On the Security of Key Extraction from Measuring Physical Quantities

Key extraction via measuring a physical quantity is a class of information theoretic key exchange protocols that rely on the physical characteristics of the communication channel to enable the computation of a shared key by two (or more) parties that share no prior secret information. The key is supposed to be information theoretically hidden to an eavesdropper. Despite the recent surge of research activity in the area, concrete claims about the security of the protocols typically rely on channel abstractions that are not fully experimentally substantiated. In this work, we propose a novel methodology for the {\em experimental} security analysis of these protocols. The crux of our methodology is a falsifiable channel abstraction that is accompanied by an efficient experimental approximation algorithm of the {\em conditional min-entropy} available to the two parties given the view of the eavesdropper. We focus on the signal strength between two wirelessly communicating transceivers as the measured quantity and we use an experimental setup to compute the conditional min-entropy of the channel given the view of the attacker which we find to be linearly increasing. Armed with this understanding of the channel, we showcase the methodology by providing a general protocol for key extraction in this setting that is shown to be secure for a concrete parameter selection. In this way we provide a first comprehensively analyzed wireless key extraction protocol that is demonstrably secure against passive adversaries. Our methodology uses hidden Markov models as the channel model and a dynamic programming approach to approximate conditional min-entropy but other possible instantiations of the methodology can be motivated by our work.