O.k.

I am going up to 6 nulls and skips right now, should I go higher?

Go up to 8. We still need to confirm a solve on 8+. That may require further optimization of the hill climber first.

We are almost done with up to 8 and very thoroughly. I am impressed at how much you were able to run through smokie. Judging by the PC-cycles scores it seems that we have not fished up anything interesting yet. Why do the period 15 variations score 300 to 500 points higher than the period 19 variations? Is it of any significance? It is in line with previous observations.

https://docs.google.com/spreadsheets/d/ … sp=sharing

There are about 4 to 5 settings that relate to the nulls & skips hill climber that I would like to find optimal values for first before we go any further. That may take about 2 weeks. When that is done I would like to run through a few more test ciphers first also.

In the meantime, there is another matter that I would like to brainstorm/discuss with you smokie.

I did some rough calculations and estimate that so far we have processed about 13 trillion (13.000.000.000.000) AZdecrypt substitution iterations for the nulls & skips test. Every time that when AZdecrypt randomly changes the plaintext and scores it is one such iteration.

There are about 4 to 5 settings that relate to the nulls & skips hill climber that I would like to find optimal values for first before we go any further. That may take about 2 weeks. When that is done I would like to run through a few more test ciphers first also.

In the meantime, there is another matter that I would like to brainstorm/discuss with you smokie.

O.k. what is it?

I am still wondering whether period 39 is related to period 19. We had this hypothesis that under certain circumstances some period 38 bigrams could shift to period 39. My thoughts about such a shift is that it is improbable. And because of that the circumstances of such an occurrence should be specific. I would like to review this possibility again, look for examples where the stars align, and what the circumstances would need to be. Perhaps I have already figured these out.

Period 19 could be seen as a knight’s chess move in a 17 by 20 grid, move 1 square down and 2 to the right. Period 38 could in that way be seen as 2 squares down and 4 to the right. Period 39 is then 2 squares down and 5 to the right. Suppose that in a 17 by 20 grid the period 38 bigrams would *somehow* line up vertically, so that the first symbols of each bigram would be found in column 1 to 9 and that the second symbol of each bigram would be found in the column 9 to 17. Then could a shift from period 38 to period 39 be achieved by adding a extra column in the middle of the cipher?

As stated, this would require a rather vertical alignment of the period 38 bigrams in a 17 by 20 grid. And is that not exactly what we have in the 340 at period 39? Do not consider specifically that adding a column is what required, see it as a example mechanism.

I decided not to take another look at the period 19 and 39 bigrams for the moment. Will focus on optimizing the nulls & skips solver, I hope to get that done before the end of the month.

I am still wondering whether period 39 is related to period 19. We had this hypothesis that under certain circumstances some period 38 bigrams could shift to period 39. My thoughts about such a shift is that it is improbable. And because of that the circumstances of such an occurrence should be specific. I would like to review this possibility again, look for examples where the stars align, and what the circumstances would need to be. Perhaps I have already figured these out.

Period 19 could be seen as a knight’s chess move in a 17 by 20 grid, move 1 square down and 2 to the right. Period 38 could in that way be seen as 2 squares down and 4 to the right. Period 39 is then 2 squares down and 5 to the right. Suppose that in a 17 by 20 grid the period 38 bigrams would *somehow* line up vertically, so that the first symbols of each bigram would be found in column 1 to 9 and that the second symbol of each bigram would be found in the column 9 to 17. Then could a shift from period 38 to period 39 be achieved by adding a extra column in the middle of the cipher?

As stated, this would require a rather vertical alignment of the period 38 bigrams in a 17 by 20 grid. And is that not exactly what we have in the 340 at period 39? Do not consider specifically that adding a column is what required, see it as a example mechanism.

I worked on something similar to this. A knight’s tour variation, or transposition that looks like knight’s tour when it is done, trying to explain the strange herringbone pattern caused when highlighting the cells that are P16 reading LRBT, and which have the exact same symbols as cells highlighted P19 reading RLTB.

Basically, certain cells would be designated for only P19, and certain cells would be designated only for P16 ( or with another variation P38 or P39 ). Transcribe the message into the cells, and encode. But a large proportion would have to be designated for P19 to have so many repeats, and such a large proportion would probably preclude generation of enough P38 or P39 that you need, and especially for P15 and P29.

