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An attack tree decomposes 'the attacker wins' into the OR/AND combinations of sub-goals that would achieve it. Where STRIDE is a checklist, attack trees are an actual logic structure — each leaf is a specific technique with a cost, and the root is reachable if any sufficient path is. They're how you reason about which control gives you the most marginal security per dollar.
Root goal: 'attacker reads my customers' PII'. OR branches: (1) compromise the DB host, (2) abuse an over-permissive query API, (3) phish an internal employee with prod access. Each branch decomposes further; each leaf has a cost.