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Suppose there is a communications channel between two parties. Suppose I want to send information through this channel, but I want to make it look like noise. Ie, I don't necessarily want to encrypt it, though I'm not prohibiting encryption - the point is I want to be able to transmit information to someone else such that what is sent across the channel cannot be distinguished from random noise by any potential eavesdropper.

Maybe something like the above is impossible to do "perfectly", but in any case the question I'm asking is - what is the correct term/keywords for problems in the spirit of what I described above?

Is there a mathematical theory of something of this type?

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It's not an exact match to your question, but you're probably looking for something in the field of steganography.

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  • $\begingroup$ The primary goal of steganography is to hide the fact that you're communicating at all. As you suggest, it is not clear that the OP is concerned about this aspect. It would depend on whether the OP is thinking that there is always, or at least commonly, (sufficient) noise in the communication channel or not. $\endgroup$
    – Derek Elkins left SE
    Commented Mar 14, 2018 at 7:53
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As @mhum suggests, looking at techniques from the field of steganography is probably an excellent starting point... but you might also be interested in subliminal channels.

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