Unless, you have two keys of fewer than 63 symbols, one key for P19 and one for P38 or P39. Then you could probably get the repeats for both periods. However, then you would be able to detect that by drafting the message into different shapes and find that only one set of symbols appears in certain columns, and the other set of symbols appear in the other columns. The 340 doesn’t appear that way. The symbols are generally uniform distributed. Of course, you could have two keys, and they could share some symbols, but not all. You could make a message, find a way to detect the two distinct symbol sets by reorganization, and then look at the 340 to see if it is similar. I have done this but to no avail.

Somewhere on my computer is the work, or probably somewhere in this thread LOL. We could revisit that some time in the future if you like.

I am glad that you want to continue pursuing the null skip hypothesis. Route transposition, with some gibberish and / or mistakes, is the simplest explanation for what we have. Largo recently expressed some doubts because there is no solution yet, but it is not at all fully explored, especially considering that only a small handful of nulls or skips make an otherwise correctly untransposed message into a jigsaw puzzle.

I am not surprised that our last week’s experiments turned up nothing. For P19 you would have 17×19 or +/- 323, meaning about 17 nulls. For P15 you would have 22×15, or about 330, meaning about 10 nulls. We have only gone to 8. My hypothesis is that he transposed the plaintext, but decided on a final 340. He added nulls, somewhere, as filler, and perhaps made some skip mistakes. I would like to pursue some obvious first options, like the signature, and certain symbols, like the regional bias symbols. Combine that approach with the null skip program, in a lot of different ways, starting with the easiest and working up. See if we get lucky. I figure that if this is correct, maybe we could have a partial solve by the end of the year.

I can wait until you fine tune the program, if you want, so we don’t have loose ends to go back to, such as the un-worked parts of the spreadsheet. Or we can take it another similar direction if you want. I would like to stay with variations of the general hypothesis for a while so that we can say that it has been thoroughly explored.

I have been working a little bit on the 1,953 pairs of symbols, only 7 of which when deleted cause a P19 increase. Most of them include the regional bias symbols, and a couple of them include the darkened triangle and the A in the ZODAIK signature. I made a spreadsheet that makes P20 messages and checks for similar combinations, but right now not enough work done except that for smaller P20 spikes, there are a lot of combinations, and for taller P20 spikes there are fewer combinations, similar to the 340. Which makes sense.

On the left are the symbols, when paired with another symbol also highlighted, and deleted, increase P19. On the right, regional bias symbols at five rows.

Left
H
V
backward K
W
theta
darkened triangle
A

Right
H
P
W
theta
circle filled in on the right side

Some are the same, and some are in the signature, but not regional bias.

Hey,

I worked on something similar to this. A knight’s tour variation, or transposition that looks like knight’s tour when it is done

One of my last implementations before stopping working on z340 was the knights move. At that time I had tested different variations, for example different starting positions. The source code was anything but optimal and maybe a little naive. I had written all created transpositions in a batch file for AZDecrypt, but received no noticeable results. So that these experiments were not in vain, here are parts of the source code (written in C#). These are not executable without all the rest, but should show what I tried at that time. The idea based on the magic square from the FBI-Files. The rule to create such is shown at the following link: https://pavlopoulos.wordpress.com/2010/ … crete-art/ (Scroll down to the end of the page).

Some simple experiments

int[,] matrix = Helper.CreateKnightsMoveMatrix(17, 20, 0, 0);
StreamWriter streamWriter = new StreamWriter("Generated Ciphers/Analyzing knights move.txt");

streamWriter.WriteLine("results_sub_directory=knightsmove");
streamWriter.WriteLine();

int highestBigramCount = 0;
int fileIndex = 1;

for (int y=0; y<20; y++)
{
	for (int x=0; x<17; x++)
	{
		Snippet transposedSnippet = new Snippet(cipherOriginal340);
		transposedSnippet.Mirror();

		int[,] matrix = Helper.CreateKnightsMoveMatrix(17, 20, x, y, true);

