A Model for Adversarial Wiretap Channels
Abstract: In the wiretap model of secure communication, Alice is connected to Bob over a noisy channel that is eavesdropped by Eve. The goal is to provide (asymptotic) reliability and perfect secrecy assuming that the Eve has unlimited computational power. The model has attracted considerable attention in recent years because it provides a natural model for passive eavesdropping in wireless communication. We consider a wiretap model with active adversaries, and define adversarial wiretap (AWTP) channels using a (ρr, ρw) wiretap adversary who can read a fraction ρr, and modify a fraction ρw of a sent codeword. The code components that are read and/or modified can be chosen adaptively, and the subsets of read and modified components could be different. AWTP codes provide secrecy and reliability for communication over AWTP channels. We define the security and reliability of AWTP channels and use these definitions to evaluate the security and reliability of codes for these channels. This paper has two main contributions. First, we prove an upper bound on the rate of AWTP codes for (ρr, ρw)-AWTP channels. Second, we give an explicit construction of a perfectly secure AWTP code family with efficient decoding that achieves the bound and, hence, obtain the secrecy capacity of AWTP channels for large alphabets. AWTP model is a natural extension of Wyner's wiretap models, and somewhat surprisingly, it is also closely related to a seemingly unrelated cryptographic primitive, secure message transmission (SMT). This relation results in a new (and the only known) bound on the transmission rate of 1-round (ε, δ)-SMT protocols. We discuss our results, give their relations to other works, and propose directions for future work.