Kryptos Solution

At one point, I was going to say that my recent discovery was a red herring. I was about to post and say as much when I saw something that made me rethink everything. The reason I thought it was a red herring is because I saw one of the clues as indicating a specific cipher for K4. All this time, I thought this clue was indicating a different cipher (which I did use at some point with K4). But this different cipher just started to "click". Pieces started falling in place. So I thought the previous discovery was just a coincidence. That is, until I started looking further into the details.

Take a look at D^YAH^R. The real one.

Here is the relevant section taken from Jim Gillogly's site.



Notice something odd? Something subtle? Look at the spacing between characters! It's not D^YAH^R, but rather D^{Y A} H^R.

Why is this important? Because I now have a plan of attack for K4. If this ends up being true, LOTS of people are going to be kicking themselves.

I can now say that if I had a supercomputer, I could probably break K4 by brute force (if the cipher is correct). But I don't have a supercomputer. So I'm instead gonna look for clues on an alternate entry into the plaintext. I have at least three leads. My only worry right now is if it's been super-encoded. If that's true, then I'll have to keep looking. But I'm now REALLY doubtful that there are multiple encoding schemes at play.

What I can say as well is that my new discovery may be telling me more than I'm currently seeing. The Fibonacci theory from earlier also plays a big part. I'll keep working on this and report my results when I'm done.

Update: After looking at it some more, a few of my leads have dissipated. Only one lead remains. But I still think I have the correct cipher. If I can find the key, then I'm good.

I remember how some people mentioned that the misspelled words in Kryptos form a Fibonacci sequence.


IQLUSION
GRUUND
DESPARATLY
UNDERGRUUND


2,3,5,8

While we can find plenty of misspelling in the clues for positions 2 and 3, there is only one word that is misspelled in the fifth position. Same thing for the eighth position. Those words are DESPARATLY and UNDERGRUUND respectively. Even the other positions have multiple candidates. DIGETAL has a misspelling in the fourth character and I mentioned how I believed RETNNA was a misspelling of RETINA. So I'm thinking the Fibonacci sequence is meant to stand out. It's a clue that should strike us as odd.

How does this relate to D^YAH^R? I noticed a Fibonacci sequence here too, but backwards. If we take the whole sequence from the beginning (or rather the END), we get END^YAH^R. Let's reverse it.

^RH^AYDNE

Now do you see the pattern? The R is 1 character. H is 1 character. AY is 2. DNE is 3.

1,1,2,3

That's the true beginning of a Fibonacci sequence (unless you want to start at 0).

1+1=2
2+1=3

However, we can't continue since we're at the END. This is when I saw on wikipedia that the Fibonacci sequence can actually start with negative numbers. Let's put the original sequence back in order.

END^YAH^R

3, 2, 1, 1

Here's the clever part. What if the raised letters are there just to differentiate from the negative numbers at the beginning of the sequence? Like so.

-3, 2, -1, 1

(-3)+2 = -1
2+(-1) = 1

Continuing on...

(-1)+1 = 0
1+0 = 1
0+1 = 1
1+1 = 2
1+2 = 3
2+3 = 5
3+5 = 8

And we have our regular Fibonacci sequence. It would start at the very next character after D^YAH^R. Taking K3 and extracting groups containing as many letters as each item in the Fibonacci sequence, you get this.

END
YA
H
R
- (0)
O
H
NL
SRH
EOCPT
EOIBIDYS
...

I won't list the whole thing. The groups get quite large rather quickly. Extracting the first letter of each group, we get the following.

EYHROHNSEEHLETTAZ

The beginning doesn't make much sense. But the last part says SEE H LETTAZ. H is the 8^th letter. Could mean SEE 8 LETTERS using A-Z normal alphabet. Perhaps an indication to use the surrounding tableau alphabet in some fashion. Remember that this is a part of the tableau that has never been used (unless one accepts that it's only there as a clue for the straddling checkerboard).

What of the earlier letters in the sequence? EYH almost looks like EYE or I. Could it be the proverbial candle? The letter H is also specifically pointed out. Maybe this is the clue meant by SEE H LETTAZ. In any case, we get EYRON or rather IRON when we remove the H's. This is element 26, a link to AZ which has 26 letters. Is there something in the sculpture made of iron? The lodestone made of Magnetite. Magnetite has Fe₃O₄. So it has three Iron and four Oxygen atoms in each molecule. This could be a link to the compass rose since Magnetite was used in early compasses.

I just checked wikipedia and it says that you can also write Magnetite as FeO·Fe₂O₃. Could be a coincidence, but look at the amount of atoms. 1, 1, 2, 3. That's a Fibonacci sequence.

