Contents:-

# About the banner

The banner is 100 data points from the CMOS camera sensor within the Photonic Instrument. It is served up in sequential RGB format from decoded JPEG frames. Effectively, 100 image raster byte values. It’s intended to look fancy, but is not raw entropy per-se for the reasons stated here and here. Therefore the Shannon entropy rate is approximately 0.023 bits/raster byte. This gives a whopping total of 2.3 Kolmogorov random bits for $H(\text{banner})$, as $\frac{100}{640 \times 480 \times 3} \times 21,400$ bits conservatively based on 1 bit of entropy per .jpg file byte.

It does look ever so wobbly and random though doesn’t it? The data for the banner arrives as a 100 byte array, looking something like:- [20,10,6,20,8,4,18,6,2,16,4,2,16,4,3,17,5,3, 17,5,2,16,4,0,13,1,1,15,3,6,20,8,7,21,9,2, 16,4,0,13,1,2,16,4,3,17,5,0,14,2,2,20,19,5, 21,20,6,22,21,9,21,21,10,20,20,12,17,18,10, 15,16,9,13,14,17,21,22,13,17,18,9,13,14,5,9, 10,3,11,11,6,14,14,9,19,19,15,23,22,11,18].

It’s slightly counter intuitive as to how the above sequence might be represented by only 2.3 truly random bits. That’s because it’s a pseudo random sequence generated by the decoding of a JPEG algorithm operating on a much smaller .jpg file. You might think of this .jpg as akin to a one off seed for a PRNG. Hence Golden Rule 3; Don’t try to extract more entropy than actually exists. Or $\text{Ext}: \{0,1\}^n \to \{0,1\}^m$ such that $\Sigma{m_i} < |\text{.jpg}|$ for every and each image frame, and $m_i < n_i$ for any individual extraction operation $i$.

This odd quirk of mathematics/cryptography is further empirical proof of the perils of computational indistinguishability, and how easy it is to cock-it all up.