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Asilomar Conference on Signals, Systems and Computers (ACSSC)

Helper-assisted asymmetric two key generation

Huishuai Zhang, Yingbin Liang, Lifeng Lai

Published Nov 1, 2014• 2 citations
Publisher

Abstract

The problem of simultaneously generating an asymmetric key pair with assistance of a helper is studied. In this setting, each of four terminals, i.e., a base station X0, two cellular nodes X1and X2, and a helper X3, observes a component of correlated sources. The cellular nodes X1and X2wish to generate secret keys K1and K2with the base station X0, respectively, under the help of terminal X3. Both keys should be concealed from an eavesdropper that has access to the public discussion, while K2is also required to be concealed from terminal X1. An outer bound on the key capacity region is derived. It is shown to be achievable under certain condition, and hence the key capacity region is characterized under such condition.

DOI
10.1109/acssc.2014.7094398

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The problem of simultaneously generating an asymmetric key pair with assistance of a helper is studied. In this setting, each of four terminals, i.e., a base station X0, two cellular nodes X1and X2, and a helper X3, observes a component of correlated sources. The cellular nodes X1and X2wish to generate secret keys K1and K2with the base station X0, respectively, under the help of terminal X3. Both keys should be concealed from an eavesdropper that has access to the public discussion, while K2is also required to be concealed from terminal X1. An outer bound on the key capacity region is derived. It is shown to be achievable under certain condition, and hence the key capacity region is characterized under such condition.
The problem of simultaneously generating two keys for a cellular model is investigated, in which each of four terminals, X0, X1, X2, and X3observes one component of correlated sources. The terminal X0 wishes to generate secret keys K1and K2respectively, with terminals X1and X2under the help of terminal X3. They are allowed to communicate over a public channel. Both K1and K2are required to be concealed from an eavesdropper that has access to the public discussion. The key capacity region is established by designing a unified achievable strategy to achieve the cut-set outer bounds, which greatly simplifies the proof.
The problem of simultaneously generating multiple keys for a cellular source model with a helper is investigated. In the model considered, there are four terminals, X0, X1, X2, and X3, each of which observes one component of a vector source. Terminal X0wishes to generate two secret keys K1and K2, respectively, with terminals X1and X2under the help of terminal X3. All terminals are allowed to communicate over a public channel. An eavesdropper is assumed to have access to the public discussion. Both symmetric and asymmetric key generations are considered. In symmetric key generation models, model 1a (with a trusted helper) requires that the two keys are concealed from the eavesdropper, and model 1b (with an untrusted helper) further requires that the two keys are concealed from the helper in addition to the eavesdropper. The asymmetric key generation models 2a and 2b are the same as symmetric key generation models 1a and 1b, respectively, except that the key K2is further required to be concealed from terminal X1. For all models studied, the key capacity region is established by designing a unified achievable strategy to achieve the cut-set outer bounds. We also study the problem of generating more than two keys and characterize its key capacity region when all the cellular terminals are required to generate independent keys with the base station.
A cellular source model for key generation is proposed and studied, in which a central terminal χ0wishes to generate K1with terminal χ1and K2with terminal χ2, respectively, via public discussion. Each terminal observes a component of a correlated source sequence. The K1is required to be concealed from an eavesdropper that has access to the public discussion, while the key K2needs to be concealed from both the eavesdropper and terminal χ1. The key capacity region is established by showing that the cut-set upper bound is achievable.
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.
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.
This paper investigates the problem of generating two secret keys (SKs) simultaneously over a five-terminal system with terminals labelled as 1, 2, 3, 4 and 5. Each of terminal 2 and terminal 3 wishes to generate an SK with terminal 1 over a public channel wiretapped by a passive eavesdropper. Terminal 4 and terminal 5 respectively act as a trusted helper and an untrusted helper to assist the SK generation. All the terminals observe correlated source sequences from discrete memoryless sources (DMS) and can exchange information over a public channel with no rate constraint that the eavesdropper has access to. Based on the considered model, key capacity region is fully characterized and a source coding scheme that can achieve the capacity region is provided. Furthermore, expression for key leakage rate is obtained to analyze the security performance of the two generated keys.