This question is inspired by the disappearance of Malaysian Air 370. Let's suppose the plane crashed into the ocean. These are hotly contested waters where various countries (US, China, India, others) probably have listening devices (hydrophones) that could detect the distance to the source of the sound. Thus, each listening device defines a circle on which the crash occurred. However, to locate the point of the crash, we have to combine the circles from competing interests who are not willing to divulge the location of their listening devices (ie, the center of the circle). Is there an algorithm that will allow the relevant parties to cooperatively compute the crash locus (simplistically, the intersection of the circles) without revealing the location of their respective circle centers?
What about the case where the listening devices provide a bearing, but not a range?