# Virtual Cubes

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### Enigma Pocket Cube

This is a minimalist version of Cryptography Cube with the following new features:
• it's a 2x2x2 cube
• it uses 26 English letters only
• two letters are paired if there is a continuous path between them, and this path might go across multiple faces
• every letter has a chance to be paired with every other letter (except with itself)

The layout of the Enigma Pocket Cube was created in 2021 by Stefan Berinde.

#### Encryption and decryption

Encryption and decryption is similar to Cryptography Cube. Each letter has an orientation given by the surrounding pentagon. From the initial state we apply a 'key' by displacing each character in the key one quarter turn in the direction indicated by its orientation. The correspondence between a 'plaintext' and a 'ciphertext' character is given by paired letters onto the cube. Furthermore, after each encoding/decoding of a plaintext character, that character must be rotated up one quarter turn (for example) to change the permutation.

Here is a sample text to decode using the above description:
Key: CUBE
Ciphertext: QURBH BBZAU WZNEK BB

This cube can be used as an introductory example to the more complex Cryptography Cube. For short text messages the security offered by this cube will probably suffice.

It can also be used as a test case for cryptanalysis attack algorithms. In this regard we list below some design constraints that can be exploited by such attacks.

#### The parts of the cube

The cube has 8 corners, 3 tiles each. The 26 letters will fit on 24 tiles only if some tiles contains two letters. So every tile is divided in two regions. Such a region contains either a letter or a path segment.

A corner has 6 regions in total, with an even number of letters and an even number of path exits. If we place only two or four letters on a corner, we have a unique solution.

5 (corners) × 4 (letters) + 3 (corners) × 2 (letters) = 26 (letters)

We say two letters are on the same orbit if they can exchange places by using standard cube moves. We have two different orbits. Letters from different orbits are easily paired by placing them next to another, but letters on the same orbit needs a special path to be connected, which will go from one tile to another across the same corner. We have 6 such paths (3 left-handed and 3 right-handed). We also have 4 central paths used to pair letters on the same face, and another special path used to connect two letters from adjacent tiles sharing the same edge.

Ideally, the probability that any two given letters are paired should be 1/26. Here it varies significantly, depending on the letters, if they are on the same orbit and/or on the same corner. The range of probabilities is between 1/20 and 1/200, excluding pairing a letter with itself, which is not possible. For better results please check Enigma Rubik's Cube.

#### Comparison with the Enigma

The number of distinct states of this cube is about 106. Enigma machine had 1023 distinct configurations.

Happy encoding!

(The decoded plaintext: THEGR EATER NORUB IK)