Scoring Azure permissions with metric spaces

In this work, we introduce two complementary metrics for quantifying and scoring privilege risk in Microsoft Azure. In the Control Plane, we define the WAR distance, a superincreasing distance over Write, Action, and Read control permissions, which yields a total ordering of principals by their configuration power. In the Data Plane, we present a blast radius distance for measuring the maximum breadth of data exfiltration and forgery, leveraging the natural ultrametry of Azure Tenants clustering hierarchy Together, these metrics offer a unified framework for proactive IAM analysis, ranking, lifecycle monitoring, and least privilege enforcement.