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I have a question about true random.

I have a true random bytes generated by a RNG device. With the true Random bytes i made news bytes from the description(bits by bits) of the bytes true random.

Process Example:

  1. RNG True Random -> 10101011
  2. Mathematicaly process over each bits of RNG True Random (one-way)
  3. New TrueR from process (2) -> 1100011010111110001100111100011010

So is the new TrueR considerated as true random binary ?

thanks :)

Skydr0w
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  • basically: no. only "true random" is "true random" - and processing means: part of your randomity is _processed_ and by definition not _random_ anymore. that being said: voting to close as off-topic, since it's not about _coding_ but mathematical theory. – Franz Gleichmann Jul 15 '20 at 13:11
  • thank you i will delete it and post it on mathematical theory ;) – Skydr0w Jul 15 '20 at 13:13
  • Please [do not post the same question on multiple sites](https://meta.stackexchange.com/q/64068). – D.W. Jul 15 '20 at 20:50
  • The result might or might not be true random depending on the processing you do. Each case requires analysis. – President James K. Polk Jul 16 '20 at 11:33

1 Answers1

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If the new bit array has the same length or is smaller than the source array, it might be true random (e.g. if you take every 2nd bit, or if you XOR each bit with an equally long array of bits).

But if you create a longer array, then the extra bits have been created from old bits by an algorithm in a reproducible way. Therefore they cannot be random.

Let's do a simple example. We create new bits by copying each bit from the source followed by the inverse of this bit:

10101011 --> 1001100110011010

Now, we have pairs of bits, where one is always the inverse of the other one. A real algorithm might be much more complicated (I think of SHA256) and the result might look random, but it is not, because the algorithm creates non-random complex relations between the bits.

Olivier Jacot-Descombes
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  • Even if you have same length or is smaller output, it still might end up quite non-random, e.g. bit shuffle sith that all ones are positioned below all zeroes will produce quite interesting result – Severin Pappadeux Jul 15 '20 at 19:21
  • Yes, not every algorithm guarantees that the randomness will be preserved. It would be interesting to know if this could be proved for every algorithm or if we run into a kind of [Halting problem](https://en.wikipedia.org/wiki/Halting_problem). – Olivier Jacot-Descombes Jul 16 '20 at 09:57