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:-

HER>pl^VPk|1LTG2d
Np+B(#O%DWY.<*Kf)
By:cM+UZGW()L#zHJ
Spp7^l8*V3pO++RK2
_9M+ztjd|5FP+&4k/
p8R^FlO-*dCkF>2D(
#5+Kq%;2UcXGV.zL|
(G2Jfj#O+_NYz+@L9
d<M+b+ZR2FBcyA64K
-zlUV+^J+Op7<FBy-
U+R/5tE|DYBpbTMKO
2<clRJ|*5T4M.+&BF
z69Sy#+N|5FBc(;8R
lGFN^f524b.cV4t++
yBX1*:49CE>VUZ5-+
|c.3zBK(Op^.fMqG2
RcT+L16C<+FlWB|)L
++)WCzWcPOSHT/()p
|FkdW<7tB_YOB*-Cc
>MDHNpkSzZO8A|K;+

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.

3 thoughts on “Decent 2010 paper on the Zodiac Killer Ciphers…

  1. BrookeStephen on August 1, 2012 at 12:00 am said:

    Amazing work! Outstanding website!
    I also derived rules on repeating cycles from the resolved 408 cypher and tried to apply them to the 340. I noticed the repetition of picts, and built 3D models in VRML to resolve the patterns – very visible for 408, not so much for 340.
    My guess as to technique for generating msgs was piles of paper picts, say 3 or 4 different picts per alpha, and while writing the msg, use the pict at the top of the pile for that alpha, then place the pict at the pile bottom.
    Of course there are variations.
    With that said, it would appear that 340 just uses more avg picts per pile – not sure if its just for E,I,T,L,S (most used in 408) or for all alphas…
    Performing cycle evaluation and generating 3D models in VRML for 340 yields much flatter landscape (height Y is freq of repeat in pairs, unique pict-posn is X, Z is every other following unique pict).
    Thing about 408 is max of 10 repeating cycles, 340 is much lower (6). Problem is, some cycles are reversed mid-msg, or minor changes are made to a cycle’s order in a patterned way.
    I was happy to find groups of 3 or 4 picts that seemed appropriate for half the total # of their cycles.
    You can visually identify the pattern of multiple repeats much easier in VRML landscape…
    In the 408, at the very front are these sky-scrapers…
    01 08 8 03 08 8 06 08 8
    01 06 8 03 06 9
    01 03 9
    And as we now know, 1,3,6,8 all represent the alpha “i”.
    I’ll send you a pic of the VRML city-scape if you’d like.
    Also – I have to ask this! – why do you presume that there are errors in the messages? There are multiple picts per alpha and some cases of multiple alphas per pict… seems to me like all encryption is still encryption! No rules!!

  2. BrookeStephen on August 1, 2012 at 1:44 am said:

    I left out the really important points… d’oh!
    If repeating cycles from grammer (ch,sh,th) can be considered noise when we’re focusing on matching picts to alpha, then by increasing the avg number of picts per alpha, Zodiac has decreased the cycles to the level of the background or “grammer” noise…
    He may have overreacted after seeing his 408 resolved so quickly, leaving his message un-resolvable without a brute-force effort.
    Also, with all the groups of picts in 340 that I am able to discern having lower repeat numbers and smaller groups, than those in the 408, I’ll have to try more permutations in that brute-force effort.

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