View Full Version : K4

The Unreasoner
11-19-2014, 07:09 PM
I miss having fun on TL. So I thought I'd start a thread with a more lighthearted intent.

This thread is about the final 97 or 98 characters of ciphertext on Sanborn's Kryptos sculpture.

We have recently gained a new clue (from Sanborn himself):
The six cipher letters are NYPVTT and when deciphered, they read BERLIN.
This seems to be evidence against transposition in general, and since frequency analysis techniques show that there are simply not enough vowels in k4 for it to be transposed English (or French, and probably any Romance language, although the new clue reminds me that I don't have good enough data on German to rule out all transpositions).

This seems to indicate that it is a (relatively) straightforward substitution cipher. And since there tend to be hints in the preceding section (ABSCence of light, ID BY ROWS (though apparently that was an error?)) What might it be? WONDERFULTHIGS as a key? Putting a CANDLE into a BREACH?

Or could it be some kind of hill cipher, even though 97 is prime? One huge matrix? Padded plaintext?

So, K4 brainstorming: what have you got?

11-20-2014, 07:04 AM
Uh... for those that don't have a clue: Any chance you could tell us who or what K4, Sanborn and Kryptos are?

yks 6nnetu hing
11-20-2014, 07:26 AM
Uh... for those that don't have a clue: Any chance you could tell us who or what K4, Sanborn and Kryptos are?

oooh, ooh, naming acronyms and vague terminology! I like this game :D

I got the following request the other day:
"could you dig up for me the SSS data in the Geophys/Bathy section, maybe labeled as UXO. For both ZNL and BGU, dated 2011 and I want the final reports please, which are in German"

uh. sure. Would you like the raw sound files to go with those?

11-20-2014, 09:30 AM
"could you dig up for me the SSS data in the Geophys/Bathy section, maybe labeled as UXO.
Speciale Sicherheits Schützung, perhaps labelled as Unidentifizierbare Xylometrische Objekte.

PS I had to consult a dictionary to come up with a candidate for the "X", though I varied on that a bit after I'd found a possibility.

The Unreasoner
11-20-2014, 01:09 PM
Uh... for those that don't have a clue: Any chance you could tell us who or what K4, Sanborn and Kryptos are?

We talked about it a bit on another thread...I guess I assumed it was all well-understood.

Sanborn is an artist, he made the Cyrillic Projector. And Kryptos, the art installation at the CIA headquarters. While it has pools, compasses, and lodestone, the main item is this:
It has four panels, the two on the right show a Vigenere Tableu with KRYPTOS generating the keyed alphabet.

The two on the left have four encrypted messages. The first two use a vigenere variant, and the third uses an affine like transposition. The fourth, or K4, remains unsolved. Publicly, at least.

In 1997, a computer scientist in California cracked the first three messages, which led to the CIA admitting they did so in 1995. In 2000, the NSA admitted that they cracked the first three in 1992.

To date, K4 remains unsolved. There are many resources on Kryptos, Elonka Dunin has some great stuff, and great links. Google it. There are morse code messages scattered about he installation (like T IS YOUR POSITION). K3 decoded to a paraphrased account of the excavation of Tutankhamen's tomb, ending with "Do you see anything, Q?" The answer famously is known to be 'Wonderful things', though 'Yes, and it is wonderful' is more accurate.

The sort of mind that can pick apart the mysteries in RJ's books might be able to put a big dent in this. And the collective intelligence of TL could solve it, possibly.

11-20-2014, 02:20 PM
But but but we just have collective madness:(:(

11-21-2014, 03:51 AM
This makes my head hurt :p

11-21-2014, 03:55 AM
We just have to pool our collective ignorance, then we can't go wrong.

11-21-2014, 04:20 AM
We just have to pool our collective ignorance, then we can't go wrong.

Do I have to become an elected official for that?

The Unreasoner
11-21-2014, 01:58 PM
Bizarrely, the day after I made this thread, Sanborn released another clue, specifically that the word after BERLIN is CLOCK. So I'll be toying with this.

Meanwhile, keep in mind that your relative ignorance is no real problem.People less ignorant have had as little success solving it. I was just trying to brainstorm new, testable ideas.

The Unreasoner
11-21-2014, 05:11 PM
So apparently, there is a famous clock that is often called the Berlin Clock:
Its real name is Mengenlehreuhr.

Now, as Sanborn himself points out, there are several notable clocks in Berlin. But this one (while it is no longer in Berlin) is especially interesting, because it would seem to legitimize a nonstandard grouping method. In other words, the first 12 letters might be encrypted in blocks of 3, the next 28 in blocks of 7, and so on. This is obviously potentially huge, since it offers a way to get around the fact that 97 is prime.

My only hesitation is that it would mean a significant hint is in the plaintext itself, so it would only be visible (in the normal course of things) when it is no longer useful. Of course, we should balance that against the fact that these clues were not chosen idly. The question is, how badly do we think Sanborn wants this solved? Is this clue simply useful plaintext? Or is it significant on another level?

