Here’s some more on the Zodiac Killer ciphers, specifically the interesting uncracked one (“Z340”). Though most of the images of this on the Internet are both monochrome and somewhat overexposed, here’s a link to a nice image of Z340 at a high-enough resolution to be useful. Thanks to this, I think you can see that the correction on row 6 is from a ‘right-facing K’ to a ‘left-facing K’, which could well be a copying error from an intermediate draft.
What’s more, it allows us to transcribe the ciphertext with a high degree of confidence that we’ve got it right: so here’s the transcription that Dave Oranchak and glurk use, which should be more than good enough for non-Zodiac experts wanting to play with it too:-
OK, today’s thought follows on from my most recent Zodiac Killer post, which wondered to what degree cryptologists could make use of the likely presence in Z340 of broadly the same kind of homophone cycles present in the earlier Z408 ciphertext. Well blow me down if I didn’t just run into exactly that today, a paper by Håvard Raddum, Marek Sýs called “The zodiac killer ciphers” published in Tatra Mountains Maths Publ. 45 (2010), pp.75–91: the fulltext is freely downloadable here. There’s an earlier (slightly less formal) 2009 presentation here.
The two authors found evidence of low-level (i.e. length = 2 or 3) homophone cycle structure in the Z340 but not in its transposed version, which is a good indication that the cipher itself isn’t (diagonally) transposed. However, having myself written codes to look for homophone cycles in Z340, I think their assumption that it is a single homogenous cipher is not really justified: they would have got much more striking values had they divided it into two.
Really, the challenge with searching for homophone cycles in Z340 that they failed to address is that the statistical significance of the length 2 or length 3 homophone cycles they found is relatively low compared with the Z408 cipher. How many standard deviations are these actually away from the centre of the distribution? The biggest statistical problem with searching for best homophone cycles is that you have a lot to choose from, which I believe reduces the statistical significance of any you do happen to find. It’s a kind of statistical “darts paradox”: hitting the bullseye once in a million throws doesn’t suddenly make you a great darts player.
Still, they build up a lot of theoretical machinery (though I somehow doubt that you can reliably build n-cycles out of (n-1)-cycles given the many deviations from the cycle scheme the Zodiac Killer makes), which may well prove useful. Definitely something to ponder on.