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Assume that bits $A$ and $B$ each have .5 bits of entropy per bit. Fair enough (and I'll assume that we're talking about Shannon entropy) The two-bit result of the concatenation $A‖B$ has 1 bit of entropy total, and it retains the entropy density of .5 bits of entropy per bit. Not so fast. The concatenation has between 0.5 and 1 bits of entropy. The ...


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Actually a stronger statement holds. It is enough for one of two bits to have maximum Shannon entropy, for their XOR to also have maximum Shannon entropy, provided they are statistically independent. If $A$ has probability distribution $(p,1-p)$ with $\Pr[A=0]=p$ and $B$ has probability distribution $(q,1-q)$ with $Pr[B=0]=q$ and they are independent random ...


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In the comment above, I take it that Paul Uszak, must be referring to a CSPRNG, and not a TRNG (realized with hardware in relation to real chaos from the non-computer-world)... TRNGs can be used as great supplements and will make any [CS]PRNG work even better though. User Space Entropy manipulation, i.e. manipulating entropy from the application layer should ...


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The question really asks for a sample of data from a source with a known entropy rate. I suggest starting with the simplest: sources with zero entropy rate. Examples from which the first megabytes can be readily obtained: a source producing only bytes at zero. a source cycling over the 256 bytes incrementally. a source consisting of the SHA-256 hashes of ...


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In practice you won't learn anything from this exercise. The entropy guessing methods in NIST SP 800-90B, even if they're state of the art, are very easy to fool. It's probably safe to assume that the true entropy of the source isn't substantially higher than what these tests tell you it is, but it could easily be much lower. Even the output of a non-...


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