The Unreasoner
11-21-2014, 07:02 PM
I think I've got it:

Several hill ciphers, with groups of different sized blocks. When I get home I'm going to break BERLINCLOCK into a bunch of sets of blocks, and pray he only used one key per group. Then hope at least one sampling is invertible mod 26.

I base this on two things: Sanborn's recent statements on that clock, and several statements in the past he made about studying matrix methods, and using them. While there are a number of classical systems (and Kryptos is theoretically solvable with pen and paper, so we can rule out modern methods, and probably matrices much larger than 5x5) that could be said to use matrices, only the hill cipher (to my knowledge) uses them in the true mathematical sense. And the Berlin Clock grouping would provide the unique twist he is rumored to have added.

The Unreasoner
11-21-2014, 07:06 PM
Just out of curiosity, what would be the maximum value for n where an nxn matrix could be said to be invertible by hand?

In your opinion.

11-21-2014, 08:28 PM
Just out of curiosity, what would be the maximum value for n where an nxn matrix could be said to be invertible by hand?

In your opinion.

Well that depends on how you define "by hand". If all you mean is that the calculations must be done without calculators then I'd say if the a(ij) are tricky enough even a 2x2 will be a major headache. If the content must be relatively simple say roots of 1 in C then it's just a matter of patience and keeping notes. It's been ages since I've done that stuff but I'd say 8x8 I'd be able to keep track of within one 40 A5 notebook, though my stamina might not be up to the task.

The Unreasoner
11-21-2014, 08:52 PM
They're integers mod 26, so trickiness isn't the limiting factor. Imo, a four function calculator could be used, even if it were more or less necessary, without leaving the set of 'classical cryptography'.

The Unreasoner
11-21-2014, 09:31 PM
The Berlin Wall fell at 10:45 pm, which is 4,2,9,0 on the Berlin Clock.

This is awesome, becauae it lets us get rid of the pesky seven in 97, by setting the third rows groups equal to 3, putting 27 letters in the row.

That means we just need to find integers that satisfy 4x+2y=70

Assuming I am on the right track, of course.

The Unreasoner
11-21-2014, 09:33 PM
Although they would have to be quite large, around 10. Are 10x10 matrices easy to invert mod 26?

Actually, there are a lot of ways to get the seven, now that I think about it.

Integer triples that satisfy 4x+2y+9z=97

And I think I'll bound it to between 2 and 9.

The Unreasoner
11-21-2014, 10:09 PM



Here's a spacing I like. I bolded the letters for which we know the plaintext.
Unfortunately, there isn't one complete block to work with. I could just have a computer list the possibilities and then check the values against the distribution of letters in english, but my laptop screen is cracked, and my desktop doesn't have Maple.

Any ideas?

Looking for a 7x7 matrix where [1,13,24,15,21,19,19]*[M]=[?,1,4,18,11,8,13] mod 26

The Unreasoner
11-21-2014, 10:28 PM
I can't believe I'm the only one excited by this. Daekyras? We got a new clue the day after I started the thread. A mystery 24 years old.
That's the Cyrillic Projector. How awesome is that?

The Unreasoner
11-21-2014, 10:56 PM
Check this out:

What if the ciphertext or plaintext of K1-3 are the key, adding an autokey element? Some letters are slightly out of position, and apparently the spelling errors were intentional, with significant location. Also, the XLAYERTWO/IDBYROWS issue, when resolved, was indicated to potentially be important in solving K4.

These give us markers to sample the text for a key, potentially. That way, the x,y,z from above would have to also satisfy 4x^2+2y^2+9z^2=d, where d is the number of sampled letters.

The Unreasoner
11-24-2014, 05:06 PM
Now that I think about it, a hill cipher set up in the manner I described is not something I think a reasonable person could call 'solvable', certainly not with pen and paper techniques.

So what are we looking for? A system that provides diffusion of some sort, variable block size, possibly incorporating a table or matrix, and with strong aesthetics (probably visual, but possibly acoustic (homophonic/morse) or more abstractly mathematical).

So what about a straddling checkerboard, possibly with nfid elements? In support, there are rumors of stenographic methods being employed in K4, and the Word of Sanborn says it is solvable with only the information online. There is a part of K3 that has the letter Y,A, and R slightly out of place. Indicators for the checkerboard? Certainly they are the only clear candidates for stenographic data. And the key is (allegedly) recoverable.

The Unreasoner
11-24-2014, 07:54 PM
Looking at nfid groups (5x5 bifid, 3x3x3 trifid, 6x6 bifid, 4x4x4 trifid). I was wondering, would an encryption system that takes multiple types of input (like digits and letters, or ascii binary strings) do enough to mask the English language on its own? Supposing it did, could you construct a plaintext that yielded only letters in the ciphertext?

