4-TEEN Routes
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4-TEEN Routes
by _pi » Sat Oct 08, 2011 9:17 am
Here is a new idea I am proposing on how to approach the Z340. It is subjective for sure but it fits very well, in my opinion, to the structure of the Z340. If nothing more, I hope it will entertain you…
The decryption of the Z408 cipher required a 2-step approach:
1. Combine the 3 ciphers received by different newspapers in a single cipher using the correct order.
2. Decrypt the resulting cipher using a homophonic substitution approach.
At a high level, I hypothesize that the zodiac followed a similar approach with the Z340 as he did with the Z408. However, instead of communicating the Z340 into multiple sub-ciphers that need to be combined together, I believe he pre-combined, out of order, n sub-ciphers into a single resulting cipher. In order to decrypt the Z340, we need to determine how these n sub-ciphers have been fused together and how they need to be rearranged to form a new homophonic substitution cipher.
I think that solving the Z340 will require such a 2-step approach where the 1st step will preprocess the cypher and the 2nd step will apply a homophonic substitution to solve the cipher. I think the reason why the cipher wasn’t solved yet is because that 1st step in the Z340 is substantially more complex than in the Z408.
The pre-decryption approach I am proposing here deals only with this 1st step.
The major hypothesis that I initially make is that the “Halloween Card” sent by the zodiac almost a year after he sent the Z340 contains multiple clues on how to decipher the Z340. Here are the elements from that card that I think are clues and how I subjectively interpret them in the context of the Z340:
1. By fire/By gun/By knife/By rope. I am not interested in the words themselves but their disposition: some words are written from left to right and some words from top to bottom. Let’s say that this means that some portions of the Z340 must be read horizontally and some others vertically.
2. Paradice/Slave. Again, I am not interested in the words themselves but their disposition: they form a “+” sign that separates the 4 “By xxx” structures. The “+” symbol in the Z340 is by far the most frequent symbol and it might be used to find order in the Z340 chaos.
3. 4-TEEN. I initially thought this referred to the then-current alleged victim count since this value would have made sense in the chronological progression of this count in each of his communications. However, the number “14” written in the first skeleton’s hand probably serves that purpose. I think the word “4-TEEN” is meant to draw our attention to the numbers 4 and 14 (and their interrelation) and how they are relevant to solving the Z340.
4. The second skeleton (the one with both feet pointing to the right). The strange positioning of that skeleton’s arms and legs might mean something. More on that later…
Taking the clues #1, #2 and #3 into account, here is my theory on how the Z340 must be pre-processed:
After having spent quite some time trying to determine if drawing these routes was at all possible, I found out that it was indeed possible but that more than 1 solution (although the number of possible solutions seems quite low) could be found even though these route constraints, especially given the Z340 layout, are very limiting.
That’s where clue #4 comes into play. I make the hypothesis that the zodiac placed the arms and legs of the skeleton in such a way that, when overlaying the skeleton on the Z340 cipher, the 4 limbs would point to the 4 “+” signs starting the routes. I believe this yields a unique pre-processing solution, taking into account all the instructions I mentioned above:
340TranspoSolution.gif [ 58.14 KiB | Viewed 576 times ]
Regarding the diagram above, each route is drawn in a different color. A circle marks the start of each route. Each “+” symbol is marked by a little bump in the route. The end of a route is marked by a small square; this also marks the extra remaining symbol for each route.
I believe it is very probable that this is how the zodiac scrambled the Z340 cipher and this is how it should be “read” in order to reconstitute a new cipher that will be solvable using homophonic substitution deciphering strategies.
_pi
Other Notes
The decryption of the Z408 cipher required a 2-step approach:
1. Combine the 3 ciphers received by different newspapers in a single cipher using the correct order.
2. Decrypt the resulting cipher using a homophonic substitution approach.
At a high level, I hypothesize that the zodiac followed a similar approach with the Z340 as he did with the Z408. However, instead of communicating the Z340 into multiple sub-ciphers that need to be combined together, I believe he pre-combined, out of order, n sub-ciphers into a single resulting cipher. In order to decrypt the Z340, we need to determine how these n sub-ciphers have been fused together and how they need to be rearranged to form a new homophonic substitution cipher.
I think that solving the Z340 will require such a 2-step approach where the 1st step will preprocess the cypher and the 2nd step will apply a homophonic substitution to solve the cipher. I think the reason why the cipher wasn’t solved yet is because that 1st step in the Z340 is substantially more complex than in the Z408.
The pre-decryption approach I am proposing here deals only with this 1st step.
