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I like the pivots and am always looking to see how they can fit into a structure.. Pity they don't in this case..

Mr lowe wrote:I like the pivots and am always looking to see how they can fit into a structure.. Pity they don't in this case..

They don't, but I still like the connection between the pattern and one pivot's corner symbol. And the "move 3 down, 3 across" link. Not sure if it means anything, though! When I get time, I will try to run all the different variations of your scheme, to see if any other patterns pop out. Then I'll try to feed them into azdecrypt.

Mr lowe wrote:Am I right in saying that a period 30 columnar scy brings together period 19s in the rows..?

I'm not sure. It might be bringing some but not all of them, because when I count the number of repeating bigrams in the result, it comes out to 21. Original Z340 has 25 repeats, but applying the normal (non-columnar) scytale of period 19 yields 37 repeats.

Ok .. Gunna crash and burn ..hope I don't dream of pivots..
Cheers

doranchak wrote:Written to a grid of width 30, to better show the effect of scytale of diameter (period) 30:

mr-lowe-scytale-pattern-3.png

(Update: I hope someone can verify my steps, because I'm worried that I made some mistake somewhere.)

Looks o.k. to me. I like how the H and + symbols show up in the upper left and lower right corners of the 12 row part of the message, defining the offset.

There are:

Four of the H symbols;
Six of the diagonal box symbols;
Ten of the F symbols; and
24 of the + symbols.

It is like two period 57 unigram repeats that create two period 94 bigram repeats, boxed in with two period 37 repeats, all symmetrical. That is very strange.

smokie treats wrote:Looks o.k. to me. I like how the H and + symbols show up in the upper left and lower right corners of the 12 row part of the message, defining the offset.

Are you referring to these:

No, I meant these:

Oh! Yes, the symmetry there is intriguing. And the symbols there in the middle line up with a period of 57, which is a multiple of 19, for whatever that's worth.

OK, I finished a quick shuffle test. The test does these steps:

1) Shuffle the Z340 randomly
2) Look for "Mr Lowe patterns" and count them by length

Patterns are only sought from left to right in the shuffled cipher texts. All positions are considered, not just the first.

The steps are repeated 1,000,000 times.

In Mr Lowe's transposition, his pattern has a length of 8. Among the 1,000,000 shuffles, only 74 of them had a Mr Lowe pattern of length 8. A single occurrence of the pattern of length 8 corresponds to a sigma of 116.25 (or put another way, the observation of a pattern of length 8 is 116.25 standard deviations from the expected value for random cipher texts).

That's about a 1 in 13514 chance. Now, the other thing you have to consider is the pattern can be sought for among many different orientations and reading directions. This should have the effect of increasing the probability of finding it, especially if you include many variations of scytale, grid widths, positions in the cipher, etc. But each variation is not purely random, so it's hard to say what effect it would have on the real probability.

your work is awesome doranchak ..Thanks for taking the time... trouble is for me I don't understand if what you put up is good bad or indifferent.
doranchak can you run it through a solver in all directions to see if anything pops up when you get a moment.