There is one last thing to note about these letters. The last Z is found within K4. In fact, the group begins with a double Z. There are 51 letters remaining in the last group when we reach the end of K4. Not sure if that means anything. What's odd about it is that I did not count the '?' as part of the previous group. If I include it as part of the ciphertext, then the last letter is still Z because of the double letters. However, this time there are only 50 characters left. A nice round number.

If we do have a reference to the lodestone, then we know it sits atop the word POSITION (covering part of the S). The full Morse code reads T IS YOUR POSITION. T is the 20^th letter. 20 letters from the Z is a T leaving 30 letters at the end of K4. And there are indeed 30 letters in the AZ alphabet in the tableau.

Actually, there's one more thing I noticed just now. The characters that begin the official positive Fibonacci sequence after DYAHR are OHN representing numbers 1, 1 and 2. Just before the '?' in K4, we have OHW. The W is different, but OH is identical. Could this be a clue that K4 begins at OHW instead of OBKR? If so, this would make exactly 100 characters. The Z could indicate how K4 is actually split in two parts of 50 characters each that are perhaps meant to be put back together somehow.

There's a new Kryptos wiki up. I hope you join in and update it. I've included a recap of my theory under my account there. This is probably the most concise and easy to follow recap ever. It explains what my theory is based upon and how all the other clues fit in.

Today, I was trying something just for the fun of it. I was wondering if there was a way to align the three question marks found in K2. I was using the entire top portion of the plaintext which includes both K1 and K2. Here are the offsets from the beginning of K1 if we count the question marks as a character.

101
227
289

In order to align the question marks found at these offsets, we want the remainder of a certain alignment (columns) to be the same in all three cases. We will call c the number of columns used and f the offset where the question marks will be located. So this value of f is what we want. Each of the question marks will use up a different amount of rows that we'll call r1 to r3.

101 = r1*c+f
227 = r2*c+f
289 = r3*c+f

This isn't too good. We have three equations with five unknowns. We have two variables too many.

We can modify the equations by putting f on one side.

101-r1*c=f
227-r2*c=f
289-r3*c=f

Now that everything is equal to f, we can produce three new equations by matching up the first line with the second, first line with the third and finally, the second line with the third.

101-r1*c=227-r2*c
227-r2*c=289-r3*c
101-r1*c=289-r3*c

Take the first new equation and move the numbers on one side.

101-r1*c=227-r2*c
r2*c-r1*c = 227-101
c(r2-r1) = 126

Do the same thing for the other two equations.

227-r2*c=289-r3*c
r3*c-r2*c = 289-227
c(r3-r2) = 62

101-r1*c=289-r3*c
r3*c-r1*c = 289-101
c(r3-r1) = 188

We write out those three equations again.

c(r2-r1) = 126
c(r3-r2) = 62
c(r3-r1) = 188

Here, even though we have three equations and four unknowns, we can still find out one of the variables. We note that c can divide into all three numbers. So this reduces to a problem of greatest common divisor or GCD. This is 2. So c is equal to two. This means the only way to match up the question marks is by having two columns. Not a very exciting result. The question marks would be either in the first column or the second. Since 101 is odd, then it would be in the second column.

Here is the interesting part. If we divide our three equations by c (2), we get the following.

r2-r1 = 63
r3-r2 = 31
r3-r1 = 94

What does r2-r1 mean? It's the difference in rows between the second and first question mark where they are lined up in the same column. Same thing for the other differences but for their respective digits/rows. It seems like an awful coincidence that these numbers appear. While 94 doesn't seem to be noteworthy, I have found a rotation cipher that uses exactly 94 characters or digits related to the arrowhead outcropping.

The other numbers are obvious. 31 is the number of characters in each row of K4 as well as in the last three rows of K2. And 63 is the number of characters in K1. The number 94 could end up being more important than we think. Especially if one thinks about the fact that CANDLE has 6 characters. Added up, that would make 100 characters all together. This would mean that three characters can't be used in K4, or some other transformation that would produce 94 letters or digits.

Here are some other weird facts. 63+31=94 (This is expected from the equations, but I find it fascinating now that it's revealed). Also, 2*31+1=63 and 3*31+1=94. If we were to continue, 4*31+1=125. This number is a cube. It's also 5*25. 125 is also the number of letters between the first and second question marks. And 5*31+1=156. That last one isn't very interesting until you look at what character this would end up on. 156*2+101 = 413. The 413^th character is the F in the very last FOUR in the coordinates (where it says FOUR SECONDS WEST X LAYER TWO).

To have a better idea of how the question marks are separated, think of it this way. The second question mark is separated from the first by (31*2+1)*2 characters (or twice the length of K1) and the third question mark is separated from the second by 31*2 characters (or twice the length of one of the rows of K4 or one less than the length of K1).

