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IEEE Journal on Selected Areas in Communications

Key Agreement over a Generalized Multiple Access Channel Using Noiseless and Noisy Feedback

Somayeh Salimi, Mikael Skoglund, Jovan Dj. Golić, Mahmoud Salmasizadeh, Mohammad Reza Aref

Published Aug 23, 2013• 11 citations
Publisher

Abstract

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.

DOI
10.1109/jsac.2013.130910

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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.
A secret key agreement framework 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. 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 broadcast channel (BC) from user 3 to users 1 and 2. Secret key sharing is intended where GDMMAC and BC can be successively used. In this framework, an inner bound of the secret key capacity region is derived. Moreover, for a special case where the channel inputs and outputs of the GDMAC and the BC form Markov chains in some order, the secret key capacity region is derived. Also the results are discussed through a binary example.
In this paper, the effect of using an insecure and noiseless feedback channel in increasing secret key rates is investigated. There is a generalized discrete memoryless multiple access channel (GDMMAC) between two transmitters and a receiver where, in addition to the receiver, both of the transmitters receive noisy channel outputs. Furthermore, an insecure and noiseless feedback channel exists from the receiver to the transmitters. Each of the transmitters intends to share a secret key with the receiver while keeping it concealed from the other transmitter. For this setup, an inner bound of the secret key capacity region is derived. For some special cases, the secret key capacity region is obtained, and the effect of the feedback channel usage is discussed through a binary-erasure example as well as in the Gaussian case.
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.
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 channel model for secret key generation between three terminals is considered. In this model, there is a two-user generalized multiple access channel (MAC) in which, in addition to the receiver, both transmitters receive noisy channel outputs. There is also a one-way public channel from the transmitters to the receiver. In this model, each of the transmitters intends to share a secret key with the receiver using the MAC and the public channel where the transmitters are eavesdroppers with respect to each other. In this setup, the channel outputs at the transmitters are only used for eavesdropping and not as inputs to the encoders. For the secret key rate pair, we derive the inner bound of the secret key capacity region. Thorough an example, it is shown that unlike the broadcast channel model, using a one-way public channel from the transmitters to the receiver is beneficial.
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.