How do we distinguish information in an unknown code from stochastic noise, if that information is not encoded with an error-correcting code that we know of? Could someone send information without us distinguishing it from environmental noise, having only a second person who distinguishes what they have to look at to distinguish that message from noise, we are obviously talking about a very noisy environment, for example some physical process that generates noise and not just about a type because, depending on the process that generated it, there could be many kinds of noise that meet different types of statistical distribution.
Can we transmit messages without knowing that they are messages?
Yes, of course.
The answer is yes with quite a few different interpretations of the question.
That is a question for an expert on encryption and steganography. I can only guess that it is possible. We would have to measure differences from the background noise. Since the information can be just that a message is sent, so we cannot expect the content to mean anything more than that. But even that minimal message requires it to be measurably different from the background noise. Otherwise you cannot even know that a message was sent. Besides any means of decoding would also be a means of distinguishing it from the background noise. Then a difference exists and that fact makes it likely that differences can be measured in some way even when the method of decoding is not known.
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It is possible, in principle at least, to transmit messages in such a way that they can’t be distinguished from random noise. In practice, it’s a pretty hard problem.
One way that it can be done is using an algorithm called a one time pad – where the key that is used to encrypt the message is larger than the message itself. If the one time pad consists of truly random noise, then the message itself will be indistinguishable from random noise to anyone who does not also have a copy of the key.
The problem is that this isn’t a very practical form of cryptography. Usually when you’re encrypting messages you’re going to want a key that is small enough to be shared with those who need to have it, and on top of that you’re going to want to be able to reuse it.
For many of the strongest algorithms currently in use today, there is no known way to distinguish their output from random noise. However, that doesn’t mean to say that there won’t be a way in the future. Coming up with a truly secure encryption algorithm is a problem that taxes the best mathematicians (which is why it’s constantly drummed into us as programmers that we should never, ever, ever try to write our own) and there’s no guarantee that someone in the future won’t find a weakness in one of the existing ones. There are several algorithms that were considered strong twenty years ago that are no longer in use because they have since been broken. This is a bit of a headache for administrators of website infrastructure because you have to keep updating your SSL/TLS software so that your users can connect to your site securely.
Another difficulty is in generating truly random numbers. The most common algorithms used by computers only generate numbers that are pseudorandom – they form a sequence that is very, very long, but that can be predicted once you’ve observed it for a while. (For example, one popular PRNG, the Mersenne Twister, has a period of 2^{19937} - 1, but you can predict which number will come next after observing the first 624 numbers that it outputs.) Some random number generators adopt a hardware-based approach that uses quantum mechanical effects (such as electronic noise) but these too are easy to get wrong – for example, by producing an uneven distribution of numbers.
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Incidentally here’s a paper by someone who performed the standard statistical tests for randomness on a bunch of different encryption algorithms.
In summary: some of them (e.g. Rijndael) do produce output that passes all known tests for randomness, while there are others that don’t.
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Of course, perhaps the question is, there is a mathematical property that only messages meet, perhaps a minimum efficiency of information transmission or some conserved property, I am actually asking this for theological considerations, we could disprove alleged miracles or transmission of information through assumptions fluctuations if we can tell if information is being transmitted or not in an environment, but we have to distinguish it from ambient noise and it can be very subtle at the particle scale, although in reality I would like to prove that it is true… it is my way of thinking the world, that’s the way it is…
Of course, don’t consider it, I should ask if there is an efficient way, and in what sense of the word efficient, to do that…
I’m fascinated by the message being transmitted unknowingly and unknowably in the questions. A sort of anti-pareidolia.
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