Information Theory and Reliable Communication

The broadcast nature of the wireless medium makes the communication over this medium vulnerable to eavesdropping. This paper considers the problem of secret communication between two nodes, over a fading wireless medium, in the presence of a passive eavesdropper. The assumption used is that the transmitter and its helpers (amplifying relays) have more antennas than the eavesdropper. The transmitter ensures secrecy of communication by utilizing some of the available power to produce 'artificial noise', such that only the eavesdropper's channel is degraded. Two scenarios are considered, one where the transmitter has multiple transmit antennas, and the other where amplifying relays simulate the effect of multiple antennas. The channel state information (CSI) is assumed to be publicly known, and hence, the secrecy of communication is independent of the secrecy of CSI.

Guaranteeing Secrecy using Artificial Noise

This paper considers the transmission of confidential data over wireless channels. Based on an information-theoretic formulation of the problem, in which two legitimates partners communicate over a quasi-static fading channel and an eavesdropper observes their transmissions through a second independent quasi-static fading channel, the important role of fading is characterized in terms of average secure communication rates and outage probability. Based on the insights from this analysis, a practical secure communication protocol is developed, which uses a four-step procedure to ensure wireless information-theoretic security: (i) common randomness via opportunistic transmission, (ii) message reconciliation, (iii) common key generation via privacy amplification, and (iv) message protection with a secret key. A reconciliation procedure based on multilevel coding and optimized low-density parity-check (LDPC) codes is introduced, which allows to achieve communication rates close to the fundamental security limits in several relevant instances. Finally, a set of metrics for assessing average secure key generation rates is established, and it is shown that the protocol is effective in secure key renewal-even in the presence of imperfect channel state information.

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Wireless Information-Theoretic Security

The capacity of the Gaussian wiretap channel model is analyzed when there are multiple antennas at the sender, intended receiver and eavesdropper. The associated channel matrices are fixed and known to all the terminals. A computable characterization of the secrecy capacity is established as the saddle point solution to a minimax problem. The converse is based on a Sato-type argument used in other broadcast settings, and the coding theorem is based on Gaussian wiretap codebooks. At high signal-to-noise ratio (SNR), the secrecy capacity is shown to be attained by simultaneously diagonalizing the channel matrices via the generalized singular value decomposition, and independently coding across the resulting parallel channels. The associated capacity is expressed in terms of the corresponding generalized singular values. It is shown that a semi-blind "masked" multi-input multi-output (MIMO) transmission strategy that sends information along directions in which there is gain to the intended receiver, and synthetic noise along directions in which there is not, can be arbitrarily far from capacity in this regime. Necessary and sufficient conditions for the secrecy capacity to be zero are provided, which simplify in the limit of many antennas when the entries of the channel matrices are independent and identically distributed. The resulting scaling laws establish that to prevent secure communication, the eavesdropper needs three times as many antennas as the sender and intended receiver have jointly, and that the optimum division of antennas between sender and intended receiver is in the ratio of 2:1.

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Secure Transmission With Multiple Antennas—Part II: The MIMOME Wiretap Channel

