As per some advice, I’ve contemplated the notion (actually, the likelihood) of trying to pull another meaning out of deciphered letters. Depending upon how things are done, it’s possible but not likely. The author would likely use the methods that would make this possible as steganography to cover a secret message with a fake one. I wouldn’t say I completely understand what I’m trying to say or that someone else hasn’t described this. I’ll try and work it out the best I can and we’ll stumble through it together shall we? (I’ll steal definitions from my friend Wiki) For Kryptos, we have to consider whether there’s a good chance which justifies the search or if it’s just possiblity and therefore a dead end.

Let’s start with an identity in terms of mathematics…

Identities

An identity is an equality that remains true regardless of the values of any variables that appear within it, to distinguish it from an equality which is true under more particular conditions.

A common example of the first meaning is the trigonometric identity

 \sin ^2 \theta +  \cos ^2 \theta = 1\,

which is true for all complex values of θ (since the complex numbers \Bbb{C} are the domain of sin and cos), as opposed to

\cos \theta = 1,\,

which is true only for some values of θ, not all. For example, the latter equation is true when  \theta = 0,\,, false when \theta = 2\,

Contextual Identities

This isn’t some fancy definition, I’m just extending ideas here, just to clarify. If the message is “Skynet has become aware” then it is the only orientation of the plaintext letters that is correct. But, hey, stop right there! That sounds more like an equality! True, true. Putting the plaintext into context so to speak, we see that there are an infinite number of ways to express the finite message. So to quote the math definition, a plaintext identity is a message that remains true regardless of any variable encryptions. Practically, it means that no matter how you change and twist and distort things; by reversing the encryption algorithms or using the keys you can retrieve the one message that matters.

How does this relate to anything we care about?

Things we care about

It’s very easy to get off-track when working on a puzzle or cryptogram. If you’re in the military, you’re seeing hundreds of thousands of messages a day and you apply the methods to get the answers, run it through the human/computer machine to get an answer. If you get some code that just absolutely won’t translate, you can’t stop everything just to see if it was mistakenly enciphered by the equivalent of an unpaid intern screwing things up. It’s very different in the civilian sector however. We are often faced with one challenge and only have our experience with similar methods from other puzzles or perhaps an examination of other puzzles made by the creator. You just don’t have a lot to compare against. This is when it is very easy to invent things or imagine unlikely but plausible scenarios.

One of those that I get tempted by is to look for answers where there likely aren’t any.

I’m not saying I won’t try several different appealing ideas on the Morse code or K4 because, well, why not, it might work. It’s the investment of time and effort that must be curtailed. You have to set reasonable limits to your efforts otherwise you start building pyramids in the copperplate.

Getting back to the point

So, we have the idea that the plaintext message is the very finite solution amidst a relatively infinite realm of possible encryptions. We then want to learn to put some boundaries up and possibly progressively reduce the possibilities to a manageable finite number. We do this unconsciously and logically by saying it could be this but it’s probably not that.

If you get a solution from an enciphered text, the odds are significant that it is in fact the message the sender intended. It’s possible to get anomalies with a few tantalizing words popping up here and there that may lead us astray. I’m going to use this as a precept or argument and attempt some cryptology theory.

Dealing in absolutes

We need to work with the smallest unit of messaging. Let’s make a definition to help us understand things a little easier.

Let the plaintext be the meaningful output of one enciphering algorithm. The algorithm can be any number of steps required to produce the text. Using Kryptos as an example, the ciphertext side appears to be one ciphertext but upon attempting the K1 algrorithm we find that it doesn’t translate the whole plate. Using our definition, we make the argument that K1 is a separate cipher*.

*It’s possible and common to employ meta-ciphers or meta-puzzles where several separate parts combine in the end to give one final solution. This is likely a fair description of Kryptos. This doesn’t negate our argument but strengthens it. For the biologists out there, consider it similar to the different levels of protein arrangement (primary-one cipher, quaternary-several cipher units combined for a final solution).

Now that we have one unit

With one cipher-plaintext pair we have the liberty to make some observations and assumptions (I can’t guarantee I’m absolutely right, just working out an idea).

