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IEEE Access

Private Key and Group Key Generation Using Correlated Sources and Wiretap Broadcast Channel in Presence of One-Way Public Communication

Shixun Gong, Xiaofeng Tao, Na Li, Haowei Wang

Published Jan 1, 2019• 6 citations
Publisher

Abstract

Encryption with shared key is one of the methods to ensure secure communication. To meet the requirements of keys, this paper investigates the problem of generating private key (PK) and group key (GK) using correlated sources and discrete memoryless wiretap broadcast channel (DM-WBC), in presence of one-way public communication. In the model considered, one transmitter (Alice) and three receivers (Bob, Carol and Eve) are connected via a DM-WBC, and a one-way communication over a public noiseless channel, initiated by Alice, is available. Alice and Bob wish to share a PK that is concealed from Carol and Eve, and they also want to generate a GK with Carol that needs to keep secret from Eve. Under this model, the key capacity regions of PK and GK are established by designing joint source-channel coding schemes to achieve these regions. In PK-generation, the considered model can be viewed as a one receiver two-eavesdropper model, and Alice and Bob have access to correlated source sequences. In GK-generation, the considered model can be viewed as a two-receiver one eavesdropper model, and the three legitimate parties (Alice, Bob and Carol) all have the source observations. Furthermore, the security performance of the generated keys are analyzed by analyzing key leakage rate of each key.

DOI
10.1109/access.2019.2937799

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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.
In this paper, the problem of simultaneously generating multiple keys over a cascade of a noiseless channel and a wiretap channel is considered. The problem consists of three legitimate parties (i.e., Alice, Bob, and Carol) and an eavesdropper (Eve), where Alice and Bob wish to agree with Carol on independent secret keys, both of which should be kept secret from Eve. Alice and Bob are connected via a noiseless channel, and Bob is connected with Carol via a wiretap channel, while there is no direct connection between Alice and Carol. To Alice and Carol, Bob acts as a relay. Under this model, a full characterization of the secret-key capacity region is provided for the case in which Eve has no side information. This result shows that there exists a tradeoff between the individual secret-key rates. Then, this result is generalized to the case in which Eve has side information, and the corresponding secret-key capacity region is fully characterized.
In this paper, we study the problem of secret key generation with one-way communication, where in addition to the rate limited public channel, which can be observed by both Bob and Eve, we add a secure channel, which only connects Alice and Bob. In this model, we do not pose any constraints on the sources, i.e. Bob is not degraded to or less noisy than Eve. We propose an achievability scheme, and we also suggest a converse, which meets the achievability. Therefore, we obtain the secret key capacity for this model.
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.
In this paper, the problem of simultaneously generating multiple keys over a cascade of a noiseless channel and a wiretap channel is considered. The problem consists of three legitimate parties, i.e., Alice, Bob and Carol, where Alice and Bob wish to agree with Carol on independent secret keys. Alice and Bob are connected via a noiseless channel, and Bob is connected with Carol via a wiretap channel, while there is no direct connection between Alice and Carol. To Alice and Carol, Bob acts as a relay. Under this model, a single-letter characterization of the secret-key capacity region is provided. The result shows that there exists a trade-off between the individual secret-key rates.
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.