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IET Information Security

Simultaneously generating multiple keys in a four-terminal network

Parisa Babaheidarian, Somayeh Salimi, Mohammad Reza Aref

Published Sep 10, 2012• 3 citations
Publisher

Abstract

A source model including four terminals is considered, where three simultaneously generating three types of keys are intended. Terminals 1, 2 and 3 wish to share a common key, the secret key, which should be kept secret from terminal 4 and simultaneously terminals 1 and 2 intend to share a private key with terminal 3, which should be kept secret from each other. Also, all the keys should be concealed from terminal 4 (the external wiretapper). The authors assume that all terminals including the external wiretapper have access to distinct correlated i.i.d. sources; there is also a noiseless public channel with unlimited capacity among the terminals. The authors have investigated the model on two scenarios of key sharing depending on the direction of the public channel. Rate regions of the keys are derived. It is shown that in some special cases the inner and outer bounds of the capacity regions coincide and the capacity regions are derived.

DOI
10.1049/iet-ifs.2011.0232

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A source model including four terminals is considered, where three simultaneously generating three types of keys are intended. Terminals 1, 2 and 3 wish to share a common key, the secret key, which should be kept secret from terminal 4 and simultaneously terminals 1 and 2 intend to share a private key with terminal 3, which should be kept secret from each other. Also, all the keys should be concealed from terminal 4 (the external wiretapper). The authors assume that all terminals including the external wiretapper have access to distinct correlated i.i.d. sources; there is also a noiseless public channel with unlimited capacity among the terminals. The authors have investigated the model on two scenarios of key sharing depending on the direction of the public channel. Rate regions of the keys are derived. It is shown that in some special cases the inner and outer bounds of the capacity regions coincide and the capacity regions are derived.
A new scenario for simultaneously generating a secret key and two private keys among three Terminals in the presence of an external eavesdropper is considered. Terminals 1, 2 and 3 intend to share a common secret key concealed from the external eavesdropper (Terminal 4) and simultaneously, each of Terminals 1 and 2 intends to share a private key with Terminal 3 while keeping it concealed from each other and from Terminal 4. All four Terminals observe i.i.d. outputs of correlated sources and there is a public channel from Terminal 3 to Terminals 1 and 2. An inner bound of the “secret key-private keys capacity region” is derived and the single letter capacity regions are obtained for some special cases.
A new scenario for generating a secret key and two private keys among three Terminals in the presence of an external eavesdropper is considered. Terminals 1, 2 and 3 intend to share a common secret key concealed from the external eavesdropper (Terminal 4) and simultaneously, each of Terminals 1 and 2 intends to share a private key with Terminal 3 while keeping it concealed from each other and from Terminal 4. All four Terminals observe i.i.d. outputs of correlated sources and there is a public channel from Terminal 3 to Terminals 1 and 2. An inner bound of the "secret key-private keys capacity region" is derived and the single letter capacity regions are obtained for some special cases.
A source model for secret key generation between terminals is considered. Two users, namely users 1 and 2, at one side communicate with another user, namely user 3, while at the other side via a public channel where three users can observe i.i.d. outputs of correlated sources. Each of users 1 and 2 intends to share a secret key with user 3 where user 1 acts as a wiretapper for user 2 and vice versa. In this model, two situations are considered: communication from users 1 and 2 to user 3 (the forward key strategy) and from user 3 to users 1 and 2 (the backward key strategy). In both situations, the goal is sharing a secret key between user 1 and user 3 while leaking no effective information about that key to user 2, and simultaneously, sharing another secret key between user 2 and user 3 while leaking no effective information about the latter key to user 1. This model is motivated by wireless communications when considering user 3 as a base station and users 1 and 2 as network users. For both the forward and backward key strategies, inner and outer bounds of secret key capacity regions are derived. In special situations where one of users 1 and 2 is only interested in wiretapping and not key sharing, the results agree with that of Ahlswede and Csiszar. Also, the authors investigate some special cases in which the inner bound coincides with the outer bound and secret key capacity region is deduced.
A source model for secret key generation between terminals is considered. Two users, namely users 1 and 2, at one side communicate with another user, namely user 3, at the other side via a public channel where three users can observe i.i.d. outputs of correlated sources. Each of users 1 and 2 intends to share a secret key with user 3 where user 1 acts as a wiretapper for user 2 and vice versa. In this model, two situations are considered: communication from users 1 and 2 to user 3 (the forward key strategy) and from user 3 to users 1 and 2 (the backward key strategy). In both situations, the goal is sharing a secret key between user 1 and user 3 while leaking no effective information about that key to user 2, and simultaneously, sharing another secret key between user 2 and user 3 while leaking no effective information about the latter key to user 1. This model is motivated by wireless communications when considering user 3 as a base station and users 1 and 2 as network users. In this paper, for both the forward and backward key strategies, inner and outer bounds of secret key capacity regions are derived. In special situations where one of users 1 and 2 is only interested in wiretapping and not key sharing, our results agree with that of Ahlswede and Csiszar. Also, we investigate some special cases in which the inner bound coincides with the outer bound and secret key capacity region is deduced.
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
A source model for secret key generation between terminals is considered. Two users, namely users 1 and 2, at one side communicate with another user, namely user 3, at the other side via public channels where three users can observe i.i.d outputs of correlated sources. Each of users 1 and 2 intends to share a secret key with user 3 where user 1 acts as a wiretapper for user 2 and vice versa. In this model, two situations are considered: communication from users 1 and 2 to user 3 (forward key strategy) and from user 3 to users 1 and 2 (backward key strategy). This model is motivated by wireless communications when considering user 3 as a base station and users 1 and 2 as network users. In this paper, for both forward and backward key strategies, inner and outer bounds of secret key capacity regions are derived. In special attitudes where one of users 1 and 2 are only interested in wiretapping and not key sharing, our results agree with that of Ahlswede and Csiszar. Also, we investigate some special cases in which inner bound coincides on outer bound and secret key capacity region is deduced.