The major hypothesis that I initially make is that the “Halloween Card” sent by the zodiac almost a year after he sent the Z340 contains multiple clues on how to decipher the Z340. Here are the elements from that card that I think are clues and how I subjectively interpret them in the context of the Z340:
1. By fire/By gun/By knife/By rope. I am not interested in the words themselves but their disposition: some words are written from left to right and some words from top to bottom. Let’s say that this means that some portions of the Z340 must be read horizontally and some others vertically.
2. Paradice/Slave. Again, I am not interested in the words themselves but their disposition: they form a “+” sign that separates the 4 “By xxx” structures. The “+” symbol in the Z340 is by far the most frequent symbol and it might be used to find order in the Z340 chaos.
3. 4-TEEN. I initially thought this referred to the then-current alleged victim count since this value would have made sense in the chronological progression of this count in each of his communications. However, the number “14” written in the first skeleton’s hand probably serves that purpose. I think the word “4-TEEN” is meant to draw our attention to the numbers 4 and 14 (and their interrelation) and how they are relevant to solving the Z340.
4. The second skeleton (the one with both feet pointing to the right). The strange positioning of that skeleton’s arms and legs might mean something. More on that later…
Taking the clues #1, #2 and #3 into account, here is my theory on how the Z340 must be pre-processed:
- The cipher must be split in 4 parts.
- Each of these 4 parts is a route in the Z340. What this means is that the Z340 is a combination of 4 intertwined route ciphers.
- The “+” symbols are used as milestones in the routes. More specifically, each route must start with a “+” and every 14th symbol thereafter in the route must be a “+”. This means that, for all 4 routes, when reading a route from beginning to end, we would find “+” symbols at 0-index positions 0, 14, 28, 42, etc.
- A route can be “drawn” by moving in the up, down, left and right directions.
- Since there are 24 “+” symbols and each route segment has a length of 14 symbols, these routes should cover, once and only once, 336 symbols.
- I suggest that the remaining 4 symbols will be covered by extending the last segment of each route by 1 symbol.
- Once the routes are drawn on the Z340, they must be read from beginning to end, one after the other. This will create 4 sub-ciphers.
These 4 sub-ciphers should be concatenated (the proper order must be determined) to form the pre-processed cipher.
After having spent quite some time trying to determine if drawing these routes was at all possible, I found out that it was indeed possible but that more than 1 solution (although the number of possible solutions seems quite low) could be found even though these route constraints, especially given the Z340 layout, are very limiting.
That’s where clue #4 comes into play. I make the hypothesis that the zodiac placed the arms and legs of the skeleton in such a way that, when overlaying the skeleton on the Z340 cipher, the 4 limbs would point to the 4 “+” signs starting the routes. I believe this yields a unique pre-processing solution, taking into account all the instructions I mentioned above:
340TranspoSolution.gif [ 58.14 KiB | Viewed 576 times ]
Regarding the diagram above, each route is drawn in a different color. A circle marks the start of each route. Each “+” symbol is marked by a little bump in the route. The end of a route is marked by a small square; this also marks the extra remaining symbol for each route.
I believe it is very probable that this is how the zodiac scrambled the Z340 cipher and this is how it should be “read” in order to reconstitute a new cipher that will be solvable using homophonic substitution deciphering strategies.
_pi
Other Notes
- I have tried to be as precise as possible in using the same scale for both the Z340 and the skeleton. I believe that the image above is faithful to their relative proportions. The Z340 dimensions were already known but I couldn’t find dimensions for the skeleton. I have used 2 independent but corroborating means of calculating the size of the envelope containing the Halloween card: the ratio of the card’s envelope’s dimensions pointed to a standard type of envelope, and the size of the stamp (a stamp of known dimensions) was used to extrapolate the size of the envelope. Where the margin of error lies is in not knowing exactly how tight the card was fitting the envelope. I assumed it was a relatively tight fit with a clearance of about .15 inches (in total) at the top and bottom of the envelope.
- Before applying the skeleton to the solution, 3 of the 4 routes I had originally found were already starting at exactly the same place as where the skeleton is pointing. The 4th route was almost the same but reversed. This gave me a surprising confirmation that the routes and the skeleton were interrelated.
- Once the resulting new cipher is constructed, the "+" symbols will probably act as wild-card symbols. The other possibility is that they were only placed to find the routes and that they now need to be discarded.
- traveller1st
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Re: 4-TEEN Routes
by traveller1st » Sat Oct 08, 2011 11:50 am
I'm too busy sculpting fat blokes to take it all in lol. I've half wondered if he intended the elements of certain cards to be used in overlay fashion but then I had about the accuracy of that. Like the idea of applying a similar construction approach as the 408 I think we've all considered that at one time or another.
