An Interactive, Similarity Increasing Algorithm for Random Strings with Applications to Key Agreement in ad hoc Networks

A central problem in distributed computing and telecommunications is the establishment of common knowledge between two computing entities. An immediate use of such common knowledge is in the initiation of a secure communication session between two entities because the two entities may use this common knowledge to produce a secret key for use with some symmetric cipher. The dynamic establishment of shared information (e.g., secret key) between two entities is particularly important in networks with no predetermined structure such as wireless mobile ad hoc networks. In such networks, nodes establish and terminate communication sessions dynamically with other nodes which may have never been encountered before to somehow exchange information which will enable them to subsequently communicate in a secure manner. In this paper we give and theoretically analyze a protocol that enables two entities initially possessing a string each to securely eliminate inconsistent bit positions, obtaining strings with a larger percentage of similarities. Our analysis involves the modeling of the operation of the protocol with a discrete random process amenable to approximation with a continuous differential equation belonging to the class of Abel's differential equations of the first kind, whose solution involves Lambert's W function.