# Expanding on a classic

From the simple caesar to the seemingly uncrackable elliptic curve, there are countless ways to obscure - and even hide - a sensitive message. Cryptography is quite interesting in this way. I find the simpler ones - which are solvable through pen and paper - to be fun little puzzles. The only problem is, once you know how to solve a particular type, it becomes less interesting to solve another of the same. There are a handful of popular ciphers which get published everywhere - beaten to death. The unique, custom one offs are much harder to come by. So, below is my contribution.

This cipher system stands atop the shoulders of another version. It takes a classic to the next dimension, and while I could simply tell you the steps of encryption are X,Y,Z in that order - I find it more satisfying to deduce the method myself than to follow procedure.

You will, of course, need somewhere to start. So hopefully this will assist you.
Sxz pxkd, f- vj-enr, fhjl iyshjklcg ay mttuk. Oq hkbhcix-m rrui rijz ybtubr sxz.

a b c      |  M A E       B G J       N H I
d e f      |  B F D       I A D       L J K
g h i      |  H C J       - L C       M G C
j k l    |    L G I       E K M       B D -
m n o    |    N K -       N H F       E F A
p q r    |    O P Q       V Y Q       S Q Z
s t u  |      Y W U       S T X       T V W
v w x  |      S Z V       W P Z       U P Y
y z -  |      X T R       O R U       O R X


To solve this puzzle, you must decrypt this: XZIUXCFGIJ-QTCA
And give an explanation on the encryption/decryption scheme of the cipher.

Happy cracking!

hint 1:

It may help to visualize these cubes like so:

hint 2:

This cipher variation is based off of Félix Delastelle's four-square cipher

hint 3:

While the four-square cipher uses four 5x5 squares, if it is regular (the plaintext squares are a-z in order, skipping j, top left to bottom right) then all that is needed is 3 squares. The variation I created is minified using this same concept.

hint 4:

Lets do some analysis on the four-square cipher. This encryption scheme is typically represented visually, but it can also be expressed using the coordinates X and Y. For example, take the following four-square cipher.
If we were to encrypt cipher we would first split the plaintext into the pairs ci|ph|er, which could then be expressed as the coordinates (X,Y) 3,1 4,2 | 5,3 3,2 | 5,1 2,4. The process of encryption/decryption by visually following the rows and columns of a typical four-square cipher is the exact same as simply swapping the X coordinates. Plaintext 3,1 4,2 becomes the ciphertext 4,1 3,2. The full ciphertext is therefore HROWRZ.
Breaking down the four-square cipher like this makes it much easier to extend the scheme to use 3 coordinates: X,Y,Z. However, with 3 coordinates you can't just swap. You'll have to use some form of rotation ;)

hint 5:

The Four-Square cipher is a digraphic cipher, because it encodes a message using pairs of letters. The encryption/decryption scheme I have come up with is a trigraphic cipher

Solution spoiler:

Originally, I named this cipher the six-square cipher due to the use of 6 full blocks for the key, however, I overlooked the fact that these blocks are not squares like in the four-square cipher, but instead cubes due to the extra dimension. Therefore this cipher should instead be named the six-cube cipher. Cisko solved this when the ciphertext to decrypt was XZIIORIOIACKHHGRQX aka the original name. His answer is correct. I have updated the question to contain the proper (encrypted) name though, because it will nag me if I don't.

• Welcome to Puzzling! We usually don't encourage posting this many hints to start. Puzzles are supposed to be solvable without any hints. If you feel the hints are needed, just put them as part of the puzzle itself. Commented Dec 16, 2020 at 15:41
• Ah, whoops. I will keep that in mind and edit hints into the question in the future. The cipher is certainly solvable without the hints, and in fact I did provide a few subtle hints in the preface text. The numbered hints at the bottom are just there to help you get on track with the right thought process for solving, if you are lost. Commented Dec 16, 2020 at 18:02