Virtual Cubes

Cryptography Cube

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Cryptography Cube

This cube organises 48 characters into pairs to form a 'basic substitution cipher'. It allows to encrypt plaintext into ciphertext, but also to decrypt it back into plaintext. The cube can be scrambled to create a 'complex transposition cipher'. Additional single move scrambles between characters creates a 'complex polyalphabetic substitution cipher' like those used by mechanical cipher machines used in World War II. Irregular pentagon shapes display the orientation of the side parts. Because of this, the cube can also be used as a Super Cube, which has 2048 times more positions then a regular Rubik's Cube.

The layout of the Cryptography Cube was created in 2020 by Richard Ayre.

The parts of the cube

On each sticker an asymmetrical shape (irregular pentagon) indicates its orientation. In addition, the edge and corner stickers contain a character: letter, number, or other character commonly used in written text, email, URL addresses and computer file names. There are 48 characters in total, none are repeated. The centres feature a unique central glyph instead. Each glyph links 4 pairs of characters on each face, with the exception of the white centre which links 3 pairs and isolates one corner and one edge sticker. Each centre is different and void of rotational symmetry.

Terminology

The term 'cryptography', referred almost exclusively to 'encryption', is the process of converting ordinary information (called 'plaintext') into unintelligible form (called 'ciphertext'). The reverse, in other words, moving from the unintelligible ciphertext back to plaintext, is called 'decryption'. A 'cipher' (or 'cypher') is a pair of algorithms that create the encryption and the reversing decryption. The detailed operation of a cipher is controlled both by the algorithm and in each instance by a 'key'. The key is a secret (ideally known only to the communicants), usually a short string of characters, which is needed to decrypt the ciphertext.

Encryption and decryption

The Cryptography Cube should be in its initial state before use. It can be solved like any Super Cube, taking care to orientate the centres correctly. The choice of colors and orientation was intended to make solving the cube as simple as possible. In its solved state each face links 4 characters to 4 substitution characters via one of 4 lines within the centre glyph. The exception is the white centre glyph, where two characters are not paired. These two characters would remain unchanged when used in a cipher.

For example, the characters on the red face of a solved cube (ABCDEFGH) would become (CGAFHDBE). Using the cube to replace characters in the plaintext word 'HEAD' creates the ciphertext 'EHCF'. For the decryption of a ciphertext, the substitution of the characters has to be done in opposite direction.

Changing the cipher

A unique scramble algorithm known only to the user, allows to change the current cipher. The algorithm can be described in a regular cube notation. However, a simple key word, key phrase or number can be used instead by displacing each character in the key one quarter turn in the direction indicated by the irregular pentagon. Scrambling the cube results in producing a unique transposition cipher. The number of possible permutations of cipher has not yet been calculated. Each edge character can be substituted for 46 of the remaining 47 other characters. Each corner character can be substituted for 45 of the remaining 47 other characters. Each character has a 1 in 24 chance of remain the same if isolated by the white centre glyph. This characteristic gives the cube a potential flaw similar to the Enigma machine. The Enigma machine would never substitute a character for itself.

Methods for increased security

Basic substitution ciphers are vulnerable to frequency analysis attacks. To overcome this vulnerability the Cryptography Cube can be scrambled further between words or between characters. One simple method of achieving this is to rotate the plaintext character up one quarter turn, after the ciphertext character has been recorded. More complex scrambles may be used between characters for increased security. These variations in use change the cube from a 'basic transposition cipher' to a 'keyed transposition cipher', and then a 'complex shifting transposition cipher'. Other forms of ciphers may be implemented using the cube. However, these are beyond the scope of this description.

© Walter Randelshofer. All rights reserved.