Abstract
In this paper, a new wiretap channel model is proposed, where the legitimate transmitter and receiver communicate over a discrete memoryless channel. The wiretapper has perfect access to a fixed-length subset of the transmitted code word symbols of her choosing. Additionally, she observes the remainder of the transmitted symbols through a discrete memoryless channel. This new model subsumes the classical wiretap channel and wiretap channel II with noisy main channel as its special cases and is termed as the generalized wiretap channel for that reason. The strong secrecy capacity of the proposed channel model is identified. Achievability is established by solving a dual secret key agreement problem in the source model and converting the solution to the original channel model using probability distribution approximation arguments. In the dual problem, a source encoder and decoder, who observe random sequences independent and identically distributed according to the input and output distributions of the legitimate channel in the original problem, communicate a confidential key over a public error-free channel using a single forward transmission, in the presence of a compound wiretapping source who has perfect access to the public discussion. The security of the key is guaranteed for the exponentially many possibilities of the subset chosen at the wiretapper by deriving a lemma which provides a doubly exponential convergence rate for the probability that, for a fixed choice of the subset, the key is uniform and independent from the public discussion and the wiretapping source's observation. The converse is derived by using Sanov's theorem to upper bound the secrecy capacity of the generalized wiretap channel by the secrecy capacity when the tapped subset is randomly chosen by nature.
Recommended Citation
M. Nafea and A. Yener, "A New Wiretap Channel Model and its Strong Secrecy Capacity," IEEE Transactions on Information Theory, vol. 64, no. 3, pp. 2077 - 2092, Institute of Electrical and Electronics Engineers, Mar 2018.
The definitive version is available at https://doi.org/10.1109/TIT.2017.2786541
Department(s)
Electrical and Computer Engineering
Keywords and Phrases
concentration inequalities; random binning; source-channel duality; strong secrecy; Wiretap channel; wiretap channel II
International Standard Serial Number (ISSN)
0018-9448
Document Type
Article - Conference proceedings
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Institute of Electrical and Electronics Engineers, All rights reserved.
Publication Date
01 Mar 2018
Comments
National Science Foundation, Grant CCF 13-19338