Aided by advances in sensors and algorithms, systems for localizing and tracking target objects or events have become ubiquitous in recent years. Most of these systems operate on the principle of fusing measurements of distance and/or direction to the target made by a set of spatially distributed observers using sensors that measure signals such as RF, acoustic, or optical. The computation of the target's location is done using multilateration and multiangulation algorithms, typically running at an aggregation node that, in addition to the distance/direction measurements, also needs to know the observers' locations. This presents a privacy risk for an observer that does not trust the aggregation node or other observers and could in turn lead to lack of participation. For example, consider a crowd-sourced sensing system where citizens are required to report security threats, or a smart car, stranded with a malfunctioning GPS, sending out localization requests to neighboring cars - in both cases, observer (i.e., citizens and cars respectively) participation can be increased by keeping their location private. This paper presents PrOLoc, a localization system that combines partially homomorphic encryption with a new way of structuring the localization problem to enable efficient and accurate computation of a target's location without requiring observers to make public their locations or measurements. Moreover, and unlike previously proposed perturbation based techniques, PrOLoc is also resilient to malicious active false data injection atacks. We present two realizations of our approach, provide rigorous theoretical guarantees, and also compare the performance of each against traditional methods. Our experiments on real hardware demonstrate that PrOLoc yields location estimates that are accurate while being at least 500× faster than state-of-art secure function evaluation techniques.