Kryptos Solution

Quick post about a possible breach on point of entry in K4. This is what cryptographers look for. It's probably been said before, but for some reason, it never really clicked.

Let's look at K4 again.

?OBKR
UOXOGHULBSOLIFBBWFLRVQQPRNGKSSO
TWTQSJQSSEKZZWATJKLUDIAWINFBNYP
VTTMZFPKWGDKZXTJCDIGKUHUAUEKCAR

One of the things that is often mentioned are the number of double letters.

Here is K4 again with the double letters in red.

?OBKR
UOXOGHULBSOLIFBBWFLRVQQPRNGKSSO
TWTQSJQSSEKZZWATJKLUDIAWINFBNYP
VTTMZFPKWGDKZXTJCDIGKUHUAUEKCAR


There are six pairs. Nothing new here. It's been said plenty of times. We also know that there is a commonality between most of them. Let's calculate their distances from each other. We'll just number them from 1 to 6. So 12 is the distance between pair #1 and pair #2.

12: 7
13: 14
14: 24
15: 28
16: 49

We already see multiples of 7 between pairs #1, #2, #3, #5 and #6.

So five out of the six pairs are on a position that is a multiple 7. So let's write K4 in lines of 7 letters.

?OBKRUO
XOGHULB
SOLIFBB
WFLRVQQ
PRNGKSS
OTWTQSJ
QSSEKZZ
WATJKLU
DIAWINF
BNYPVTT
MZFPKWG
DKZXTJC
DIGKUHU
AUEKCAR


I included the question just to even things out. I don't know if it's actually part of the text or not.

Anyhow, we can clearly see the alignment of the double letters. Most people believe this to be very intriguing. But I don't think I've ever seen a real analysis as to what this means.

Here's the grub. Double letters after a transposition cipher indicate repeats in the original text. Here's an example. Let's take K1 and transpose it with a width of 20.

EDQMMKVFURYDFNUPSVHHLZGLLNTRFRFIEAVVXJJYYYUQQSTTDQMJUKKXYZQRLBD


Look at all those double letters! Most of them are from the repeated five letter segment VJYQT. Others are just from the same letter being encoded by the same key letter at a multiple of 20, twice the key length.

Here is the original transposition.

EDQM
MKVF
URYD
FNU
PSV
HHL
ZGL
LNT
RFR
FIE
AVV
XJJ
YYY
UQQ
STT
DQM
JUK
KXY
ZQR
LBD


Notice the five pair run? The other pairs are important too. These are the same multiple away from each other as the other pairs. So both letters of all the pairs are encrypted with the same letter.

With K1, I used a width of 20, twice the key length. Does K4 indicate a transposition as well? Is K4 double encoded? I think it is. I get an English distribution using a few different tableau's. I know they are not the right key in the tableau because some items don't match up quite right. But my experience tells me that it's just a matter of finding the correct key and modifications to the cipher, if any.

All my instincts tell me that my previous theory is correct. He used a Vigerene type cipher, maybe even converted it to digits somehow to flatten the distribution somewhat and then transposed it. This is why those double letters occur. Double letters after a transposition can indicate that the width of the transposition is a multiple of the key length. Weird thing is that the column width is 7, but that's not what we need to look at. It's the number of rows. It's 14. Ironically, half of that is 7 and that would be our key length. Then again, something like a two or four squares cipher could produce something similar.

Also, the double letters could be left as a clue. It could be a keyed columnar transposition where Sanborn intentionally moved two columns together before transposing them so as to create the double letters. IOW, I'm saying K4 appears to be a Vigenere type cipher (or something that produces repeats in the text) followed by a keyed columnar transposition where the row count (14) is a multiple of the key length (possibly 7) of the original cipher.

Transposing K4 on the opposite diagonal (from top right to bottom left), we get this.


RUCGTFUZJSQBBO
AHJWTNLZSSQBLU
CUTKVIKKQKVFUR
KKXPPWJETGRIHK
EGZFYATSWNLLGB
UIKZNIASTRFOOO
ADDMBDWQOPWSX?


We see the five double letters which are now looking a lot like repeats in a normal classical cipher. At this point, the classical cipher that was used could be almost anything. It looks like a particular word or part of a word is repeated. However, note that if a keyed columnar transposition was used, then the rows can be put in a completely different order. Not only that, but there may be different ways to transpose K4 to achieve the same result.


RUCGTFU
ZJSQBBO
AHJWTNL
ZSSQBLU
CUTKVIK
KQKVFUR
KKXPPWJ
ETGRIHK
EGZFYAT
SWNLLGB
UIKZNIA
STRFOOO
ADDMBDW
QOPWSX?


I think this deserves serious attention. It's exactly what cryptographers look for in breaking a cipher. Only thing now is trying to figure out what the original cipher was. And I think I was right all along. I think it's an END to END cipher. I think K2 talks about the original cipher. I'm also confident that the original cipher uses some kind of coordinate system. Something very visual. Could be Vigenere. But I'm thinking it's perhaps something else with a grid (matrix). Maybe two or four squares. Maybe Nihilist. Maybe bifid. Perhaps even Gronsfeld or variants. That would actually fit in very well with UNDERGRUUND. Could that be code for GRONSFELD?

Scheidt said something about a reflective cipher. A two or four square cipher would fit that notion. Finding the grids would quite the endeavor though. I have such a grid, but haven't gone back to it yet.