We address the issue of user privacy in the context of “collaborative” positioning, wherein information is passed between and processed by multiple cooperative agents with the goal of achieving high levels of positioning accuracy. In particular, we evaluate the feasibility of applying a layer of encryption to a linear least squares (LS) algorithm for providing position, velocity, and time (PVT) estimates to a user based on information exchanged between neighboring receivers. The goal of such a scheme is to facilitate the requisite transfer and processing of GNSS measurements to achieve improved performance over single-user positioning, as demonstrated in the literature, for instance in mitigating errors induced by ionospheric propagation. Additionally, we wish to maintain that other agents or outside observers do not have access to the information required to locate a given user. We accomplish this by employing “homomorphic encryption” methodologies, in which fundamental mathematical operations may be performed on encrypted data to produce encrypted outputs, without providing access to either input or output to the agent performing the operation. The performance of the LS collaborative positioning methodology is evaluated both with and without encryption, and the results compared to each other as well as to the output of “single-user positioning” where information from other receivers is not used to mitigate the effects of atmospheric interferences. We show that the application of cooperative methodology results in an increase in performance under interference conditions, as compared to the single-user approach, and additionally that the application of homomorphic encryption to this LS approach yields little or no loss in estimation performance over the traditional, unencrypted cooperative LS algorithm.