In wiretap model of secure communication the goal is to provide (asymptotic) perfect secrecy and reliable communication 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 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 that models active adversaries at this layer. We consider a @math wiretap adversary who can see a fraction @math , and modify a fraction @math , 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 and measures for these codes, and define secrecy capacity of an AWTP channel that represents the secrecy potential of the channel. The paper has two main contributions. First, we prove a tight upper bound on the rate of AWTP codes with perfect secrecy for @math -AWTP channels, and use the bound to derive the secrecy capacity of the channel. We prove a similar bound for @math -secure codes also, but in this case the bound is not tight. Second, we give an explicit construction for a capacity achieving AWTP code family, and prove its security and efficiency properties. We show that AWTP model is a natural generalization of Wyner's wiretap models and somewhat surprisingly, also provides a direct generalization for a seemingly unrelated cryptographic primitive, Secure Message Transmission (SMT).
@cite_49: The wiretap channel is a setting where one aims to provide information-theoretic privacy of communicated data based solely on the assumption that the channel from sender to adversary is "noisier" than the channel from sender to receiver. It has developed in the Information and Coding IC it has optimal rate; and both the encryption and decryption algorithms are proven to be polynomial-time.
@cite_50: The classical wiretap channel models secure communication in the presence of a nonlegitimate wiretapper who has to be kept ignorant. Traditionally, the wiretapper is passive in the sense that he only tries to eavesdrop the communication using his received channel output. In this paper, more powerful active wiretappers are studied. In addition to eavesdropping, these wiretappers are able to influence the communication conditions of all users by controlling the corresponding channel states. Since legitimate transmitters and receivers do not know the actual channel realization or the wiretapper's strategy of influencing the channel states, they are confronted with arbitrarily varying channel (AVC) conditions. The corresponding secure communication scenario is, therefore, given by the arbitrarily varying wiretap channel (AVWC). In the context of AVCs, common randomness (CR) has been shown to be an important resource for establishing reliable communication, in particular, if the AVC is symmetrizable. But availability of CR also affects the strategy space of an active wiretapper as he may or may not exploit the common randomness for selecting the channel states. Several secrecy capacity results are derived for the AVWC. In particular, the CR-assisted secrecy capacity of the AVWC with an active wiretapper exploiting CR is established and analyzed in detail. Finally, it is demonstrated for active wiretappers how two orthogonal AVWCs, each useless for transmission of secure messages, can be super-activated to a useful channel allowing for secure communication at nonzero secrecy rates. To the best of our knowledge, this is not possible for passive wiretappers and, further, provides the first example of such super-activation, which has been expected to appear only in the area of quantum communication. Such knowledge is particularly important as it provides valuable insights for the design and the medium access control of future wireless communication systems.
Our adversarial channel model can be seen as a special class of arbitrarily varying channel. For this class we can remove some of the restrictions of the above line of work. More specifically, (i) we do not assume shared randomness between the sender and the receiver, (ii) we consider an integrated adaptive eavesdropping and jamming adversary and assume that to corrupt the next symbol, the adversary uses all its knowledge up to that point; (iii) we allow adversary to choose the message distribution and so the error is worst case; and finally (iv) the secrecy measure in our case is in terms of statistical distance between the adversary's views of two adversarially chosen messages. We note that in @cite_50 , secrecy is measured as the mutual information of a random message (uniform distribution on messages) and the adversary's view. Our security definition using statistical distance is equivalent to the mutual information security when the message distribution is adversarially chosen @cite_49 .