# Live random digits

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The above is 0 bits of free, independent and identically distributed true randomness. Each 512 bit block is brought to you today by a single pass of 512 bit SHA-2 across a unique frame from the Photonic Instrument, as $\text{SHA-512}(.jpg)$.

Standard caveats apply: don’t use it for your bank’s password (we’ve seen it!). And of course we might be keeping a record of it too. And how do you know it’s random anyway? It may have come from a kiddie’s linear congruential generator like RANDU or java.util.Random. This is just intended to be an example of a working, gold standard DIY TRNG. And it’s really really random. Best build your own though!

Randomness extractors are generally applied to a biased entropy source $(X)$ with only $(1-\epsilon)s$ bits of entropy, where $\epsilon$ is a bias away from perfectly random. And the Photonic Instrument is oh so biased. All of the excessive zeros lead to a raw signal bias $\epsilon = 0.0114$ or $2^{-6.45}$. The basic idea of such an extractor is to compute $k$ output bits with high randomness from $n > k$ input bits with less randomness. This is known as the Left Over Hash Lemma.

Given that each bit of the input sequence has entropy $s$ ($s = 1$ for perfect randomness), the probability that the extractor output will deviate from a perfectly uniform $k$-bit string is in accordance[1] with $$\epsilon = 2^{-(sn-k)/2}$$ NIST generally accepts that $\epsilon \leq 2^{-64}$ is a negligible bias for a cryptographic strength random sequence. As the entropy from the Photonic Instrument arrives in batches of approximately 21.2 kbits, our $\epsilon \approx 2^{-10,000}$. We don’t know whether contemporary pseudo random functions like SHA-2 can output blocks with so little bias as it’s impossible to generate the requisite massive data sample for analysis. It should offer comfort though that such a simple extraction technique can achieve the recommended negligible bias.

References:-

[1] M. Troyer and R. Renner, A randomness extractor for the Quantis device. ID Quantique Technical Paper on Randomness Extractor, September 19, 2012.