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International Symposium on Wireless Communication Systems

Pairwise Key Agreement over a Generalized Multiple Access Channel: Capacity Bounds and Game-Theoretic Analysis

Somayeh Salimi, Frédéric Gabry, Mikael Skoglund

Published Oct 15, 2013• 1 citation
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Abstract

A pairwise key agreement between three users is considered in which each pair of the users wishes to agree on a secret key hidden from the remaining user. The three users communicate through a noisy channel where two users transmit the channel inputs and all the three users receive noisy outputs from the channel. In this setup, inner and outer bounds of the secret key capacity region are derived as well as a special case where the two bounds match. Furthermore, an achievable secret key rate region is derived for AWGN channels. In this Gaussian setup, we investigate the interaction between the two transmitting users from a game-theoretic perspective and we analyze the Nash equilibrium of the non-cooperative game considering two strategies for the transmitting users: power control and cooperative jamming. Finally we illustrate our results through numerical simulations.

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A pairwise key agreement between three users is considered in which each pair of the users wishes to agree on a secret key hidden from the remaining user. The three users communicate through a noisy channel where two users transmit the channel inputs and all the three users receive noisy outputs from the channel. In this setup, inner and outer bounds of the secret key capacity region are derived as well as a special case where the two bounds match. Furthermore, an achievable secret key rate region is derived for AWGN channels. In this Gaussian setup, we investigate the interaction between the two transmitting users from a game-theoretic perspective and we analyze the Nash equilibrium of the non-cooperative game considering two strategies for the transmitting users: power control and cooperative jamming. Finally we illustrate our results through numerical simulations.
This paper considers the problem of pairwise key agreement without public communication between three users connected through a generalized multiple access channel (MAC). While two users control the channel inputs, all three users observe noisy outputs from the channel and each pair of users wishes to agree on a secret key hidden from the remaining user. We first develop a "pre-generated" key-agreement scheme based on secrecy codes for the generalized MAC, in which the channel is only used to distribute pre-generated secret keys. We then extend this scheme to include an additional layer of rate-limited secret-key generation by treating the observed channel outputs as induced sources. We characterize inner and outer bounds on the strong secret-key capacity region for both schemes. For a special case of the "pre-generated" scheme, we obtain an exact characterization. We also illustrate with some binary examples that exploiting the generalized nature of the generalized MAC may lead to significantly larger key-agreement rates.
A secret key agreement setup between three users is considered in which each of the users 1 and 2 intends to share a secret key with user 3 and users 1 and 2 are eavesdroppers with respect to each other. The three users observe i.i.d. outputs of correlated sources and there is a generalized discrete memoryless multiple access channel (GDMMAC) from users 1 and 2 to user 3 for communication between the users. The secret key agreement is established using the correlated sources and the GDMMAC. In this setup, inner and outer bounds of the secret key capacity region are investigated. Moreover, for a special case where the channel inputs and outputs and the sources form Markov chains in some order, the secret key capacity region is derived. Also a Gaussian case is considered in this setup.
A secret key agreement setup between three users is considered in which each pair of them wishes to agree on a secret key hidden from the remaining user. The three users observe i.i.d. outputs of correlated sources and there is a noiseless public channel from each user for communication to the others. In this setup, inner and outer bounds of the secret key capacity region is derived. Moreover, some special cases are obtained in which the inner bound coincides the explicit outer bound. Also a binary-erasure example is presented through which the results are examined.
A secret key agreement framework involving three users is considered in which each of the users 1 and 2 intends to share a secret key with user 3 and users 1 and 2 are eavesdroppers with respect to each other. There is a generalized discrete memoryless multiple access channel (GDMMAC) from users 1 and 2 to user 3 where the three users receive outputs from the channel. Furthermore, there is a feedback channel from user 3 to users 1 and 2 through which user 3 sends information extracted from the received output from the GDMMAC to increase the key rates. We consider both noiseless and noisy feedback. In the case of noiseless feedback, a public channel of unlimited capacity from user 3 to users 1 and 2 is used only once. In the case of noisy feedback, a noisy broadcast channel (BC) from user 3 to users 1 and 2 can be repeatedly used, like GDMMAC. In both setups, inner bounds of the secret key capacity region are derived. The secret key capacity region is derived in some special cases where the channel inputs and outputs form Markov chains in certain orders. For illustration, the corresponding results are also derived and discussed for Gaussian channels. The cases with noiseless feedback, noisy feedback, and no feedback at all are compared with each other.
In this paper, a generalized multiple access channel (MAC) model for secret key sharing between three terminals is considered. In this model, there are two transmitters and a receiver where all three terminals receive noisy channel outputs. In addition, there is a one-way public channel from the transmitters to the receiver. Each of the transmitters intends to share a secret key with the receiver by using the MAC and the public channel, where the transmitters are eavesdroppers with respect to each other. Two strategies for secret key sharing are considered, namely, the pregenerated key strategy and the two-stage key strategy. For both of them, inner and outer bounds of the secret key capacity region are derived. Furthermore, the effect of the public channel is discussed and the two strategies are compared. In both strategies, it is assumed that the channel outputs at the transmitters are only used for eavesdropping and not as inputs to the encoders. The effect of this assumption in the presence of the public channel is analyzed for some Gaussian MACs.
A source model of key sharing between three users is considered in which each pair of them wishes to agree on a secret key hidden from the remaining user. There are rate-limited public channels for communications between the users. We give an inner bound on the secret key capacity region in this framework. Moreover, we investigate a practical setup in which localization information of the users as the correlated observations are exploited to share pairwise keys between the users. The inner and outer bounds of the key capacity region are analyzed in this setup for the case of i.i.d. Gaussian observations.