The top scoring answer, “What makes you think they don’t get caught”, by atdre, while more of a challenge to the original question, has proven to be quite appropriate, as over the last year various alleged members of Anonymous have been caught. Some through informants, others through intelligence work, however the remainder of the answers focus on the technical and structural reasons why Anonymous continues to be a major force on the Internet.
SteveS, Purge, mrnap, tylerl and others mention the usual way attackers hide on the Internet – using machines in other countries, generally owned by unwitting individuals who have not protected them sufficiently (This includes botnets – but there are also willing botnets, provided by followers of Anonymous – who allow their machines to be used for attacks) and by routing through networks such as TOR (The Onion Router) so that even if law enforcement try to trace the connection back they will fail either because there are too many connections to track, or because some of the connections will pass through countries where the Internet Service Providers are not able or willing to assist with the trace.
I think Eli hit the nail on the head, however with “because anonymous can be anyone, literally” – as while there are certainly a core group of skilled and motivated individuals, there are many thousands of individuals who will contribute to an attack, and these individuals may be different from one month to the next as the nature of Anonymous allows people to join and take part as and when they want to, if a particular cause is of interest to them.
The Lulzsec spinoff from Anonymous appeared to be a deliberately short lived group who wanted to do something less political, and more for “the lulz” – focusing on large corporates and security organisations to highlight weaknesses in controls, and nealmcb provided links in comments to articles on this group in particular. In terms of detection, the same comments apply here as to the wider Anonymous group.
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