Symmetry and something interesting

[doranchak Profile Website]

Here is a perfect example of "cipher solving" logic at work:

http://www.youtube.com/watch?v=BgdV1IVkk8E&feature=player_detailpage#t=106s

[Jazzerman Profile]

In an effort to try and get this back on track...

Doranchak, does your new additions to your cipher solving program show the likelihood of the following type of symmetry occuring on a repetitive basis?

340symm.JPG [ 80.88 KiB | Viewed 226 times ]

I haven't had much time recently to see if the type of symmetry I've noted here is prevalent in other parts of the 340 or the 408. I ask, because it seems rather odd that symbols appear doubled in the same positions on either half when the 340 is "folded" along the proverbial "mid-point" where the two "-" symbols are. Could there be something to this, or once again, is this rather odd form of symmetry fairly common in other ciphers?

[Wrench Profile]

Wow, that's interesting (though in case you don't know I'm easily impressed).

I'm not sure if I'm more impressed in what you've found, or that you actually found it. That took some lookin'.

The folding in half theory is not new of course, but this sure makes one want to take another look.

[Jazzerman Profile]

Wrench, I'm easily impressed as well, which may explain why I've noticed these things...I actually took the "folding" idea and just applied it in a different form when I first noticed some of they symmetry. So far, it seems most of the symmetry in the 340 cipher is fairly common in the 408 as well (as Doranchak and others have proven), but after finding this more intricate symmetry I've wondered about how common it might be as well. I'm in no way saying it's a valid approach, but it's rather interesting nonetheless.

[Wrench Profile]

My first thought was he wrote the same thing twice, once from top to middle, once from r19 to middle, using a different key. However, something else would have to be included since we tried to solve it in halves already.

I'm going to wait for Dorachak's take before proceeding...

[doranchak Profile Website]

CryptoScope doesn't search for these kinds of patterns yet, but I think they are quite common. Let's do some more math. Asleep yet?

As shown here, the probability of a given pair of positions having the exact same symbol is 0.02228. Thus, if we select four positions, the probability of forming TWO pairs of matches is 0.02228*0.02228 = 0.0004963984.

How many trials are we performing? Well, in the top half, we are looking at all the possible pairs that can mirror below in the second half. There are 9 rows and 17 columns, for a total of 153 positions. A pair can be formed by position 1 and any of positions 2 through 153. Similarly, a pair can be formed by position 2 and any of positions 3 through 153. And so on and so forth.

This works out to 152+151+150+...+1 = 11628 possible trials.

Therefore, we expect to find 0.0004963984 * 11628 = 5.77 mirrored pairs. Since the expected value is not significantly different from the actual value, we can conclude that these kinds of matches are not unusual.

[Jazzerman Profile]

Wrench, if you look back to the first page of this thread (actually my first post) I took Row 20 and transposed the symbols to match up with a row of symbols starting on Row 1 as a few of the symbols seemed to match pretty well...just out of pure whimsical thought I guess. Now, let's just say you're on to something when you say the cipher might be mirrored in each half. What if the transposition of several segments of symbols are required as the "key". For instance, what if we can use the ">" and "+" symbols that occur in two seperate locations on each half of the 340 and use them to rearrange the cipher symbols...I guess this might be akin to a cipher within a cipher within a cipher.

I hope this makes sense, it's really hard to express in words exactly what I'm speaking of.

Here is one example:

340plain.jpg [ 80.92 KiB | Viewed 217 times ]

Again, my point is not to try and solve anything, but rather to see if anything I might show can be disproven, that way we can put it aside in the future.

[Jazzerman Profile]

Thanks Doranchak, being a "very, very" right-brained person I'll just take your word for it that the symmetry may as well be common according to some math that I'll never understand. I'm really beginning to believe that the Zodiac just wrote a bunch of gobbletygook in the 340 to keep people like me thinking they see patterns where there aren't any.

[doranchak Profile Website]

My first thought was he wrote the same thing twice, once from top to middle, once from r19 to middle, using a different key. However, something else would have to be included since we tried to solve it in halves already.

Does zkdecrypto correctly solve the individual halves of the various 340-character test ciphers that people have come up with?

If so, then it would have probably solved a normal half of the real 340 if it had one.

If not then there is still hope that one of the halves is still using normal homophonic substitution. The nearly perfect "l*KM" homophone sequence in the top half is compelling evidence that some kind of homophonic substitution is going on.

[Wrench Profile]

Don't know, testing chunks of the 408 now.