One thing I will say is your skeleton to cipher ratio is wrong. It's been truncated and rotated to fit. I haven't scaled it 1 to 1 but I've scaled it roughly according to your feet to the double +'s and haven't rotated it and its on a hi-res of the cipher and neither truncated. The hands don't line up to the +'s. They do line up to the zodiac symbols tho.
Hope that's some help.
Trav.
Skeleton-on-340.jpg [ 102.06 KiB | Viewed 563 times ]
skel-340-axis.jpg [ 100.14 KiB | Viewed 560 times ]
EDIT: added a second file. Thought since I had the graphic up I'd mess around with rotating and scaling it. Now I have it on the 340 and prob means nothing. The reason I'm posting it is cause I've just realised it has an axis I hadn't noticed before - from top to bottom its straight and lines up with itself - thought that was interesting but don't know why lol. Also the through body axis lines up with the diagonals in the cipher grid - again don't know if that means squat. I've seen that 'hang it on the map' thingy before where there was an invisible line that the hands hung off but it's not an axis - tried it.
One thing I will say is your skeleton to cipher ratio is wrong. It's been truncated and rotated to fit. I haven't scaled it 1 to 1 but I've scaled it roughly according to your feet to the double +'s and haven't rotated it and its on a hi-res of the cipher and neither truncated. The hands don't line up to the +'s. They do line up to the zodiac symbols tho.
Hope that's some help.
Trav.
Skeleton-on-340.jpg [ 102.06 KiB | Viewed 563 times ]
skel-340-axis.jpg [ 100.14 KiB | Viewed 560 times ]
EDIT: added a second file. Thought since I had the graphic up I'd mess around with rotating and scaling it. Now I have it on the 340 and prob means nothing. The reason I'm posting it is cause I've just realised it has an axis I hadn't noticed before - from top to bottom its straight and lines up with itself - thought that was interesting but don't know why lol. Also the through body axis lines up with the diagonals in the cipher grid - again don't know if that means squat. I've seen that 'hang it on the map' thingy before where there was an invisible line that the hands hung off but it's not an axis - tried it.
Last edited by traveller1st on Sat Oct 08, 2011 12:14 pm, edited 1 time in total.
"I don’t know Chief, he’s very smart or very dumb."
Re: 4-TEEN Routes
by _pi » Sat Oct 08, 2011 12:10 pm
traveller1st wrote:One thing I will say is your skeleton to cipher ratio is wrong. It's been truncated and rotated to fit. I haven't scaled it 1 to 1 but I've scaled it roughly according to your feet to the double +'s and haven't rotated it and its on a hi-res of the cipher and neither truncated. The hands don't line up to the +'s. They do line up to the zodiac symbols tho.
I have rotated the skeleton 10 degrees counterclockwise to align it. Could you share the actual dimensions you have used for the skeleton to put it in relation to the Z340?
Before the rotation and the proper scaling, I had also noticed the alignment of the hands to the zodiac symbols.
Re: 4-TEEN Routes
by Zsearcher » Sat Oct 08, 2011 12:25 pm
Underline pi,
I like your "think out of the box" approach but you need to stay away from this:
We have heard that a hundred times but in never really turns out to be so.
If you present your idea as a possibility and one which you want us to analyze, and work out with you to see if it has merit, you will probably get a good response.
If you say you almost definitely have the correct solution when there are at least twenty very subjective parts of said solution, you won't get a good response.
Trying to help you out here.
Zs
I like your "think out of the box" approach but you need to stay away from this:
_pi wrote:I believe it is very probable that this is how the zodiac scrambled the Z340 cipher and this is how it should be “read” in order to reconstitute a new cipher that will be solvable using homophonic substitution deciphering strategies.
We have heard that a hundred times but in never really turns out to be so.
If you present your idea as a possibility and one which you want us to analyze, and work out with you to see if it has merit, you will probably get a good response.
If you say you almost definitely have the correct solution when there are at least twenty very subjective parts of said solution, you won't get a good response.
Trying to help you out here.
Zs
Re: 4-TEEN Routes
by _pi » Sat Oct 08, 2011 12:45 pm
Zsearcher wrote:I like your "think out of the box" approach but you need to stay away from this:
I believe it is very probable that this is how the zodiac scrambled the Z340 cipher and this is how it should be “read” in order to reconstitute a new cipher that will be solvable using homophonic substitution deciphering strategies.
Hi Zsearcher. You are right, this sentence is too assertive. In presenting this approach, I mentioned it was very subjective and throughout I have tried to use the terms "hypothesis/I think/I believe/etc." to underline the fact that this is a hypothesis without any proof outside of the seemingly self-corroborating aspects of the solution. I understand now that I wasn't clear enough.
