Reply To: Let’s talk about the Playfair cipher

I somehow completely missed when this post was released, naively I had assumed forum posts were strictly chronological, but clearly that’s not always the case!

A lot of the variants that come to mind seem to push Playfair toward the Bifid/Trifid other square cipher side, but one thing that feels particularly interesting is breaking the assumption that digraphs are processed independently and in order

Before encryption you could swap the letters of every odd (or even) numbered digraph or apply different rules depending on the digraph index. Something like using the standard Playfair corner/rectangle rule for odd digraphs and then swapping the ciphertext letters for even digraphs. The resulting text could still hint Playfair with the missing letters/paired structure/reasonable frequencies, but the digram distribution would be asymmetric. Lots of ways to play around with parity and turn it into some form of polyalphabetic digraph cipher, without moving into the row/column recombination like we have with bifid.

I also wonder how practical it would be to fill the grid via a path. I was watching a Numberphile video on knight’s tours earlier and that seems like a pretty (evil) option. You could choose a starting square for the grid size, precompute a knight’s tour that visits every square exactly once, then write the keyword letters along that tour path and continue filling the remaining alphabet in the same order. The encryption rules themselves wouldn’t change, but grid reconstruction would suddenly become much more painful.

Funnily enough, while thinking about path based grid fillings I realised that the thing I was imagining has a name – boustrophedon. I had absolutely no idea this word existed until about five minutes ago, but apparently it’s the very respectable term for “filling in a row right to left and from left to right in alternate lines” (like an ox ploughing a field).

I feel obliged to note that this may be the most passionate discussion of the letter Z I’ve seen, turns out removing a letter from the grid seems straightforward until you realise it also requires linguistic consistency across multiple languages. I suppose I’ll be saying “zee” now, for the sake of consistency if nothing else. Thank you @the_cryptographer_formerly_known_as_madness for posting this!

(I’m quietly hoping this doesn’t inspire too many future evil ideas for ciphers, but in any case, Harry’s the boss and is free to inflict whatever flavour of cryptographic suffering he wishes. I’m just mere mortal and making suggestions and accidentally learning new words like boustrophedon…)