The Gnosis cipher combines a simple substitution cipher with diffusion over a block. In fact, the cipher performs two stages: the first for substitution; the second for diffusion (good ciphers mix them together much more). The first stage simply substitutes each alphabetical character with a different character according to a keyed table. The substitution table can be represented by a string of 26 letters, with no repetitions; implicit in the table is a top row of ordered letters, for example:

		    Plain text letter: ABCDEFGHIJKLMNOPQRSTUVWXYZ
		    Substitution key: BNHULVDZIXKYFMCJEWQOSARPGT
		    

The substitution stage simply replaces each letter in the plain text with a different one in the keyed table. The diffusion stage operates on the intermediate substitution text in 10-character blocks. Each indexed position in a substitution text block moves to a different position in the cipher text block. Basically, we just use the same kind of table as with the substitution stage. For example:

		    Starting Index: 0123456789
		    Diffused Index: 5136097482
		    

In each substitution text block, just look at an index position and record the character found there in the corresponding position indicated by the keyed diffusion table. Of course, an encryption will usually involve performing diffusion on multiple sequential blocks.

Reversing the algorithm is simple; just use the tables in the opposite order. A key for the algorithm consists of 26 letters followed by 10 digits, with no value repetitions of either (more compact representations of the key are easily possible). Every key will encode the same plain text to a different cipher text, which is our goal.

The Gnosis cipher is not a particularly good algorithm, as they go (although it is not terrible for a pencil-and-paper one). But the nice thing about it is that it implements the most important elements found in strong algorithms.