The paper introduces the concept of geo-indistinguishability, a formal notion of privacy for location-based systems (LBSs) that protects users' exact locations while allowing approximate information to be released. This concept formalizes the idea of protecting a user's location within a radius \( r \) with a level of privacy that depends on \( r \), corresponding to a generalized version of differential privacy. The authors propose a mechanism to achieve geo-indistinguishability by adding controlled random noise to the user's location, specifically using a planar Laplace distribution. They demonstrate how this mechanism can enhance LBS applications with geo-indistinguishability guarantees without compromising the quality of the application results. The paper also compares their mechanism with state-of-the-art mechanisms, showing that it offers the best privacy guarantees among those that do not depend on the adversary's prior knowledge. The contributions of the paper include a formal definition of geo-indistinguishability, a mechanism to achieve it, and a comparison with existing methods.The paper introduces the concept of geo-indistinguishability, a formal notion of privacy for location-based systems (LBSs) that protects users' exact locations while allowing approximate information to be released. This concept formalizes the idea of protecting a user's location within a radius \( r \) with a level of privacy that depends on \( r \), corresponding to a generalized version of differential privacy. The authors propose a mechanism to achieve geo-indistinguishability by adding controlled random noise to the user's location, specifically using a planar Laplace distribution. They demonstrate how this mechanism can enhance LBS applications with geo-indistinguishability guarantees without compromising the quality of the application results. The paper also compares their mechanism with state-of-the-art mechanisms, showing that it offers the best privacy guarantees among those that do not depend on the adversary's prior knowledge. The contributions of the paper include a formal definition of geo-indistinguishability, a mechanism to achieve it, and a comparison with existing methods.