I understand this is a very subjective approach but I tried to keep within the realm of logic and reason.
I apologize that I was too assertive or made it sound as if this approach was the only approach. I guess that when I work on an idea, I eventually get somewhat attached to it and perhaps when I arrived at the end of my post, I sounded a bit too much convinced for my own good. I didn't mean any disrespect to the members here and to all the work that has already been done on this topic.
Re: 4-TEEN Routes
by Zsearcher » Sat Oct 08, 2011 12:50 pm
No problem _pi.
Almost everyone that works on a solution starts convincing themselves it is correct. If you can detach yourself from your work and look at it objectively as we will do, it will make everything go smoother.
You acknowledged your over-enthusastic phrasing. That is a something most people do not do, so you already get a few bonus points for that.
I'm interested in looking at this when I have some time.
Very interesting stuff.
Almost everyone that works on a solution starts convincing themselves it is correct. If you can detach yourself from your work and look at it objectively as we will do, it will make everything go smoother.
You acknowledged your over-enthusastic phrasing. That is a something most people do not do, so you already get a few bonus points for that.
I'm interested in looking at this when I have some time.
Very interesting stuff.
- traveller1st
-
- Posts: 573
- Joined: Mon May 02, 2011 5:30 pm
- Location: Northern Ireland
Re: 4-TEEN Routes
by traveller1st » Sat Oct 08, 2011 12:54 pm
_pi wrote:I have rotated the skeleton 10 degrees counterclockwise to align it. Could you share the actual dimensions you have used for the skeleton to put it in relation to the Z340?
Before the rotation and the proper scaling, I had also noticed the alignment of the hands to the zodiac symbols.
I didn't use exact dimensions. I just took it from the card and stuck it in there then scaled it roughly to get it close to yours by eye. So it's not in scale to the 340 just in proportion. 167 w x 195 h in mm is the size the skeleton came in at from the card before I scaled it
"I don’t know Chief, he’s very smart or very dumb."
Re: 4-TEEN Routes
by doranchak » Sat Oct 08, 2011 1:59 pm
If Zodiac did use this kind of system, then if the correct routes are discovered and unravelled, the resulting homophonic cipher might show larger numbers of repeated n-grams and sequential homophones. If you transcribe your routed cipher to plaintext, you could feed it into CryptoScope and investigate the statistics to see if the result resembles "normal" homophonic ciphers.
Discovering all possible routes seems like a variation of Hamiltonian path searches. The cipher symbols would be the nodes of the graph, and the problem is to find a tour of every node where each node is visited only once. Then you'd impose your extra constraints (the +'s in the right spots, the length of the tour, the fixed start/end nodes, and the generation of exactly 4 routes).
It does seem like there'd be a small number of possible paths, but it's hard to say because even in the general unconstrained problem it seems hard to estimate the total number of Hamiltonian paths without doing a laborious exhaustive search.
Long story short: Man, this would be challenging to implement in software. :)
But I think this kind of meandering route is very unconventional in codemaking. Traditional route ciphers tend to use simpler pattern rules in their construction. Examples: "every other letter going backwards to the front and then every other letter going forwards to the end again", "clockwise spiral", "rail fence", etc. If he really did use such a convoluted scheme of meandering routes, he truly did not want anyone to ever stumble upon the solution.
Discovering all possible routes seems like a variation of Hamiltonian path searches. The cipher symbols would be the nodes of the graph, and the problem is to find a tour of every node where each node is visited only once. Then you'd impose your extra constraints (the +'s in the right spots, the length of the tour, the fixed start/end nodes, and the generation of exactly 4 routes).
It does seem like there'd be a small number of possible paths, but it's hard to say because even in the general unconstrained problem it seems hard to estimate the total number of Hamiltonian paths without doing a laborious exhaustive search.
Long story short: Man, this would be challenging to implement in software. :)
But I think this kind of meandering route is very unconventional in codemaking. Traditional route ciphers tend to use simpler pattern rules in their construction. Examples: "every other letter going backwards to the front and then every other letter going forwards to the end again", "clockwise spiral", "rail fence", etc. If he really did use such a convoluted scheme of meandering routes, he truly did not want anyone to ever stumble upon the solution.
Re: 4-TEEN Routes
by _pi » Sun Oct 09, 2011 8:27 pm
Hi doranchak. Thanks a lot for taking the time to have a look at this idea. I took your webtoy's transcription of the Z340 and applied it to this approach. I did start to look at some statistics using your web tools and will spend some time on that (mostly figuring out all the stats your tools provide).
