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An analysis of steganographic systems subject to the following perfect undetectability condition is presented in this paper. Following embedding of the message into the covertext, the resulting stegotext is required to have exactly the same probability distribution as the covertext. Then no statistical test can reliably detect the presence of the hidden message. The authors refer to such steganographic schemes as perfectly secure. A few such schemes have been proposed in recent literature, but they have vanishing rate. They prove that communication performance can potentially be vastly improved; specifically, the basic setup assumes independently and identically distributed (i.i.d.) covertext, and they construct perfectly secure steganographic codes from public watermarking codes using binning methods and randomized permutations of the code.
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