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arXiv:1404.6471 · IEEE Transactions on Information Theory

The Capacity Region of the Source-Type Model for Secret Key and Private Key Generation

Huishuai Zhang, Lifeng Lai, Yingbin Liang, Hua Wang

Published Jul 17, 2014• 25 citations
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Abstract

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.

DOI
10.1109/tit.2014.2340400

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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.
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.
Encrypting information with pre-agreed key is an effective method to ensure information security. With the increasing requirement for key rate, this paper investigates the problem of simultaneously generating a secret key (SK) and a private key (PK) over three legitimate terminals with a trusted helper via public discussion that a passive eavesdropper completely access to. The legitimate terminals and the helper observe the correlated source sequences from the outputs of discrete memoryless source (DMS). The legitimate terminals wish to generate an SK that is concealed from the eavesdropper, and two designated legitimate terminals want to generate a PK that needs to be additionally keep secret from the third legitimate terminal. Under this model, the SK-PK capacity region is fully characterized, and the source coding scheme is further provided to show that the region is achievable. The security performance of the generated keys is analyzed in terms of key leakage rate.
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 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 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.