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, and the rates at which the following two types of keys can be generated simultaneously: (i) all the three terminals generate a (common) secret key, which is effectively concealed from an eavesdropper; and (ii) a designated pair of terminals generate a private key, which is effectively concealed from the remaining terminal as well as the eavesdropper. Furthermore, we develop an approach for the construction of a new class of provably secure secret keys by terminals in several simple multiterminal source models, which exploits innate connections between secret key generation and multiterminal Slepian-Wolf near-lossless data compression (sans secrecy restrictions). Implementations of these constructions using low density parity check (LDPC) channel codes are illustrated