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IEEE International Symposium on Information Theory (ISIT)

Secrecy capacities for multiterminal channel models

Imre Csiszár, Prakash Narayan

Published Jan 1, 2005• 7 citations
Publisher

Abstract

We derive single-letter characterizations of (strong) secrecy capacities for models in which a "helper" terminal is connected to an arbitrary number of "user" terminals by a discrete memoryless channel (DMC). The helper terminal governs the input of the DMC, over which it transmits to the user terminals that observe the corresponding outputs; transmissions over the DMC are secure. Additionally, following each transmission over the DMC, unrestricted and interactive public communication is permitted between all the terminals. A subset of the user terminals, and possibly the helper terminal, generate secrecy with the remaining user terminals acting as abettors. We distinguish between the cases in which the helper terminal may, or may not, randomize. Two kinds of secrecy capacity are considered, depending on the extent of an eavesdropper's knowledge: secret key (SK) and private key (PK) capacity. These secrecy capacities are shown to be achievable with noninteractive communication between the terminals and with no public transmission from the helper terminal. When the helper terminal is forbidden to randomize, the needed transmission over the DMC entails only that of a constant sequence. It is also shown that additional randomization at the user terminals does not serve to enhance the secrecy capacities

DOI
10.1109/isit.2005.1523724

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We derive single-letter characterizations of (strong) secrecy capacities for models in which a "helper" terminal is connected to an arbitrary number of "user" terminals by a discrete memoryless channel (DMC). The helper terminal governs the input of the DMC, over which it transmits to the user terminals that observe the corresponding outputs; transmissions over the DMC are secure. Additionally, following each transmission over the DMC, unrestricted and interactive public communication is permitted between all the terminals. A subset of the user terminals, and possibly the helper terminal, generate secrecy with the remaining user terminals acting as abettors. We distinguish between the cases in which the helper terminal may, or may not, randomize. Two kinds of secrecy capacity are considered, depending on the extent of an eavesdropper's knowledge: secret key (SK) and private key (PK) capacity. These secrecy capacities are shown to be achievable with noninteractive communication between the terminals and with no public transmission from the helper terminal. When the helper terminal is forbidden to randomize, the needed transmission over the DMC entails only that of a constant sequence. It is also shown that additional randomization at the user terminals does not serve to enhance the secrecy capacities
We derive single-letter characterizations of (strong) secrecy capacities for models with an arbitrary number of terminals, each of which observes a distinct component of a discrete memoryless multiple source, with unrestricted and interactive public communication permitted between the terminals. A subset of these terminals can serve as helpers for the remaining terminals in generating secrecy. According to the extent of an eavesdropper's knowledge, three kinds of secrecy capacity are considered: secret key (SK), private key (PK), and wiretap secret key (WSK) capacity. The characterizations of the SK and PK capacities highlight the innate connections between secrecy generation and multiterminal source coding without secrecy requirements. A general upper bound for WSK capacity is derived which is tight in the case when the eavesdropper can wiretap noisy versions of the components of the underlying multiple source, provided randomization is permitted at the terminals. These secrecy capacities are seen to be achievable with noninteractive communication between the terminals. The achievability results are also shown to be universal.
We consider the problem of characterizing the secret key (SK)-capacity for an arbitrary number of terminals, each of which observes a distinct component of a discrete memoryless multiple source, with unconstrained public communication allowed between these terminals. Our main contribution is the determination of SK-capacity for an arbitrary subset of terminals with the remaining terminals serving as "helpers," when an eavesdropper observes the communication between the terminals but does not have access to any other information. We also determine the private key (PK)-capacity when the eavesdropper additionally wiretaps some of the helper terminals from which too the key must then be concealed.
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 setAAAof 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 fromAAA. 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 setAAA, it can generate the secret key at the outset and transmit it over the noisy channel, suitably encoded, whereupon the output terminals inAAAsecurely 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.
We consider the generation of common randomness (CR), secret or not secret, by two user terminals with aid from a "helper" terminal. Each terminal observes a different component of a discrete memoryless multiple source. The helper aids the users by transmitting information to them over a noiseless public channel subject to a rate constraint. Furthermore, one of the users is allowed to transmit to the other user over a public channel under a similar rate constraint. We study the maximum rate of CR which can be thus generated, including under additional secrecy conditions when it must be concealed from a wiretapper. Lower bounds for the corresponding capacities are provided, and single-letter capacity formulas are obtained for several special cases of interest.
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 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.