Satellite operators have high incentives to protect their satellites from collision due to the high cost of designing, building, launching and maintaining the satellites. Unfortunately, the fact that satellite owners often view the satellite trajectories as private posts a serious barrier to coordination between different operators for more accurate collision detection and prevention. This privacy concern becomes more apparent for satellites used for military purposes given that satellites location could reveal countries’ military operations, intelligence-gathering methods, interests in specific regions of the Earth, or technology capabilities.
A 2014 report from the RAND Corporation proposed a method that enables satellite operators to calculate collision probabilities (conjunction analysis) without sharing private information about the trajectories of their satellites using cryptographic tools for the first time. Two years later, a paper optimized the implementation proposed in the RAND paper. However, even with the optimization, this method is still too slow to feasibly run it on all of the objects to detect possible collisions and thus is impractical if the operator owns multiple satellites.
In this work, I propose and implement a new method that is able to detect the satellites at risk of collision without revealing the location information using “fuzzy” private set intersection (PSI) and PSI with significantly reduced running time. The running time of our method is dramatically quicker and making our method much more scalable. Thus, it is able to run on every pair of first 751 satellites extracted from the most recent satellites tle data provided by Space-Track with 5.5 × 10^7 AND gates, where the sate of art of conjuction analysis would take 5.7 × 10^10 MULT gates. And each MULT gate requires different number of AND gates depending on the number of bits and implementations. However, the speed comes with the expense of accuracy. With difference choice of parameters, there are different levels of false positives and false negatives rates. When the collision distance is 500km, there can be around 20% false negatives rates.
← Back to Projects