On the design of agent agreement protocol using linear error-correcting codes

Abstract

In a number of situations, it is necessary for two agents who may have never communicated in the past to, jointly, create a shared information item which can serve as a basis for subsequent protocols that the agents may wish to execute (e.g., negotiation or encryption protocols). One way to create this shared piece of information is to have the two agents start with one random bit string each and then engage in a protocol that enables them to transform, gradually, bit differences (in their strings) into bit agreements. In a previous work, an efficient protocol was proposed which was based on the use of the Extended Golay error-correcting code in order to locate and “correct” bit differences. In this work we generalize this protocol in order to use any generic error-correcting code and derive theoretical performance bounds on the efficiency, based on the characteristics of the employed code. The proposed generalized protocol is fair, in that the final strings (which have the same bits in the majority of positions) depend on the strings possessed by both agents while each agent contributes to the same degree in the formation of these strings. Finally, the proposed protocol is lightweight (both computationally and with respect to message exchanges) and, thus, can be implemented in embedded systems and resource limited devices.