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IEEE International Symposium on Information Theory (ISIT)

Key agreement over multiple access channel using feedback channel

Somayeh Salimi, Mahmoud Salmasizadeh, Mohammad Reza Aref

Published Jul 1, 2011• 6 citations
Publisher

Abstract

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.

DOI
10.1109/isit.2011.6033897

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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 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.
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.
The physical layer security in the up‐link of the wireless communication systems is often modelled as the multiple access wiretap channel (MAC‐WT), and recently it has received a lot attention. In this paper, the MAC‐WT has been re‐visited by considering the situation that the legitimate receiver feeds his received channel output back to the transmitters via two noiseless channels, respectively. This model is called the MAC‐WT with noiseless feedback. Inner and outer bounds on the secrecy capacity region of this feedback model are provided. To be specific, we first present a decode‐and‐forward (DF) inner bound on the secrecy capacity region of this feedback model, and this bound is constructed by allowing each transmitter to decode the other one's transmitted message from the feedback, and then each transmitter uses the decoded message to re‐encode his own messages, i.e. this DF inner bound allows the independent transmitters to co‐operate with each other. Then, we provide a hybrid inner bound which is strictly larger than the DF inner bound, and it is constructed by using the feedback as a tool not only to allow the independent transmitters to co‐operate with each other but also to generate two secret keys, respectively, shared between the legitimate receiver and the two transmitters. Finally, we give a sato‐type outer bound on the secrecy capacity region of this feedback model. The results of this paper are further explained via a Gaussian example, and from this example, we see that the noiseless feedback helps to enhance the achievable secrecy rate region of the Gaussian MAC‐WT without feedback.