I like the idea that K4 is a digraphic cryptosystem.  What does the ciphertext indicate?  It’s useful to analyze the text to see what patterns emerge.  We have no immediate reason to think that K4 starts with a different letter so we begin with the traditional OBKR and start counting letter pairs.

Typically you need a larger amount of ciphertext to observe digraphic patterns.  K4 is a small sample but is it possible to see patterns emerge?

No.

Counting by hand, I found almost no repeats.  Two EK’s, two SS’s and two TJ’s.  I won’t say it’s impossible I made a mistake but three repeated digraphs does not give much to analyze.  For those new to looking, you can write the alphabet horizontally and then note the second letters of digraphs under the initial letter as a means of keeping track.  It’s also possible to make a big 676-space grid that lets you count each occurrence of a digraph.

What do you do when you’ve got the frequencies?

As in monographic frequencies, you can look for patterns and compare the most common with a chart that has the higher frequency digraphs occurring in the language.  You’ll see repeats when the digraph occurs in the same starting position (1st or 2nd) but if they are out of phase then the repeats will be masked.

You can use a digraphic phi test to analyze the data.  I don’t see enough repeats to warrant the analysis in K4 and this is the straight 97 letters (R left dangling) with no modifications.

It can be hard to make conclusive decisions about such a short ciphertext but if you combine the lack of apparent digraph repeats with my recent efforts to reverse various polygraphic cipher systems then I will at this point relinquish my nagging feeling that it is a digraphic-transposition combination at work in K4.  This is not so much as saying that it’s impossible they are at work but that I’m happy that I’ve tried hard enough to get them to work and am willing to focus on other possibilities.