Privacy Preserving Underwater Collaborative Localization using Time Lock Puzzles

This paper considers the issue of localizing a lost Autonomous Underwater Vehicle (AUV) using range and position measurements transmitted by an assisting AUV. Revealing the position of the assisting AUV could compromise its own safety and thus we need a privacy-preserving solution to this problem. Since this is a challenging task in the underwater domain, we propose to adopt Time Lock Puzzles, which keep the data of the assisting AUV encrypted until enough sequential work has been performed by the lost AUV. This ensures the safety of the assisting AUV, which gets enough time to move away from the revealed location. The generated delays are handled by augmenting the states of the lost AUV with the state of the lost AUV at the instant it receives a measurement. The augmented states are estimated with an Extended Kalman Filter. The efficacy of the proposed method is presented through a simulation campaign that shows how an AUV can be localized using delayed measurements by leveraging only single-range measurements.