1 Secure Wireless Communications via Exhaustive Cooperative Jamming Against a Single Eavesdropper Toni Draganov Stojanovski, Senior Member, IEEE and Ninoslav Marina, Senior Member, IEEE Abstract—The use of multiple network configurations for cooperative jamming with the aim to increase the region with information-theoretic secrecy is analysed. The case with a single eavesdropper at an unknown location is investigated. A pre- master key message is broken into multiple data blocks, which are then sent for different network configurations. Provided that the secrecy capacity for a given eavesdropper’s position is positive for at least one configuration, the corresponding data block can be securely delivered to the receiver, and thus the eavesdropper can not discover the master key. Index Terms—Information-theoretic secrecy, secrecy capac- ity, cooperative jamming. I. I NTRODUCTION Information theory provides security on the physical level: a message can be transmitted reliably from a transmitter to a receiver while no information on the message is divulged to the eavesdropper. In 1975, Wyner defined the wiretap channel and established the possibility to create perfectly se- cure communication links without relying on cryptographic algorithms [1]. The eavesdropper is kept in total ignorance of the transmitted message to the legitimate receiver, hence it may not decode any confidential information from its obser- vations. Leung-Yan-Cheong and Hellman characterized the secrecy capacity of the additive white Gaussian noise wiretap channel [2], and Csiszár and Körner generalized Wyner’s approach by considering the transmission of confidential messages over broadcast channels [3]. How to achieve the secret communication using infor- mation theoretic secrecy in the presence of eavesdroppers is an open question. Cooperative jamming and cooperative relaying are two of the most common approaches. In the cooperative jamming [4], friendly nodes, which are close to the eavesdropper, jam the eavesdropper to help increase the achievable secrecy rates for the transmitter by decreasing the signal-to-noise ratio at the eavesdropper.. Modern cryptography still follows the principle of Kerck- hoffs [5] from 1883: Secrecy of a cryptographic system is based on the secrecy of the secret key, and not on the secrecy T. D. Stojanovski is with the University for Information Science and Technology "St. Paul the Apostle", Ohrid, Macedonia and with the Euro- pean University, Skopje, Macedonia. e-mail: toni_stojanovski@ieee.org N. Marina is with Ecole Polytechnique Federale de Lausanne. He is also with University for Information Science and Technology "St. Paul the Apostle", Ohrid, Macedonia and Princeton University, Princeton, USA. The work of N. Marina is supported by the European Commissions FP7 People Programme under the Marie Curie International Outgoing Fellowship Grant 237669. of the cryptographic algorithm. Secret keys between com- municating parties are exchanged in two ways: (i) through physically secure channels e.g. a diplomatic suitcase; (ii) through public-key cryptographic protocols e.g. RSA, Diffie- Helman. The exchanged secret key is called master key, and is typically used to encrypt and exchange session keys, which are then used to encrypt the data flow between the two parties. Usually, the master key between the two parties is changed very infrequently. Here we examine the possi- bility to use information-theoretic secrecy to exchange a master-key between the two communicating parties. Secrecy capacity determines how quickly the master key will be exchanged between the two parties. Since the master key changes very rarely, transmitting it at even very small rates is sufficient. Once the master key is exchanged, the legitimate parties can start communicating at maximum data rate since their communication channel is cryptographically protected achieving computational secrecy [6]. The key ingredient in our approach to handle unknown eavesdropper locations is to split the pre-master key message into a large number B of data blocks. The two communicat- ing nodes ensure that the entire pre-master key message is received correctly at the receiving node, which is required for the computation of the master key. Each data block is sent for a different network configuration of jammers. As the number B of transmitted blocks grows, the eavesdropper is facing a more difficult task of being able to intercept in a larger number of network configurations. In Section II we present the system model. The main result of this work, that using multiple network configurations for cooperative jamming can reduce the vulnerability region is given in Section III. Section IV concludes the paper. II. SYSTEM MODEL AND PROBLEM FORMULATION We consider two-dimensional wireless network with two communication nodes: a transmitter at position (0, 0) and a receiver at position (1, 0), N friendly nodes (jammers), and a passive eavesdropper. The passive eavesdropper does not transmit any signal, and tries to intercept the information that is transmitted between the pairs of legitimate nodes, hence reducing the secrecy capability of the network. Its location is unknown to the two communicating nodes. In our model each network node (transmitter or jammer) is equipped with only a single omni-directional antenna. Due to cost and size limitations of multiple-antenna nodes, node cooperation is a more effective way of exploiting single-antenna nodes to increase the secrecy capacity.