Inspired by the challenges of designing a robust, and undetectable covert channel, in this paper we introduce a design methodology for timing covert channels that achieve provable polynomial-time undetectability. This means that the covert channel can not be detected by any polynomial-time statistical test that analyzes the samples of the covert traffic and the legitimate traffic. The proposed framework is based on modeling the covert channel as a differential communication channel, and the formulation for modulation/demodulation processes that are derived according to the communication model. The proposed scheme incorporates a trellis structure in modulating the covert message. The trellis structure is also used at the covert receiver to perform iterative demodulation/decoding of the covert message that significantly enhances the channel reliability. In addition, the paper presents an adaptive modulation strategy that improves the channel robustness without compromising the stealthiness of the channel. The combination of the adaptive modulation and the trellis structure gives the covert channel considerable flexibility and low error rate at the covert receiver. In fact, performance analysis of the channel reveals that the proposed covert communication scheme withstands extremely high levels of network noise and adversarial disruption, while it maintains an outstanding undetectability level and covert rate.
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