# A special case of zero-knowledge computation

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?

• how about write a program in which you enter the center of your circle and radius, once it is entered, it gets encrypted in such a way that one cannot get it back, except the program itself(with a key that is hardcoded into the program). The country that makes the program then enters their data. It is passed to another country(who cannot retrieve the first country's data) and so on. when done, you give the command to compute(big red button?) and done. Would that work? – Guy Mar 19 '14 at 16:03
• unless the computation can be carried out without decrypting the data, I would argue that the proposed approach will always be vulnerable to intercepting the data. – Llaves Mar 19 '14 at 23:19
• a spontaneous idea would be to raise the phone coordinates into higher dimensions and apply a large number of modular transformations like a hash, the only requirement being that the area in which the plane is expected remains consistent. (so everyone initially only uses phones outside of this range) after that, the range can be decreased and phones in greater proximity could be used safely. not sure if that leads anywhere though. – guest May 21 '14 at 9:13
• – user57159 Jun 3 '14 at 19:43
• The way you're wording this question makes me think the easiest approach to this might, actually, not be from cryptography, but from the study of sensor networks. Using computational topology, sensor networks can be completed knowledge of the coordinates of the sensors (even if it was just one country that laid them all down and then forgot where they were). There are algorithms for that you can read about in Edelsbrunner's book. – Alexander Gruber Oct 11 '14 at 17:03