		Snippet knightsMoveSnippet = transposedSnippet.UntransposeByMatrix(matrix);

		knightsMoveSnippet.WriteToTextFile(fileIndex.ToString(), streamWriter);
		streamWriter.WriteLine();
		fileIndex++;
		
		int bigramCount = 0;

		knightsMoveSnippet.GetRepeatedNgrams(2, ref bigramCount);
		
		highestBigramCount = Math.Max(highestBigramCount, bigramCount);
	}
}

streamWriter.Close();

Console.WriteLine("Highest Bigram Count: " + highestBigramCount);

Create Knights Move Matrix

#region Methods
// ------------------------------------------------------------------------------------------------------------------
public int[,] CreateKnightsMoveMatrix(int width, int height, int startX, int startY, bool muhammadMode = false)
{
	// TODO: Way too complicated...refactor!
	this.width = width;
	this.height = height;

	rect = new int[width, height];

	int currentX = startX;
	int currentY = startY;

	int correctionXStep = 2;
	int correctionYStep = 2;

	if (muhammadMode)
	{
		correctionXStep = 4;
		correctionYStep = 1;
	}

	int length = width * height;

	for (int i = 0; i < length; i++)
	{
		if (rect[currentX, currentY] != 0)
		{
			currentX -= correctionXStep;

			if (currentX < 0)
				currentX += width;

			currentY += correctionYStep;

			if (currentY >= height)
				currentY -= height;
		}

		rect[currentX, currentY] = i + 1;

		currentX += 2;
		currentY -= 1;

		if (currentX >= width)
			currentX -= width;

		if (currentY < 0)
			currentY += height;
	}
	
	return rect;
}

especially considering that only a small handful of nulls or skips make an otherwise correctly untransposed message into a jigsaw puzzle.

Indeed! I remember once implementing tests in which I "injected" symbols at different positions and then performed the usual tranpositions. The same again with inserting longer sequences instead of single symbols. This should simulate that symbols were forgotten at some point. I did the same thing in a second test, but I removed symbols because they might have been written twice by mistake. My program created some hundreds of thousands of variations, but even this was unfortunately without result
It’s a pity that I didn’t rely on a public repository and open source like f.reichmann right from the start. Then I would surely have programmed cleaner and could now publish my work

Translated with http://www.DeepL.com/Translator

I can wait until you fine tune the program, if you want, so we don’t have loose ends to go back to, such as the un-worked parts of the spreadsheet. Or we can take it another similar direction if you want. I would like to stay with variations of the general hypothesis for a while so that we can say that it has been thoroughly explored.

Yes, we wait for tuning of 4 to 5 variables related to the hill climber.

I am not surprised that our last week’s experiments turned up nothing. For P19 you would have 17×19 or +/- 323, meaning about 17 nulls. For P15 you would have 22×15, or about 330, meaning about 10 nulls. We have only gone to 8. My hypothesis is that he transposed the plaintext, but decided on a final 340. He added nulls, somewhere, as filler, and perhaps made some skip mistakes. I would like to pursue some obvious first options, like the signature, and certain symbols, like the regional bias symbols. Combine that approach with the null skip program, in a lot of different ways, starting with the easiest and working up. See if we get lucky. I figure that if this is correct, maybe we could have a partial solve by the end of the year.

You say possibly up to 17 nulls, do you think such ciphers would still produce clear p19 bigram peaks? I am okay with exploring some of your options.

Largo and I corresponded briefly about the magic square construction method/reading rule found in the FBI files some time ago. Largo dug up some information that I was unable to find.

This magic square construction method – I stress: not to be confused with the knight’s tour – is to this day still relatively unknown and was first discovered by the African Muhammad ibn Muhammad in 1732. Here is a book from Watkins that seems to have some good information about Muhammad and his construction method: https://books.google.be/books/about/Acr … edir_esc=y

Given the obscurity of this construction method it is not unlikely that the author of the 21 by 21 magic square in the Zodiac FBI was not aware of it and invented it on the spot.

There is some correlation/coincidence with the 340 and this construction method that I noted in: viewtopic.php?f=81&t=3591

This coincidence maxes out in the most bizarre way after reading entries from Gareth’s Penn book Times 17. First of all, Gareth Penn did not author the 21 by 21 magic square in the Zodiac FBI files. The story goes that Mr. Penn started to receive one ring phone calls at some point. He carefully noted these on his calendar grid. From these calendar entries he was somehow able to deduct a 17 by 17 magic square and the knight’s move, I kid you not. I would very much like to speak to Mr. Penn, that may be able to clear my mind about this issue a bit.