Physical (PHY) layer security approaches for wireless communications can prevent eavesdropping without upper layer data encryption. However, they are hampered by wireless channel conditions: absent feedback, they are typically feasible only when the source-destination channel is better than the source-eavesdropper channel. Node cooperation is a means to overcome this challenge and improve the performance of secure wireless communications. This paper addresses secure communications of one source-destination pair with the help of multiple cooperating relays in the presence of one or more eavesdroppers. Three cooperative schemes are considered: decode-and-forward (DF), amplify-and-forward (AF), and cooperative jamming (CJ). For these schemes, the relays transmit a weighted version of a reencoded noise-free message signal (for DF), a received noisy source signal (for AF), or a common jamming signal (for CJ). Novel system designs are proposed, consisting of the determination of relay weights and the allocation of transmit power, that maximize the achievable secrecy rate subject to a transmit power constraint, or, minimize the transmit power subject to a secrecy rate constraint. For DF in the presence of one eavesdropper, closed-form optimal solutions are derived for the relay weights. For other problems, since the optimal relay weights are difficult to obtain, several criteria are considered leading to suboptimal but simple solutions, i.e., the complete nulling of the message signals at all eavesdroppers (for DF and AF), or the complete nulling of jamming signal at the destination (for CJ). Based on the designed relay weights, for DF in the presence of multiple eavesdroppers, and for CJ in the presence of one eavesdropper, the optimal power allocation is obtained in closed-form; in all other cases the optimal power allocation is obtained via iterative algorithms. Numerical evaluation of the obtained secrecy rate and transmit power results show that the proposed design can significantly improve the performance of secure wireless communications.

Improving Wireless Physical Layer Security via Cooperating Relays

The problem of secret communication between two nodes over a wireless link is considered, where a passive eaves- dropper may overhear the communication. It is desired that the eavesdropper be unable to decode the message. We show that secrecy can be achieved by adding artificially generated noise to the information bearing signal such that it does not degrade the intended receiver's channel. We consider two different scenarios; one in which the transmitter has multiple transmit antennas and the other in which the transmitter has a single antenna but 'helper' nodes are available. In the multiple antenna scenario, the degrees of freedom provided by the multiple antennas is used to generate artificial noise intelligently so that it degrades only the eavesdropper's channel. In the multiple helper scenario, even though the transmitter does not have multiple antennas, the helper nodes simulate the effect of multiple antennas and allow the transmitter to generate artificial noise as in the previous case.

Secret communication using artificial noise

We consider the problem of secret communications between two nodes over a wireless link in the presence of multiple passive eavesdroppers which may collude. Both the transmitter and the receiver are assumed to have multiple antennas and the multiple colluding eavesdroppers are modeled by an eavesdropper with multiple antennas. Communication is secret if the eavesdropper is unable to decode the message whereas the receiver can decode the message without making any errors. Thus, we deal with the problem of secrecy in a MIMO scenario. It is shown how the transmitter can use the multiple antennas to add artificially generated noise to the information signal such that the artificial noise only degrades the eavesdropper's channel. Thus, even if the eavesdropper has a 'better' channel than the receiver, secret communication is made possible by selectively degrading the eavesdropper's channel. The secrecy of communication is achieved by exploiting the physical characteristics of the wireless medium and it is independent of the secrecy of channel state information (CSI)

Secret communication in presence of colluding eavesdroppers

In this paper, we consider end-to-end secure communication in a large wireless network, where the locations of eavesdroppers are uncertain. Our framework attempts to bridge the gap between physical layer security under uncertain channel state information of the eavesdropper and network level connectivity under security constraints, by modeling location uncertainty directly at the network level as correlated node and link failures in a secrecy graph. Bounds on the percolation threshold are obtained for square and triangular lattices, and bounds on mean degree are obtained for Poisson secrecy graphs. Both analytic and simulation results show the dramatic effect of uncertainty in location of eavesdroppers on connectivity in a secrecy graph.

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Modeling location uncertainty for eavesdroppers: A secrecy graph approach

Methods and apparatuses are provided that include calibrating transmit power of a femto node based on measuring one or more parameters related to usage of the femto node. The femto node can temporarily increase transmit power and analyze received measurement reports to determine a transmit power calibration. The femto node can additionally measure uplink received signal strength indicators over multiple time periods following handover of a user equipment (UE) to determine whether to increase transmit power to cover the UE.

Satashu Goel

Papers

Guaranteeing Secrecy using Artificial Noise

Secret communication using artificial noise

Secret communication in presence of colluding eavesdroppers

Modeling location uncertainty for eavesdroppers: A secrecy graph approach

Method and apparatus for calibrating transmit power of a FEMTO node