  While the existing literature on Differential Privacy (DP) auditing
predominantly focuses on the centralized model (e.g., in auditing the DP-SGD
algorithm), we advocate for extending this approach to audit Local DP (LDP). To
achieve this, we introduce the LDP-Auditor framework for empirically estimating
the privacy loss of locally differentially private mechanisms. This approach
leverages recent advances in designing privacy attacks against LDP frequency
estimation protocols. More precisely, through the analysis of numerous
state-of-the-art LDP protocols, we extensively explore the factors influencing
the privacy audit, such as the impact of different encoding and perturbation
functions. Additionally, we investigate the influence of the domain size and
the theoretical privacy loss parameters $\epsilon$ and $\delta$ on local
privacy estimation. In-depth case studies are also conducted to explore
specific aspects of LDP auditing, including distinguishability attacks on LDP
protocols for longitudinal studies and multidimensional data. Finally, we
present a notable achievement of our LDP-Auditor framework, which is the
discovery of a bug in a state-of-the-art LDP Python package. Overall, our
LDP-Auditor framework as well as our study offer valuable insights into the
sources of randomness and information loss in LDP protocols. These
contributions collectively provide a realistic understanding of the local
privacy loss, which can help practitioners in selecting the LDP mechanism and
privacy parameters that best align with their specific requirements. We
open-sourced LDP-Auditor in \url{https://github.com/hharcolezi/ldp-audit}.
