Fixed-Composition Shuffle Asymptotics in the Full-Support Gaussian Regime

Abstract

Fixed-composition shuffle asymptotics in the full-support regime. We identify the Fisher parameter I_pi = v^T Sigma_pi^+ v, prove JSD(T_{n,k} || T_{n,k+1}) = I_pi/(8n) + O(n^-2), and derive the local privacy-curve expansion delta(t mu_n) = mu_n{phi(t) - t Phi(-t)} + O(n^-1), where mu_n = sqrt(I_pi/n). Exact finite-n accounting formulas are also provided.