The primary analog ciphers use substitution and transposition. There are many incarnations as well as an infinite number of possibile steganographic opportunities. We are going to stay at the simple level of just the ciphertext and plaintext, we’ll assume you’ve gotten through all of the layers to the basic ciphering.

I’ve read and it should be fairly understandable that it doesn’t matter how many substitution ciphers, it will be reduced to the effect of using one. Mixing mono-, di-, tri- graphic substitution seems to complicate it but it doesn’t matter because at the end X will be Y or YY or !@#)$_&%#)(&*@!#$ and it is essentially just a substitution.

Transpositions would seem at first to be different. Turn it this way, take that column, reverse the letters and then spread them out across the table… I think these are easier to visualize. It doesn’t matter how much you twist, how much you turn, it’s simply a transposition at the end. It helps us to view them as layers of transposition but it boils down to a final movement from A to B with a simple or complex algorithm describing how to get there. If you don’t believe me, try to imagine how many ways you can get to the bathroom. Walking. Running. Going in through the window. Blasting a hole through the wall. Climbing on the ceiling. Skipping. Does it actually change where you end up?

Combining substitution and transposition really just ends up as one algorithm in the end.

It’s basically just about following the rules and then learning the rules.

No matter how complicated, considering the basic unit of one plaintext encrypted by one cipher algorithm, there is only one absolute message that can be recovered, barring an accident. It’s not possible to get a different message using the same method on the same ciphertext.

That’s one of the joys of it all for cryptologists. It’s very neat and tidy, like a mathematical proof. You can just give someone the method and they will be able to follow the exact same steps to the answer.

Complications

Is it possible to get different messages out of the same ciphertext?

Yes, of course it is. Take your average word seek, a table of letters that folks read through and circle the words they find. If I told Angelina to look for words horizontally after she built the table of ciphertext, she could find one message. Brad could find a different message I left for him in the vertical orientation and Jennifer still another in the diagonal words.

This is not a violation of the concept. Each searcher is using a different algorithm but on the same ciphertext, thereby using an independent pair of plaintext/cipher method. To find each message, we cannot consider using the same algorithm but must instead possess the correct variants.

This increases the difficulty of assembly for the creator however. It becomes harder the more you attempt to use all of the ciphertext for independent messages and dramatically increases with the number of messages. I have no measure of difficulty to present to you but one can imagine there are practical limits to what can be accomplished with the upper end being safely classified as really, ridiculously hard.

Let’s look at it differently

Analog ciphering techniques came and went, at least for military/political applications. They’ve moved on to secure methods where it doesn’t matter if you know there’s a ciphered text (for the most part) because you can send it out with little fear that many folks will be able to crack it. The private sector is always looking for fun and games so it’s a little more likely that someone would put several different possible translations into one bit of ciphertext. The previously described reasons are for steganographic security and the ability to have several people look at the same problem and get different messages.

Final thoughts

It’s possible but should only be considered when no complete message has been obtained, when there is some evidence that it could be, or that you know of recovered plaintext from a different source that is not found in your initial deciphering.

I would again consider Kryptos a good example of how one can make the argument that there is more than the initial plaintext. Palimpsest and abscissa were keywords in the solutions of K1 and K2 but we as of yet do not have convincing arguments as to where we were meant to obtain them. Yes, you can argue all you want. You can say the morse code sheets were palimpsest in the rocks or that eevirtuallyeeeeeeeinvisible is a good description. You can claim the compass represents abscissa or that digetaleeeinterpretatiu is abscised. I would reject these as correlations without causation, I see no clear indication to use these words to work towards a solution. It has proved easier to brute force sections 1-3 rather than using keyed methods. If Kryptos is a linear artistic description and cryptological challenge then we have at best taken a disjointed path to our solutions.

I wanted to consider, logically, the evidence and reasons I have to look so diligently for keyword retrieval. I feel there’s enough cause to suspect a message we have yet to recover but my enthusiasm is tempered by the knowledge of how easy it is to stray from the likely and end up only considering the endless possible solutions.

You made it to the end, I’m impressed…

Kryptos Fan

Advertisements