Security of L2FE-Hash for non-uniform input distributions

Prove that the L2FE-Hash fuzzy extractor remains computationally secure when the input embedding distribution X is non-uniform but well-behaved, in the sense that each disjoint ε-ball (representing a user identity) in the support C_ε has bounded probability mass; specifically, show that the L2FE-Hash output conditioned on the helper string retains sufficient min-entropy and is computationally indistinguishable from random under these non-uniform conditions.

Background

The paper proves L2FE-Hash security as a fuzzy extractor under the assumption that the input distribution X is uniform over a union of disjoint ε-balls (C_ε). This yields computational indistinguishability of outputs from uniform, thereby satisfying fuzzy extractor security and the ideal primitive’s security property.

Real-world face embedding distributions are typically non-uniform. The authors identify a broader, practical class—non-uniform but well-behaved distributions with bounded mass per ε-ball—and conjecture that L2FE-Hash remains secure under such distributions by maintaining sufficient min-entropy in its outputs conditioned on helper data.

A proof would extend the theoretical guarantee of L2FE-Hash to more realistic distributions encountered in practice and solidify its applicability beyond the uniform-support assumption.