Maybe this is some feature of Sanborn's original matrix. Perhaps he left clues as to how to rebuild it and it's showing through the question marks. 31, 63 and 94 are very strange numbers to appear. Also, we have exactly 100 letters before the first question mark and 125 letters between the first two question marks. There are but 61 letters between the second and third question mark, so that one is different. However, 289 (location of third question mark) less 225 (number of LETTERS before second question mark) makes 64. Lastly, there are 484 (4*11*11) letters between the third and fourth question mark if we include the two missing characters.

Here's another coincidence. If you take 24*31+1=745, that makes EXACTLY how many characters there are before the last four lines of ciphertext (this would include the last portion of K3 as well as all of K4). This is without the X before LAYERTWO and without the missing E in DESPARATLY. If you're using the plaintext, it will be the exact number of characters immediately before THE MIST. And as for K1 and K2, we all know how 14*31+1=435 is the total number of characters in K1 and K2 with the question marks included in that count.

There are some really strange oddities going on with how this text is laid out. It's all speculation at to what this means, if anything. Still, I'm becoming more and more convinced that Sanborn didn't just put all four parts together after the fact. I think this was planned in advance. One thing I'm considering doing is figuring out if the question marks will line up if I can shift the entire grid over. In other words, what if I don't start at the first letter of K1? What if I start at another character? Could the question marks line up then?

For this to happen, 62 and 126 must have a different GCD than 2. Unfortunately, that is exactly the GCD. If there were two characters less in between the second and third question marks, then we could indeed line them up. There are only two candidates. Remove the two X's or remove the two U's. Removing the X's would be my first choice since it's located at 31 characters from the previous question mark. The GCD is now 62. So we can align on either 31 or 62 characters. After trying this out, I noted that while it does line up, it's kind of ugly the patterns where the words should line up. I also noticed that the other X's are still there. So it was better to remove the UU. By shifting by 7 characters (the word BETWEEN), everything did line up.

BETWEEN
SUBTLESHADINGANDTHEABSENCEOFLIG
HTLIESTHENUANCEOFILUSIONITWASTO
TALLYINVISIBLEHOWSTHATPOSSIBLE?
THEYUSEDTHEEARTHSMAGNETICFIELDX
THEINFORMATIONWASGATHEREDANDTRA
NSMITTEDUNDERGRNDTOANUNKNOWNLOC
ATIONXDOESLANGLEYKNOWABOUTTHIS?
THEYSHOULDITSBURIEDOUTTHERESOME
WHEREXWHOKNOWSTHEEXACTLOCATION?
ONLYWWTHISWASHISLASTMESSAGEXTHI
RTYEIGHTDEGREESFIFTYSEVENMINUTE
SSIXPOINTFIVESECONDSNORTHSEVENT
YSEVENDEGREESEIGHTMINUTESFORTYF
OURSECONDSWESTXLAYERTWOSLOWLYDE

SPARATELYSLOWLYTHEREMAINSOFPASS
AGEDEBRISTHATENCUMBEREDTHELOWER
PARTOFTHEDOORWAYWASREMOVEDWITHT
REMBLINGHANDSIMADEATINYBREACHIN
THEUPPERLEFTHANDCORNERANDTHENWI
DENINGTHEHOLEALITTLEIINSERTEDTH
ECANDLEANDPEEREDINTHEHOTAIRESCA
PINGFROMTHECHAMBERCAUSEDTHEFLAM
ETOFLICKERBUTPRESENTLYDETAILSOF
THEROOMWITHINEMERGEDFROMTHEMIST
XCANYOUSEEANYTHINGQ?OBKR
UOXOGHULBSOLIFBBWFLRVQQPRNGKSSO
TWTQSJQSSEKZZWATJKLUDIAWINFBNYP
VTTMZFPKWGDKZXTJCDIGKUHUAUEKCAR

We added the missing E from DESPARATLY and the missing X before XLAYERTWO. We removed not just the two UU's, but also the misspelled Q from IQLUSION. I'm wondering if the word BETWEEN doesn't go under THEMIST. See the blank area there. Also note how XCANYOUSEEANYTHINGQ? starts right at the beginning of that line. Unfortunately, the last question mark does not line up. It is 11 characters away from the end of the line. What we do see is that question mark lining up over the word RUG vertically. Usually, we find a key underneath the rug.

What if the word BETWEEN is what's sitting between THEMIST (subtle shading) and K4 (abscence of light)? This would be some kind of nuanced illusion. It's almost as if the plaintext is sitting in plain view. We only need to reveal what lies within the mist.

