We consider the generation of a secret key (SK) by the inputs and the output of a secure multipleaccess channel (MAC) that additionally have access to a noiseless public communication channel. Under specific restrictions on the protocols, we derive various upper bounds on the rate of such SKs. Specifically, if the public communication consists of only the feedback from the output terminal, then the rate of SKs that can be generated is bounded above by the maximum symmetric rate $R_f^\ast$ in the capacity region of the MAC with feedback. On the other hand, if the public communication is allowed only before and after the transmission over the MAC, then the rate of SKs is bounded above by the maximum symmetric rate $R^\ast$ in the capacity region of the MAC without feedback. Furthermore, for a symmetric MAC, we present a scheme that generates an SK of rate $R_f^\ast$ , improving the best previously known achievable rate $R^\ast$ . An application of our results establishes the SK capacity for adder MAC, without any restriction on the protocols.We consider the generation of a secret key (SK) by the inputs and the output of a secure multipleaccess channel (MAC) that additionally have access to a noiseless public communication channel. Under specific restrictions on the protocols, we derive various upper bounds on the rate of such SKs. Specifically, if the public communication consists of only the feedback from the output terminal, then the rate of SKs that can be generated is bounded above by the maximum symmetric rate $R_f^\ast$ in the capacity region of the MAC with feedback. On the other hand, if the public communication is allowed only before and after the transmission over the MAC, then the rate of SKs is bounded above by the maximum symmetric rate $R^\ast$ in the capacity region of the MAC without feedback. Furthermore, for a symmetric MAC, we present a scheme that generates an SK of rate $R_f^\ast$, improving the best previously known achievable rate $R^\ast$. An application of our results establishes the SK capacity for adder MAC, without any restriction on the protocols.

arXiv:1902.08970Feb 24, 20190 citations

Secrecy Generation for Multiaccess Channel Models

Imre Csiszár, Prakash Narayan

Shannon theoretic secret key generation by several parties is considered for models in which a secure noisy channel with multiple input and output terminals and a public noiseless channel of unlimited capacity are available for accomplishing this goal. The secret key is generated for a setAof terminals of the noisy channel, with the remaining terminals (if any) cooperating in this task through their public communication. Single-letter lower and upper bounds for secrecy capacities are obtained when secrecy is required from an eavesdropper that observes only the public communication and perhaps also a set of terminals disjoint fromA. These bounds coincide in special cases, but not in general. We also consider models in which different sets of terminals share multiple keys, one for the terminals in each set with secrecy required from the eavesdropper as well as from the terminals not in this set. Partial results include showing links among the associated secrecy capacity region for multiple keys, the transmission capacity region of the multiple access channel defined by the secure noisy channel, and achievable rates for a single secret key for all the terminals.Shannon theoretic secret key generation by several parties is considered for models in which a secure noisy channel with multiple input and output terminals and a public noiseless channel of unlimited capacity are available for accomplishing this goal. The secret key is generated for a setAof terminals of the noisy channel, with the remaining terminals (if any) cooperating in this task through their public communication. Single-letter lower and upper bounds for secrecy capacities are obtained when secrecy is required from an eavesdropper that observes only the public communication and perhaps also a set of terminals disjoint fromA. These bounds coincide in special cases, but not in general. We also consider models in which different sets of terminals share multiple keys, one for the terminals in each set with secrecy required from the eavesdropper as well as from the terminals not in this set. Partial results include showing links among the associated secrecy capacity region for multiple keys, the transmission capacity region of the multiple access channel defined by the secure noisy channel, and achievable rates for a single secret key for all the terminals.

IEEE Transactions on Information TheoryAug 29, 201220 citations

Secrecy generation for multiple input multiple output channel models

Imre Csiszár, Prakash Narayan

Shannon theoretic secret key generation by several parties is considered for models in which a secure noisy channel with multiple input and output terminals and a public noiseless channel of unlimited capacity are available for accomplishing this goal. The secret key is generated for a set A of terminals of the noisy channel, with the remaining terminals (if any) cooperating in this task through their public communication. Single-letter lower and upper bounds for secrecy capacities are obtained when secrecy is required from an eavesdropper that observes only the public communication and perhaps also a set of terminals disjoint from A. These bounds coincide in special cases, and the lower bounds are not tight in general. We also consider models in which different sets of terminals share multiple keys, one for terminals in each set with secrecy required from the eavesdropper as well as the remaining terminals in the other sets. Partial results include showing links among the associated secrecy capacity region for multiple keys, the transmission capacity region of the multiple access channel defined by the secure noisy channel, and achievable rates for a single secret key for all the terminals.Shannon theoretic secret key generation by several parties is considered for models in which a secure noisy channel with multiple input and output terminals and a public noiseless channel of unlimited capacity are available for accomplishing this goal. The secret key is generated for a set A of terminals of the noisy channel, with the remaining terminals (if any) cooperating in this task through their public communication. Single-letter lower and upper bounds for secrecy capacities are obtained when secrecy is required from an eavesdropper that observes only the public communication and perhaps also a set of terminals disjoint from A. These bounds coincide in special cases, and the lower bounds are not tight in general. We also consider models in which different sets of terminals share multiple keys, one for terminals in each set with secrecy required from the eavesdropper as well as the remaining terminals in the other sets. Partial results include showing links among the associated secrecy capacity region for multiple keys, the transmission capacity region of the multiple access channel defined by the secure noisy channel, and achievable rates for a single secret key for all the terminals.

