How do you calculate the cost to achieve the root goal in an Attack Tree?

Work bottom-up: AND nodes sum their children's costs, OR nodes take the minimum — the root value is the cheapest complete attack path.

* Attack-tree cost propagation — OR takes the cheapest child, AND sums children; the root is the cheapest whole path. *

Worked example — an "Open Safe" attack tree with a cost on each leaf:

Starting from leaves, work up:

1. AND nodes: Sum children (e.g., Eavesdrop = Listen $20K + Get Target to State Combo $40K = $60K)
2. OR nodes: Take minimum (e.g., Get Combo From Target = min(Threaten $60K, Blackmail $100K, Eavesdrop $60K, Bribe $20K) = $20K)

Full calculation:

• Learn Combo path = min($75K, $20K) = $20K
• All OR children of Open Safe: Pick Lock $30K, Learn Combo $20K, Cut Safe $10K, Install Improperly $100K
• Root goal cost = $10K (Cut Open Safe is cheapest)

Defensive insight: To protect the safe, invest in making "Cut Open Safe" harder/more expensive, since it's the current cheapest attack.

Go deeper:

• Bruce Schneier — Attack Trees — the OR = min / AND = sum value-propagation method.