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

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

On Multiterminal Secrecy Capacities

Imre Csiszár, Prakash Narayan

Shannon-theoretic secret key generation by several parties is considered for source models in which the distinct components of a multiple source observed separately by multiple terminals, and for channel models in which a secure noisy channel with one input terminal and multiple output terminals, and, additionally in both cases, a public noiseless channel of unlimited capacity, are available for accomplishing this goal. The secret key is generated for a set A of terminals, with the remaining terminals (if any) cooperating in this task through their public communication. We show that for source 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, secrecy capacity can be achieved with noninteractive communication, the key being generated by any chosen terminal in the secret key-seeking set A of terminals obliviously of the public communication. 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. The latter partially fills a gap in the authors' previous work [6].Shannon-theoretic secret key generation by several parties is considered for source models in which the distinct components of a multiple source observed separately by multiple terminals, and for channel models in which a secure noisy channel with one input terminal and multiple output terminals, and, additionally in both cases, a public noiseless channel of unlimited capacity, are available for accomplishing this goal. The secret key is generated for a set A of terminals, with the remaining terminals (if any) cooperating in this task through their public communication. We show that for source 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, secrecy capacity can be achieved with noninteractive communication, the key being generated by any chosen terminal in the secret key-seeking set A of terminals obliviously of the public communication. 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. The latter partially fills a gap in the authors' previous work [6].

IEEE International Symposium on Information Theory (ISIT)Jun 1, 20070 citations

Capacity of a shared secret key

Imre Csiszár, Prakash Narayan

Shannon theoretic shared secret key generation by multiple terminals is considered for a source model in which the components of a discrete memoryless multiple source and a noiseless public channel of unlimited capacity are available for accomplishing this goal. A shared secret key is generated for distinct coalitions of terminals, with all the terminals cooperating in this task through their public communication. A communication from a terminal can be a function of its observed source component and of all previous communication. Member terminals of a coalition unite in recovering the key. Secrecy is required from an eavesdropper that observes the public interterminal communication. A single-letter characterization of the shared secret key capacity is obtained. When the key must be concealed additionally from subsets of coalition members, we provide an upper bound for the strict shared secret key capacity.Shannon theoretic shared secret key generation by multiple terminals is considered for a source model in which the components of a discrete memoryless multiple source and a noiseless public channel of unlimited capacity are available for accomplishing this goal. A shared secret key is generated for distinct coalitions of terminals, with all the terminals cooperating in this task through their public communication. A communication from a terminal can be a function of its observed source component and of all previous communication. Member terminals of a coalition unite in recovering the key. Secrecy is required from an eavesdropper that observes the public interterminal communication. A single-letter characterization of the shared secret key capacity is obtained. When the key must be concealed additionally from subsets of coalition members, we provide an upper bound for the strict shared secret key capacity.

IEEE International Symposium on Information Theory (ISIT)Jun 1, 201012 citations

Information-Theoretic Key Agreement of Multiple Terminals—Part II: Channel Model

Amin Gohari, Venkat Anantharam

This is the second part of a two-part paper on information-theoretically secure secret key agreement. This part covers the secret key capacity under the channel model. In this model, multiple terminals wish to create a shared secret key that is secure from an eavesdropper with unlimited computational resources. The terminals are all connected to a noiseless and authenticated but insecure channel, called the “public channel.” Furthermore, the terminals have access to a secure but noisy discrete memoryless broadcast channel (DMBC). The first terminal can choose a sequence of inputs to the DMBC, which has outputs at the other terminals and at the eavesdropper. After each channel use, the terminals can engage in arbitrarily many rounds of interactive authenticated communication over the public channel. At the end, each legitimate terminal should be able to generate the secret key. In this paper, we derive new lower and upper bounds on the secrecy capacity. In each case, an example is provided to show that the new bound represents a strict improvement over the previously best known bound. This part of the paper is not standalone, and is written under the assumption that the reader has access to Part I, which is published in the same issue.This is the second part of a two-part paper on information-theoretically secure secret key agreement. This part covers the secret key capacity under the channel model. In this model, multiple terminals wish to create a shared secret key that is secure from an eavesdropper with unlimited computational resources. The terminals are all connected to a noiseless and authenticated but insecure channel, called the “public channel.” Furthermore, the terminals have access to a secure but noisy discrete memoryless broadcast channel (DMBC). The first terminal can choose a sequence of inputs to the DMBC, which has outputs at the other terminals and at the eavesdropper. After each channel use, the terminals can engage in arbitrarily many rounds of interactive authenticated communication over the public channel. At the end, each legitimate terminal should be able to generate the secret key. In this paper, we derive new lower and upper bounds on the secrecy capacity. In each case, an example is provided to show that the new bound represents a strict improvement over the previously best known bound. This part of the paper is not standalone, and is written under the assumption that the reader has access to Part I, which is published in the same issue.

IEEE Transactions on Information TheoryJul 21, 201074 citations

New bounds on the information-theoretic key agreement of multiple terminals

Amin Gohari, Venkat Anantharam

We study the problem of information-theoretically secure secret key agreement under the well-known source model and channel model. In both of these models the parties wish to create a shared secret key that is secure from an eavesdropper with unlimited computational resources. In the channel model, the first party can choose a sequence of inputs to a discrete memoryless channel, which has outputs at the other parties and at the eavesdropper. After each channel use, the parties can engage in arbitrarily many rounds of interactive authenticated communication over a public channel. At the end, each party should be able to generate the key. In the source model, the parties wishing to generate a secret key (as well as the eavesdropper) receive a certain number of independent identically distributed copies of jointly distributed random variables after which the parties are allowed interactive authenticated public communication, at the end of which each party should be able to generate the key. We derive new lower and upper bounds on the secret key rate under the source model and the channel model, and introduce a technique for proving that a given expression bounds the secrecy rate from above in the channel model. Our lower bounds strictly improve what is essentially the best known lower bound in both the source model and the channel model. Our upper bound in the channel model strictly improves the current state of art upper bound. We do not know whether our new upper bound in the source model represents an strict improvement but it includes the current best known bound as a special case.We study the problem of information-theoretically secure secret key agreement under the well-known source model and channel model. In both of these models the parties wish to create a shared secret key that is secure from an eavesdropper with unlimited computational resources. In the channel model, the first party can choose a sequence of inputs to a discrete memoryless channel, which has outputs at the other parties and at the eavesdropper. After each channel use, the parties can engage in arbitrarily many rounds of interactive authenticated communication over a public channel. At the end, each party should be able to generate the key. In the source model, the parties wishing to generate a secret key (as well as the eavesdropper) receive a certain number of independent identically distributed copies of jointly distributed random variables after which the parties are allowed interactive authenticated public communication, at the end of which each party should be able to generate the key. We derive new lower and upper bounds on the secret key rate under the source model and the channel model, and introduce a technique for proving that a given expression bounds the secrecy rate from above in the channel model. Our lower bounds strictly improve what is essentially the best known lower bound in both the source model and the channel model. Our upper bound in the channel model strictly improves the current state of art upper bound. We do not know whether our new upper bound in the source model represents an strict improvement but it includes the current best known bound as a special case.

IEEE International Symposium on Information Theory (ISIT)Jul 1, 200814 citations

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.