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 since the two entities may use this common knowledge in order 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 in order 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. This can help the nodes establish a shared set of bits and use it as a key with some shared key encryption scheme.