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IEEE Information Theory Workshop (ITW)

The secret key capacity for multiple terminals

Imre Csiszár, Prakash Narayan

Published Aug 27, 2003• 9 citations
Publisher

Abstract

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.

DOI
10.1109/itw.2002.1115401

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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.
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 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
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.
The problem of simultaneously generating a secret key (SK) and private key (PK) pair among three terminals via public discussion is investigated, in which each terminal observes a component of correlated sources. All three terminals are required to generate a common secret key concealed from an eavesdropper that has access to public discussion, while two designated terminals are required to generate an extra private key concealed from both the eavesdropper and the remaining terminal. An outer bound on the SK-PK capacity region was established in [1], and was shown to be achievable for one case. In this paper, achievable schemes are designed to achieve the outer bound for the remaining two cases, and hence the SK-PK capacity region is established in general. The main technique lies in the novel design of a random binning-joint decoding scheme that achieves the existing outer bound.
We consider a model for secrecy generation, with three terminals, by means of public interterminal communication, and examine the problem of characterizing all the rates at which all three terminals can generate a "secret key," and - simultaneously - two designated terminals can generate a "private key" which is effectively concealed from the remaining terminal; both keys are also concealed from an eavesdropper that observes the public communication. Inner and outer bounds for the "secret key-private key capacity region" are derived. Under a certain special condition, these bounds coincide to yield the (exact) secret key-private key capacity region
The problem of simultaneously generating a secret key (SK) and private key (PK) pair among three terminals via public discussion is investigated. In this problem, each terminal observes a component of correlated sources. All three terminals are required to generate the common SK to be concealed from an eavesdropper that has access to the public discussion, while two designated terminals are required to generate an extra PK to be concealed from both the eavesdropper and the remaining terminal. An outer bound on the SK-PK capacity region was established by Ye and Narayan, and was shown to be achievable for a special case. In this paper, the SK-PK capacity region is established in general by developing schemes to achieve the outer bound for the remaining two cases. The main technique lies in the novel design of a random binning-joint decoding scheme that achieves the existing outer bound.