As I said before, this is just speculation at this point. It does have some nice properties. A lot of words line up. The question marks line up. THEMIST finds itself over something that has apparently disappeared. X CAN YOU SEE ANYTHING Q starts on its own line. There are many things to try here. Different offsets. You could remove different letters, or keep different ones in (like Q). You could also remove IQLUSION instead of BETWEEN and then remove the Q just before the last question mark. In this case, you'd get a similar grid except that IQLUSION would now go below THE MIST. If one does exactly that, then the Q would be directly above the word AIR in K4 if you read upwards. And if you look directly above QLU, you can see AIR several lines up. Directly below QLU, we see RNG. All this could be the first indication of re-enacting the K3 riddle.

Have fun!

Update!

Check this out. Let's remove XCANYOUSEEANYTHINGQ?OBKR all together.


SPARATELYSLOWLYTHEREMAINSOFPASS
AGEDEBRISTHATENCUMBEREDTHELOWER
PARTOFTHEDOORWAYWASREMOVEDWITHT
REMBLINGHANDSIMADEATINYBREACHIN
THEUPPERLEFTHANDCORNERANDTHENWI
DENINGTHEHOLEALITTLEIINSERTEDTH
ECANDLEANDPEEREDINTHEHOTAIRESCA
PINGFROMTHECHAMBERCAUSEDTHEFLAM
ETOFLICKERBUTPRESENTLYDETAILSOF
THEROOMWITHINEMERGEDFROMTHEMIST
UOXOGHULBSOLIFBBWFLRVQQPRNGKSSO
TWTQSJQSSEKZZWATJKLUDIAWINFBNYP
VTTMZFPKWGDKZXTJCDIGKUHUAUEKCAR


There are three lined up T's just as there are in the top section. Horizontally above it, we see AIR and vertically below the T's, we also see AIR. Then we see FLM vertically from the horizontal word FLAME. Could be a coincidence. But we also see TOP as seen from the NOVA clip. At the beginning, we see TUT and ROQM (=ROOM). Not sure if the word DRUG means anything, but perhaps it being next to the word ILL is some kind of clue for helping us to line things up.

From the word TOP, it would seem some kind of transposition is required. If so, then I've already figured this part out. However, TOP is on the wrong side from what I've done. So maybe this is something new.

What's a NULL cipher? It's where you extract certain letters from a larger text. You can use anything you'd like. For example, the first letter of each word. Perhaps the last letter (or any other letter of each word). You can use a repeated date where each digit will tell you how many letters to skip before extracting the letter.

In Kryptos, Gary Phillips used a specific type of NULL cipher where you write two texts one over the other and then extract the letters that are identical. Using a different masking technique, I found the word NUL in K2's ciphertext. This may seem like nothing, but it came from one of my recent breakthroughs. There were a great deal of clues leading here. I will skip all that and simply show what I have found.


SAGEXTHIRTYEIGHTDEGREESFIFTYSEV
ECDMRIPFEIMEHNLSSTTRTVDOHW?OBKR

ENMINUTESSIXPOINTFIVESECONDSNOR
UOXOGHULBSOLIFBBWFLRVQQPRNGKSSO

THSEVENTYSEVENDEGREESEIGHTMINUT
TWTQSJQSSEKZZWATJKLUDIAWINFBNYP

ESFORTYFOURSECONDSWESTXLAYERTWO
VTTMZFPKWGDKZXTJCDIGKUHUAUEKCAR


This is the plaintext of K2's last four lines. Note that the missing X has been added in before LAYERTWO and that I have then adjusted each line to have 31 characters. I also used the end of K3's ciphertext followed by K4's ciphertext in order to make four lines of 31 characters. There are a few different ways that I could have arranged this text, but only one other configuration gave anything.

I mention the layout above because it has even spacing on the top two lines. It also has a very peculiar feature in that three of the letters starts on a number mentioned in K2's coordinates. The E on the first line starts EIGHT. On the next line, we have S on SIX and F on FIVE. The other two letters are NR.

NR 865

Looks like NUMBER 865.

What does it mean? I don't know. I'm looking at different possibilities. The other letters, aside from those used for 865 could be anagrammed to RETNNA (misspelled RETiNA). There is another arrangement from the above NULL cipher that gives OVERSEAS-D (other anagrams may be possible). Not sure what the extra D would signify. One could also try anagramming RETNNA and include ESF as well. In order, the letters are ERSFNTNAE.

Also, if you look at the question mark in K2 and count the number of letters in front, you'll get the digits 687. Flip them around and you get 876. This is the number of letters in the tableau. But it's also the number of letters on the bottom half of the sculpture.

432 433 = 865
433 434 = 867
--- --- ---
865 867 = 1732


Is there a connection with those question marks to the NULL cipher that indicates 865? I don't know. And how does the fourth question mark enter the picture? Well, we did use it in the NULL cipher to produce 865 while the other question marks created the number 867, albeit out of order. Aside from that, I'm not where this would lead. But I haven't been looking at it for long either.