IEEE International Symposium on Information Theory (ISIT)Jun 1, 200914 citations

Secret key rate region of multiple access channel model

Somayeh Salimi, Mahmoud Salmasizadeh, Mohammad Reza Aref

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 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.

International Symposium on Information Theory and its ApplicationsOct 1, 20101 citation

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

Somayeh Salimi, Mikael Skoglund, Jovan Dj. Golić +2 more

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 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.

IEEE Journal on Selected Areas in CommunicationsAug 23, 201311 citations

Secrecy Capacities for Multiterminal Channel Models

Imre Csiszár, Prakash Narayan

Shannon-theoretic secret key generation by several parties is considered for models in which a secure noisy channel with one input terminal and multiple output terminals and a public noiseless channel of unlimited capacity are available for accomplishing this goal. The secret key is generated for a set $A$ of terminals of the noisy channel, with the remaining terminals (if any) cooperating in this task through their public communication. Single-letter characterizations of secrecy capacities are obtained for models in which secrecy is required from an eavesdropper that observes only the public communication and perhaps also a set of terminals disjoint from $A$ . These capacities are shown to be achievable with noninteractive public communication, the channel input terminal sending no public message and each output terminal sending at most one public message, not using randomization. Moreover, when the input terminal belongs to the set $A$ , it can generate the secret key at the outset and transmit it over the noisy channel, suitably encoded, whereupon the output terminals in $A$ securely recover this key using public communication as above. For models in which the eavesdropper also possesses side information that is not available to any of the terminals cooperating in secrecy generation, an upper bound for the secrecy capacity and a sufficient condition for its tightness are given.Shannon-theoretic secret key generation by several parties is considered for models in which a secure noisy channel with one input terminal and multiple output terminals and a public noiseless channel of unlimited capacity are available for accomplishing this goal. The secret key is generated for a set$A$of terminals of the noisy channel, with the remaining terminals (if any) cooperating in this task through their public communication. Single-letter characterizations of secrecy capacities are obtained for models in which secrecy is required from an eavesdropper that observes only the public communication and perhaps also a set of terminals disjoint from$A$. These capacities are shown to be achievable with noninteractive public communication, the channel input terminal sending no public message and each output terminal sending at most one public message, not using randomization. Moreover, when the input terminal belongs to the set$A$, it can generate the secret key at the outset and transmit it over the noisy channel, suitably encoded, whereupon the output terminals in$A$securely recover this key using public communication as above. For models in which the eavesdropper also possesses side information that is not available to any of the terminals cooperating in secrecy generation, an upper bound for the secrecy capacity and a sufficient condition for its tightness are given.

IEEE Transactions on Information TheoryMay 29, 2008154 citations

R_f^\ast

in the capacity region of the MAC with feedback. On the other hand, if the public communication is allowed only before and after the transmission over the MAC, then the rate of SKs is bounded above by the maximum symmetric rate

R^\ast

in the capacity region of the MAC without feedback. Furthermore, for a symmetric MAC, we present a scheme that generates an SK of rate

R_f^\ast

, improving the best previously known achievable rate

R^\ast

. An application of our results establishes the SK capacity for adder MAC, without any restriction on the protocols.

A

of terminals of the noisy channel, with the remaining terminals (if any) cooperating in this task through their public communication. Single-letter characterizations of secrecy capacities are obtained for models in which secrecy is required from an eavesdropper that observes only the public communication and perhaps also a set of terminals disjoint from

A

. These capacities are shown to be achievable with noninteractive public communication, the channel input terminal sending no public message and each output terminal sending at most one public message, not using randomization. Moreover, when the input terminal belongs to the set

A

, it can generate the secret key at the outset and transmit it over the noisy channel, suitably encoded, whereupon the output terminals in

A

securely recover this key using public communication as above. For models in which the eavesdropper also possesses side information that is not available to any of the terminals cooperating in secrecy generation, an upper bound for the secrecy capacity and a sufficient condition for its tightness are given.