The Unreasoner
11-25-2014, 03:24 AM
How would you imagine going about building a straddling checkerboard around the Berin Clock? I still don't like the fact that it seems that the clue is hidden by that which it is a clue to, but I think he would really like the visuals of it. It's table-like, good for cryptography. But why the clock? The Berlin Wall had just fallen, probably the most iconic moment in recent history to draw from at the time. But we're talking about the clock. Sanborn has talked a bit about the wall, must have been thinking about it. And clocks tell time. But which time? The is 'recoverable'. It has to be 10:45, right? Or maybe a 'minutes to midnight' thing?

Also, this has been bugging me:
Why misspell it that way? The other misspellings had a wrong letter, not a missing letter. And losing one e wasn't very helpful in masking the letter distribution. But the cipher is different, so a different method? Or is there a larger importance?

There is also the fact that K1-2 each end a row. But not K3. Maybe something there?

The Unreasoner
11-28-2014, 05:55 PM
Some of these diffusion methods have plaintexts of different length than the ciphertext. Which makes me wonder how to interpret Sanborn's clues. Does NYPVTT decrypt to BERLIN? Or is it that BERLIN appears where NYPVTT is now after decryption?

I think it has to be a variable length block cipher, but there simply arent any compellingly good candidates. And I keep coming back to the fact that the keys are recoverable. What exactly does that mean?

The Unreasoner
05-07-2015, 06:54 PM
I've seen some exciting progress in the last few days...the result of better data of english frequencies. I'll post when the computation is done.

Also, as a hypothetical: suppose someone had a quantum computer at least as powerful as Dwave II (or even a nondeterministic Turing machine)-

Would a brute force attack make sense? How would you execute it? (26 substitution states)(97 positions)? Only the affine variants? A weighted search based on character frequencies?

eht slat meit
05-07-2015, 11:18 PM
I hadn't heard of this before, so I was interested to get a visual on this and did a google image search.

Curiosity - Is this some sort of trick of the light specific to a single picture, or does there appear to be writing on the top half of the sculpture made up of the letters when you look at it in a certain way, like those 3d stereograms that you interpret by unfocusing your eyes?

eht slat meit
05-10-2015, 11:40 PM
Wow, this thing is totally fascinating. I'm not much on crypotograms, but the history surrounding the sculpture and the clues, as well as the rabbit-trails it offers are cool. That's the really interesting part of it to me, and seems to offer some insight into the clues that have already been unveiled.

Take that Berlin Clock he referenced for example - he tells the interviewer they should delve further into that particular clock. No particular reason clear from it, and of course that set off a firestorm of response.

Because that particular clock is tangentially related to a conspiracy theory through the death of an inventor named Dieter Binninger. His death is notable because he died with his son while piloting a private plane (not that unique) and was attempting to design a long-lasting light bulb that could supposedly go 17 years. Worked, apparently, but expensive as heck, and appears to have resulted in the original Clock briefly going away because his widow couldn't afford to maintain it.

Very Dan Brown with the related conspiracy of price-fixing on light bulbs by the Phoebus Cartel, but the relevant bit seems to be the clandestine politics of trade, and once common-place things made obsolete by the passage of time.

Which appears to be what the sculpture, as a work rather than just a math puzzle, is about.

That 'Clock of Flowing Time' is pretty darn cool too.

eht slat meit
05-11-2015, 12:47 AM
Why misspell it that way? The other misspellings had a wrong letter, not a missing letter. And losing one e wasn't very helpful in masking the letter distribution. But the cipher is different, so a different method? Or is there a larger importance?

Maybe it's a message. Analyze the word.


One is correct.
One is missing, replaced by an A.
One is missing, the word is mispelled.

There should be three 'E' here. Where did they go?

Answer: To the morse code sculpture, which is cleverly titled "Digital Interpretation" in Morse. In addition to these two words, there are 3 Es that apparently don't have any purpose whatsoever.

My guess is that applying a digital pressure on those three "dots" might move the sculpture just enough to reveal a chamber with the proof of solution and the rest of the mystery, which is of course what the sculpture is about.

The Unreasoner
05-22-2015, 03:25 PM
Could you expand on the 3d stereograms?

And what do you mean by 3 missing 'e' s?

Anyway, I've got something that uses two affine transformations, one mod 26 and another mod 290. And the frequencies of the letters and the bigrams check out (to a point...frequencies are the same, the letters are not). Chi squared and anova on trigrams was inconclusive.

Anyway, it looks like badly disguised English to a computer, but it's also still gibberish to me. Is there someone here with pgp who could make some sense of it?

Also, @eht:
Don't have too much fun here, or Nazbaque will bitch at you.

05-22-2015, 04:10 PM
Also, @eht:
Don't have too much fun here, or Nazbaque will bitch at you.

More like if he doesn't show enough interest you will bitch at him and then I will bitch at you. Of course now you just went and bitched about me with no provocation what so ever. Then again the way you and eht keep bringing me up while talking to each other is eerily similar to a pair of schoolgirls gushing about their shared celebrity crush. It seems that I must be the mutual enemy who becomes the catalyst for your bromance.

*Dramatic pose*

Should I play the villain for the sake of true love?

The Unreasoner
05-22-2015, 04:55 PM
The best celebrity crushes are mute.