One of the most popular and enduring forms of mystery fiction is the whodunit. Readers and audiences love following along to try to determine the actual identity of the attacker based on the clues and observations provided. During and after incident investigations, many folks - from the actual investigators on the case up to the armchair DFIR public - try to figure out the same thing. Unlike "whodunit" fiction, though, we may not have all the information needed. Indeed, we may never even get confirmation of the right answer.
For various reasons, infosec people (especially those who don't actually work in incident response) love to mock the idea of "attribution". Some of that is deserved because of the FUD that policymakers and vendors throw around. Some of it is not, however, and instead reflects the lack of expertise of the commenters.
What attribution means in DFIR
"Attribution" in the DFIR world means assigning some identity to the threat actor in an incident. That identity may not necessarily drill all the way down to the "real life" name and address (though in some cases it will). But it can also include correlating a set of intrusions to the same entity, which can then possibly provide some set of useful data like region or affiliation or operational aspects and observations.
This can include naming the threat actor at any level of specificity from "John Doe at 123 Main Street, Anytown" up to "state-sponsored attackers from Arstotzka". It also includes determining that a given incident belongs to a specific intrusion set, whether you name that intrusion set "APT 1337" or "Pedantic Penguin" or "PURPLERAIN".
When and how it matters
The importance of attribution varies across the type of attribution under discussion as well as the consumer of that intelligence. The law enforcement, intelligence, and military communities have an interest in the actual meatspace identity of their adversaries because they may have authority to apprehend or carry out some type of retribution - handcuffs and cruise missiles, as it were (h/t Scott Roberts. (Criminal actors have a similar interest from their perspective, whether for OPSEC validation or for their own illegal retribution.) For security and malware analysts in the private sector, however, attribution in that sense rarely matters too much unless the adversary is located in a jurisdiction where civil or criminal complaints can be brought.
However, all analysts in all sectors care about understanding the TTPs and capabilities of a given adversary as well as strategic information (e.g. motives and targeting).
Bases for proper attribution
Attribution based on geolocation of IP addresses is generally accepted to be facially invalid, on par with using dice or a magic 8-ball. (There are some exceptions when these methods turns out to produce valid conclusions, but they are just that: exceptions.) Proper attribution requires cross-validating information from across a number of disciplines. Artifacts from malware analysis and forensic examination can play a role, of course, even when they don't provide definitive answers. So do other types of sources and activities such as open-source intelligence, search warrants, interviews, informants, infiltration, and network penetration.
None of these by themselves will necessarily provide sufficient evidence for a solid assessment. For this reason, attribution depends on all-source intelligence analysis. Even when the analysis doesn't produce an actual name, evaluation of detailed TTPs and methodologies can link an incident to a larger intrusion set. Defenders and investigators can then use information found in previous investigations iteratively to improve their prevention and detection capabilities.
When attribution matters
FBI Director James Comey recently gave a speech that mostly got attention because of his mention of Sony's intrusion in the fall of 2014. But he also talked a bit about why attribution matters in the context of changing the cost/benefit calculus for adversaries:
I said we need to impose costs. What do I mean by that? I worry sometimes that whether the actor is a nation state or a criminal or a creep down the block, there's a sense that it's a freebie. That if I'm at a keyboard somehow it's free that I can break in and steal the lifeblood of an American business or steal the identity of an American citizen when it is in reality no different than kicking in your front door and walking out with your television, right? Or dragging something you love dearly out of your life. We have to treat it that way. We have to impose real costs on people who think they're alone - think they're far enough away that it's a freebie.
How those costs increase can vary. Maybe, if you're the FBI, you can go arrest folks. Or maybe you can't because of jurisdiction, but you can instead freeze their bank accounts and deny them the ability to travel to significant parts of the world. Outside of organizations like the FBI, we usually can't do that. Instead, we can beef up our network defenses against the specific TTPs used by the attackers. Perhaps we can implement some sort of deception operation to get them to expend resources pointlessly. (This can have the side benefit of gathering additional intelligence.)
Armchair investigation when treated as intelligence analysis can actually be a useful thought exercise for training and context. But it's just as important to understand what attribution means when carried out by people with the appropriate training and actual information at hand.