Information Theoretic Generation of Multiple Secret Keys

This dissertation studies the problem of secret key generation for encrypted group communication in a network, based on an information theoretic approach. This approach, which relies on a provable form of security, also provides suggestions for key constructions. We examine the problem of the simultaneous generation of multiple keys by different groups of terminals intended for encrypted group communication, in certain three-terminal source models, which capture the salient features of general multiterminal models. We characterize the rates at which two designated pairs of terminals can simultaneously generate private keys, each of which is effectively concealed from the remaining terminal…

Contents

1 Introduction
1.1 Background
1.2 Motivation
1.3 Prior Work
1.4 Overview of Dissertation
1.5 Contributions
2 The Private Key Capacity Region for Three Terminals
2.1 Introduction
2.2 Preliminaries
2.3 Statement to Results
2.4 Proofs
2.5 Generalizations
3 The Secret Key–Private Key Capacity Region for Three Terminals
3.1 Introduction
3.2 Preliminaries
3.3 Statement to Results
3.4 Proofs
3.5 Discussion
4 Secret Key and Private Key Constructions for Simple Multiterminal Source Models
4.1 Introduction
4.2 Preliminaries
4.2.1 The Secret Key Capacity and the Private Key Capacity
4.2.2 Linear Codes for the Binary Symmetric Channel
4.3 Statement to Results
4.4 Proofs
4.5 Implementation Using LDPC Codes
4.5.1 Preliminaries Concerning LDPC Codes
4.5.2 ImplementationforModel4.1
4.5.3 Simulation Results
5 The Relationship Between the Common Randomness Capacity and the Secret Key Capacity for Source Models with Rate Constraints
5.1 Introduction
5.2 Preliminaries
5.3 Previous Results
5.4 Statemen to Results
5.5 Proofs
v6 Conclusions and Future Research
6.1 Conclusions
6.2 Future Research
A Types and Typical Sequences
A.1 Types
A.2 Typical Sequences
B Proof of Proposition 4.1
C Supplemental Proofs for Theorems 5.3 and 5.4
C.1 Proof of the Markov Conditions
C.2 Idea of the Achievability Proofs
Bibliography

Author: Ye, Chunxuan

Source: University of Maryland

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