For anybody that might be interested, here is the textual version of the approach I presented (For now, I have concatenated the routes in the following arbitrary order: blue-red-green-yellow):
+5#(G<d-zlR/5t+^J
R2FBcy<FB6A+@L4y-
K9|Lz.>F+&42D(/kK
2JHzR+#*Kf)d2GTL1
.<L+Op35FPkGVzYN_
+UcXCd*|d-2O#Z+j%
;OjtlFqfbVU+M2JK^
R8p_9Mp7+z^l8*VGW
WD%ZU+M(Bc:ypSBNH
Ep+R>pl#O^VPk|Y()
+RFOKB&MTbp7pO+D5
*|E|J#yRlc<+U2z69
SNFGly|R+|>MDHNpk
7<WdW+LCz16WcC<PB
_O+FSYOHlWB|(-Cc+
;K|*/TBA8OZzSt+2L
p))GqMfUZ5-+8;t4V
cV>.FBc(+.M4BYT5b
EC4|N+5294:f^*1XB
cc+Fk)T.3zBK(Op^.
For anybody that might be interested, here is the textual version of the approach I presented (For now, I have concatenated the routes in the following arbitrary order: blue-red-green-yellow):
+5#(G<d-zlR/5t+^J
R2FBcy<FB6A+@L4y-
K9|Lz.>F+&42D(/kK
2JHzR+#*Kf)d2GTL1
.<L+Op35FPkGVzYN_
+UcXCd*|d-2O#Z+j%
;OjtlFqfbVU+M2JK^
R8p_9Mp7+z^l8*VGW
WD%ZU+M(Bc:ypSBNH
Ep+R>pl#O^VPk|Y()
+RFOKB&MTbp7pO+D5
*|E|J#yRlc<+U2z69
SNFGly|R+|>MDHNpk
7<WdW+LCz16WcC<PB
_O+FSYOHlWB|(-Cc+
;K|*/TBA8OZzSt+2L
p))GqMfUZ5-+8;t4V
cV>.FBc(+.M4BYT5b
EC4|N+5294:f^*1XB
cc+Fk)T.3zBK(Op^.
Re: 4-TEEN Routes
by _pi » Mon Oct 10, 2011 12:31 am
The arbitrary route ordering I posted above yields an IoC average by row of 0.012.
Out of curiosity, I have optimized the ordering of the 4 routes on that specific metric (there are 4! possibilities). The highest value I found was 0.015 using the following ordering of routes: Green-Red-Blue-Yellow. The associated textual representation of that cipher is:
+RFOKB&MTbp7pO+D5
*|E|J#yRlc<+U2z69
SNFGly|R+|>MDHNpk
7<WdW+LCz16WcC<PB
_O+FSYOHlWB|(-Cc+
;K|*/TBA8OZzSt+Op
35FPkGVzYN_+UcXCd
*|d-2O#Z+j%;OjtlF
qfbVU+M2JK^R8p_9M
p7+z^l8*VGWWD%ZU+
M(Bc:ypSBNHEp+R>p
l#O^VPk|Y()+5#(G<
d-zlR/5t+^JR2FBcy
<FB6A+@L4y-K9|Lz.
>F+&42D(/kK2JHzR+
#*Kf)d2GTL1.<L+2L
p))GqMfUZ5-+8;t4V
cV>.FBc(+.M4BYT5b
EC4|N+5294:f^*1XB
cc+Fk)T.3zBK(Op^.
Out of curiosity, I have optimized the ordering of the 4 routes on that specific metric (there are 4! possibilities). The highest value I found was 0.015 using the following ordering of routes: Green-Red-Blue-Yellow. The associated textual representation of that cipher is:
+RFOKB&MTbp7pO+D5
*|E|J#yRlc<+U2z69
SNFGly|R+|>MDHNpk
7<WdW+LCz16WcC<PB
_O+FSYOHlWB|(-Cc+
;K|*/TBA8OZzSt+Op
35FPkGVzYN_+UcXCd
*|d-2O#Z+j%;OjtlF
qfbVU+M2JK^R8p_9M
p7+z^l8*VGWWD%ZU+
M(Bc:ypSBNHEp+R>p
l#O^VPk|Y()+5#(G<
d-zlR/5t+^JR2FBcy
<FB6A+@L4y-K9|Lz.
>F+&42D(/kK2JHzR+
#*Kf)d2GTL1.<L+2L
p))GqMfUZ5-+8;t4V
cV>.FBc(+.M4BYT5b
EC4|N+5294:f^*1XB
cc+Fk)T.3zBK(Op^.
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