#digraphic

This cipher is a variant of several Polybius square based ciphers. Unlike some of these ciphers it is also a fractionated cipher. In its basic form it is no stronger than a simple digraphic cipher and can be mapped to a digraphic table. For the most part, the design is similar to about one and a half rounds of a more advanced cipher. However, this cipher has one feature that could make it a very tough nut to crack for pencil and paper solvers. The most interesting detail is I can't find any information online or in any books that mention such a cipher.

The lesser form performs a substitution, a minor transposition and then a substitution. The cipher is partially self inverting except for the intermediate mixing. I haven't tried to find an inverting mixing system so that may still be possible. It is also possible that there is a best mixing system and a worst case mixing system. The mixing makes the letter pairs dependent on each other and this is what makes it a digraphic cipher. There is more work to be done on the mixing stage.

Larger forms of the cipher can increase the block size. Basic experiments have been performed on the the digraphic version though block sizes up to six are not unreasonable. The digraphic version may be extended to even block sizes and the trigraphic version may be extended to multiples of three and larger odd sizes. As the block sizes grow, the need for a more complex intermediate stage increases.

The encrypt operation of the digraphic cipher starts by creating a pair of Polybius squares. For demonstration purposes, you may want to use a straight alphabet. Otherwise any alphabet mixing system may be used. Label one square left and the other right. Next divide the plaintext into letter pairs. These will also be referenced left and right. Encrypt each letter of the pairs with the respective squares and you will have a group of four digits for each letter pair. This is the mixing step for each group. Take the first digit and the last digit as a number pair and decrypt using the left square. Take the second and third digits as a number pair and decrypt using the right square. The result will be a new letter pair. Finish the rest of the message and copy the pairs into five letter groups for the final ciphertext.

The decrypt operation is the same as the encrypt operation except you have to unwind the digit swaps in the intermediate step. Both digit swaps are shown below.

Encrypt: 1234 = 1,4 left and 2,3 right.

The new digit pattern is then: 1423

Decrypt: 1234 = 1,3 left and 4,2 right

The greater form of this cipher would add a transposition stage on all the digits in the intermediate step like ADFGVX/ADFGX or even a double transposition. This would completely hide any true patterns and make the cipher much more difficult to break. The down side is you could no longer program it as a stream cipher though it could become a block cipher and it could still be used as a pencil and paper cipher. Care would be needed to hide any block signatures.

One question still remains. Why is a relatively simple cipher virtually unknown? The complexity of the cipher is no different than several of the fractionated and multiple operation ciphers. While you may get similar results with other digraphic ciphers, they can't be expanded to a larger letter block. This cipher also has the option to take full advantage of the fractionation by adding a layer of transposition for the full message text. By creating a block mode, it may be possible to use cipher block chaining (CBC) and other modes more typically used with modern binary ciphers.

The C source and a digraphic version is up on github.