Multi-user information theoretic security for wireless communication
Abstract
We show that the problem of code construction for multiple access channel (MAC)
resolvability can be reduced to the simpler problem of code construction for source resolvability.
Specifically, we propose a MAC resolvability code construction which involves a combination of
multiple source resolvability codes, used in a black-box manner, and leverages randomness
recycling implemented via distributed hashing and block-Markov coding.
We consider secret sharing where a dealer wants to share a secret with several
participants such that predefined subsets of participants can reconstruct the secret and all other
subsets of participants cannot learn any information about the secret. To this end, the dealer
and the participants have access to samples of correlated random variables and a one-way (from
the dealer to the participants), authenticated, public, and rate-limited communication channel.
For this problem, we propose the first constructive and low-complexity coding scheme able to
handle arbitrary access structures. Our construction relies on a vector quantization coupled
with distribution approximations with polar codes to handle the reliability constraints, followed
by universal hashing to handle the security constraints. We stress that our coding scheme does
not require symmetry or degradation assumptions on the correlated random variables, and does
not need a pre-shared secret among the participants and dealer.
Consider a secret sharing model where a dealer shares a secret with several participants
through a Gaussian broadcast channel such that predefined subsets of participants can
reconstruct the secret and all other subsets of participants cannot learn any information about
the secret. Our first contribution is to show that, in the asymptotic blocklength regime, it is
optimal to consider coding schemes that rely on two coding layers, namely, a reliability layer
and a secrecy layer, where the reliability layer is a channel code for a compound channel
without any security constraint. Our second contribution is to design such a two-layer coding
scheme at short blocklength. Specifically, we design the reliability layer via an autoencoder, and
implement the secrecy layer with hash functions. To evaluate the performance of our coding
scheme, we empirically evaluate the probability of error and information leakage, which is
defined as the mutual information between the secret and the unauthorized sets of users
channel outputs. We empirically evaluate this information leakage via a neural network-based
mutual information estimator. Our simulation results demonstrate a precise control of the
probability of error and leakage thanks to the two-layer coding design.
Description
Thesis (Ph.D.)-- Wichita State University, College of Engineering, Dept. of Electrical and Computer Engineering