filter.txt or look at this presentation by Alexei.
eBPF enables programmers to write code which gets executed in kernel space in a more secure and restricted environment. Yet this environment enables them to create tools which otherwise would require writing a new kernel module.
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