Extreme points of the local differential privacy polytope

Abstract

We study the convex polytope of n×n stochastic matrices that define locally ϵ-differentially private mechanisms. We first present invariance properties of the polytope and results reducing the number of constraints needed to define it. Our main results concern the extreme points of the polytope. In particular, we completely characterise these for matrices with 1, 2 or n non-zero columns.