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

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 in [1], 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.

Group Secret Key Generation in Wireless Networks: Algorithms and Rate Optimization

“…Theorem 1: Among the training-based approaches for secret key generation among three nodes, Algorithm A achieves the optimal key rate for a given tuple (T 1 , T 2 , T 3 ), which is defined in (15).…”

“…The works in [7]- [15] aimed to find informationtheoretic secrecy key capacities in a variety of source models, however, they have not provided methods to obtain the source observations. Due to channel reciprocity in time-division duplex (TDD) systems, the correlative observations can be obtained via estimates of the wireless fading channels between the legitimate users, which demonstrates the advantages of the source model based key generation approach to support secure multimedia service.…”

“…The information-theoretic secret key capacity (i.e., the optimal key rate) for the group key generation in the multi-terminal source model was first provided in [10]. Since then, several tree-based algorithms have been developed to achieve the group secret key capacity for the multi-terminal pairwise independent network (PIN) [11]- [15]. On the other hand, effective group key generation algorithms have been proposed for wireless networks by exploiting channel characteristics in [28]- [30].…”

Secret key-private key generation over three terminals: Capacity region

“…Our outline contains major key generation steps and intuitive explanation about the secrecy properties of the generated secret and private keys. The mathematical details are omitted due to the space limitations, and can be referred to [17]. In case 2,…”

“…Due to space limitations, we provide only outlines of our achievable schemes. The detailed proof can be found in [17].…”