Small compilation from Gareth Penn’s book Times 17 relating to the knight’s move:

You say possibly up to 17 nulls, do you think such ciphers would still produce clear p19 bigram peaks? I am okay with exploring some of your options.

You could make clear spikes if the nulls are confined to one or two smaller regions, leaving a large region unaffected. But more difficult to make the same stats with 63, not as difficult with fewer symbols.

EDIT: Here is one, P20, nulls in same positions as W, theta, and ZODAIK signature. Wasn’t too difficult to make, but not quite as many repeats.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 10 20 8 20 5 21 22 23 24 25 26 27 28 29 23
30 6 31 3 32 11 16 13 33 23 34 23 35 36 29 1 17
37 5 29 18 38 39 2 40 41 42 3 31 43 44 7 45 46
12 35 41 3 14 47 10 35 29 48 15 21 13 29 28 1 29
12 49 50 31 36 32 41 51 10 9 19 6 29 12 34 32 10
20 8 52 17 22 53 51 54 21 44 13 18 29 29 46 12 10
55 2 41 28 25 14 41 36 3 35 38 42 46 22 7 56 32
1 57 5 58 59 16 6 26 40 32 13 29 17 29 15 9 60
12 46 46 25 35 21 39 34 44 19 8 24 46 9 25 51 7
17 55 28 2 27 29 59 29 29 44 47 46 61 10 34 42 62
39 9 4 8 57 49 22 14 17 54 8 43 21 26 15 13 28
29 19 57 44 16 35 55 33 7 32 61 62 36 4 31 12 30
14 53 5 6 18 33 29 44 51 46 36 10 46 13 24 13 38
29 26 46 59 41 3 5 10 44 17 21 1 34 46 55 42 9
49 56 29 25 52 20 6 28 54 27 34 46 40 2 16 31 22
37 36 60 8 4 56 61 10 9 1 20 32 23 50 1 23 19
33 38 23 23 49 41 23 4 39 17 14 35 31 21 18 23 40
13 25 62 2 23 54 41 40 26 16 29 33 45 39 60 7 54
7 29 2 15 54 37 58 59 43 23 23 23 23 23 23 33 39

I was very ill with food poisoning or something for a couple of days. Feeling alive again. I left the program running and came back to only 37 restarts, maybe it started over after 1000, or the computer re-booted itself or something. Working again on the last entry.

You could make clear spikes if the nulls are confined to one or two smaller regions, leaving a large region unaffected. But more difficult to make the same stats with 63, not as difficult with fewer symbols.

Okay. The last row has 23 23 23 23 23, coincidence?

There is only one symbol that is a null, 23, and it appears in the same places that the signature and W and theta regional bias symbols appear. I don’t necessarily want to start with that, only the signature and a few symbols around it.

There is only one symbol that is a null, 23, and it appears in the same places that the signature and W and theta regional bias symbols appear. I don’t necessarily want to start with that, only the signature and a few symbols around it.

Sure.

Partial solve smokie 5/5:

Score: 22398 Ioc: 0.06665
Ngrams: 702 PC-cycles: 2652

Period(20) Nulls(47,55,293,317,320), Skips(95,136,192,273,321)

BEUSEEMEDSPECIALL
YGOODTHATNIGHTFOR
IWASVERYTIRESHOWL
ONGIHADBEENASLEEP
ICOULDNOTTELLBUTS
OMUTIMEINTHENIGHT
IWASAWARENEDBYSOU
NDSOUTSISEMYTENTA
SOFSOMEONEORSOMET
HINGWALKINGABOUTA
TFIRSTITHOUGHTITW
ASUNEOFTHEMENEUTP
REOENTLYDECIDMUIT
WASNNTANDEECANDVE
RYWIOEDWAREITHOUG
HTABOUATHEBEARTUI
LBUTSTDNOTQUITREL
IEVEITWASTHEBERMI
THEIRRESENTLYODET
HINGSHOOKTHR

Yes and I can tell that it is a partial solve without looking at the score. Getting close to P15 territory for sure. What settings are you testing? Any new developments with the algorithm?