A New Wiretap Channel Model and Its Strong Secrecy Capacity

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 codeword 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. 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 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 new wiretap channel model by the secrecy capacity when the tapped subset is randomly chosen by nature.

The Caching Broadcast Channel with a Wire and Cache Tapping Adversary of Type II

“…During cache placement, the transmitter maps M c into X n c using stochastic encoding, i.e., wiretap coding [40]. Since the rate of M c is less than 1 − α, M c is strongly secure from the adversary who observes nα symbols of X n c [38], [39]. During the delivery phase, the transmitter sends X n d as the binary representation of M d which is of length n bits, since the delivery phase is noiseless and secure.…”

“…The secrecy capacity for this model was identified in [38]. Reference [39] has introduced a generalized wiretap model which subsumes both the classical wiretap [40] and wiretap II [37] models as special cases. This generalized model was extended to multi-transmitter and multi-receiver networks in [41]- [43].…”

“…In this paper, we consider an adversary model of type II as in [36]- [39], [41]- [43], but in a cache-aided communication setting. In particular, the adversary noiselessly observes a partial subset of its choosing of the transmitted symbols over the cache placement and/or delivery phases.…”

“…Additionally, the number of possible choices for the subsets S 1 and S 2 is 2n αn < 2 2n . Thus, the combined number of the messages and the subsets is at most exponential in n. Using (42) and the union bound, as in [38], [39], we have…”

Universal covertness for Discrete Memoryless Sources

“…Proof. We first perform source resolvability with lossless reconstruction by means of "random binning" [5], [30], [31] as follows. Note that standard resolvability results [5] do not directly apply to our purposes as we require recoverability of the input from the output.…”