A Model for Adversarial Wiretap Channel

In wiretap model of secure communication, the goal is to provide (asymptotic) perfect secrecy and reliability over a noisy channel that is eavesdropped by an adversary with unlimited computational power. This goal is achieved by taking advantage of the channel noise and without requiring a shared key. The model has attracted considerable attention in recent years because it captures eavesdropping attack in wireless communication. The wiretap adversary is a passive eavesdropping adversary at the physical layer of communication. In this paper we propose a model for adversarial wiretap (AWTP) channel to capture active attacks at this layer. We consider a (ρr, ρw) wiretap adversary who can see a fraction ρr, and modify a fraction ρw, of the sent codeword. The code components that are read and/or modified can be chosen adaptively, and the subsets of read and modified components in general, can be different. AWTP codes provide secrecy and reliability for communication over these channels. We give security and reliability definitions for these codes, and define secrecy capacity of an AWTP channel. The paper has two main contributions. First, we prove a tight upper bound on the rate of AWTP codes for (ρr, ρw)-AWTP channels, and use the bound to derive the secrecy capacity of the channel. Second, we give an explicit construction for a perfectly secure capacity achieving AWTP code family. We show that our AWTP model is a natural generalization of Wyner’s wiretap models, and somewhat surprisingly, also provides a generalization of a seemingly unrelated cryptographic primitive, Secure Message Transmission (SMT). This relation is used to derive a new (and the only known) bound on the transmission rate of one round (ǫ, δ)-SMT protocols. We discuss our results, give the relations with related primitives, and propose directions for future work.