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Re: Pivots

PostPosted: Thu Sep 26, 2013 2:05 pm
by doranchak
Interesting work, trav.

traveller1st wrote:And then there's the "crop marks" with the diagonally filled box symbols in each corner (another spot of Dave's).


I didn't make this connection before, but one of the pivots has a strong resemblance to the "crop marks":

Image

Re: Pivots

PostPosted: Thu Sep 26, 2013 2:45 pm
by traveller1st
Ahhhh I had seen that but only as a cluster of symbols, completely didn't register it as part of the first pivot. Only that it was similar to the crop corners. Curious.

Re: Pivots

PostPosted: Thu Sep 26, 2013 3:03 pm
by doranchak
It gets curiouser.

That same diagonally filled square is involved with the strongest 3-symbol homophone cycle:

Image

Image

By "strongest", I mean that of all the ways to select 3 different symbols of the cipher text, Image, Image and Image produce the strongest uninterrupted cycle, suggesting homophonic substitution for a common plain text letter.

Side note: The only place the sequence breaks is right in the middle of the cipher, near where the "fold marks" appear.

Re: Pivots

PostPosted: Thu Sep 26, 2013 4:04 pm
by traveller1st
Interesting. I was wondering if the pluses might have been employed to hide or disrupt similar sequences. Just something else I was thinking about during my latest flurry of cipher poking. I wasn't thinking of it in those terms but I am now that you've posted that lol.

FWIW I checked the 408 after 'recompiling' and no pivots were produced.

Re: Pivots

PostPosted: Fri Sep 27, 2013 3:37 am
by smithy
doranchak wrote:That same diagonally filled square is involved with the strongest 3-symbol homophone cycle.....

D., that's the strongest 2-symbol homophone symbol, and the square is just getting in the way. Hee hee hee.

Does straight distribution based around your "strongest homophones" get anywhere near a sensible solve of the 340 btw?
If that's the strongest homophone, is it "E", and is the "next weakest" then a "T" and so on? Or variations thereof?
No of course not. Don't mind me, I haven't had a coffee yet.

Re: Pivots

PostPosted: Fri Sep 27, 2013 3:59 am
by doranchak
smithy wrote:If that's the strongest homophone, is it "E", and is the "next weakest" then a "T" and so on? Or variations thereof?
No of course not. Don't mind me, I haven't had a coffee yet.


No - I don't think there's any guarantee that it would be a particular letter, since the cycles are designed to hide letter frequencies.

If you order the 3-symbol cycles in the 408 by strength, it goes "I", "N", "E", "T", etc.

Also, the strength I'm referring to is a numerical estimate of the difficulty in producing the sequence by chance. For example, the ImageImageImage sequence in the 408 has more than a billion to one odds against it occurring by random chance. But the ImageImageImage sequence in the 340 has about 400,000 to one odds against it occurring by random chance.

Re: Pivots

PostPosted: Fri Sep 27, 2013 4:16 am
by smithy
D., no of course there aren't any guarantees which is why I tweaked you a bit and made my terrific joke - yes, that's what suppression's for - but my underlying question remains - pre-coffee, at least. I know the 408's plain-text order doesn't match normal distribution very well - nothing 390 characters long is ever likely to (he said, philosophically) - but if you, for instance, order the 408 symbols "by strength" with your marvellous statistical analysis, then apply ETOAIN can you "read" it? It ain't coincidence that four of the most common characters are vowels, after all.
I'm wondering how far "off" it is, I suppose. And how far off any collection is and has to be, before plain stats don't help.
Make any sense?

Re: Pivots

PostPosted: Fri Sep 27, 2013 4:25 am
by smithy
Naaaa, forget it. If I go change things out in the 408 solve in your toy or in zkd one at a time, I can get the answer pretty darn rapidly can't I.....
And I know what it's going to be.....
Oops!
Right, time for a coffee.

Re: Pivots

PostPosted: Fri Sep 27, 2013 2:12 pm
by _pi
Here is a way to read the z340 in order to flatten the two 3-character pivots and the "square-IOF" pattern:

routesAndPivots.png

The diagram breaks down the z340 in 3 bands or routes. The arrows indicate the reading order. The reading starts, in each band, from the red arrow. The pivots and patterns are highlighted in green.

Using these routes, 2 repeating trigraphs and 1 repeating tetragraph are created from the original pivots and patterns. However, this destroys the original "FBc" trigraph.

Re: Pivots

PostPosted: Fri Sep 27, 2013 3:06 pm
by doranchak
Very interesting work, pi. I wonder what will happen when we feed the various permutations of that into zkdecrypto.