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In a video posted on YouTube on Friday, the collective said that "to defend our values and our freedom, we're tracking down members of the terrorist group responsible for these attacks."
Referring to similar promises in the aftermath of the Paris and Brussels terror attacks, the hacktivist group said: "We have already expressed our determination to neutralize anybody who will attack our freedom. We'll be doing the same now...expect a total mobilization on our part."
As part of the #OpParis campaign in November 2015 - launched in response to the Paris attacks that left 130 people dead - the collective claimed to have taken down 20,000 Twitter accounts linked to Islamic State (IS, formerly ISIS/ISIL).
Months later, the hacktivist group launched #OpBrussels in response to attacks on Brussels Airport and the city's subway system. As part of that operation, the group claimed to have "severely punished" IS on the darknet by hacking the terror group's electronic portfolio and stealing money.
The group also announced a cyber war on Turkey over its alleged support of IS in December.
Anonymous, which was founded in the 4Chan forum in the late 2000s, is described on an affiliated website as a loosely-connected global network of hacktivists with a "very loose and decentralized command structure that operates on ideas rather than directives."