Jul 13, 2015

How many possible keys does the Playfair cipher have?

Dayz has a good answer, but here's a link to the Wikipedia overview of the Playfair cipher for some additional perspective:

Instead of doing the math myself, I searched for it. Someone asked the same question on another site, and this answer appears correct:

"When we consider that a Playfair key consists of the alphabet (reduced to 25 letters) spread on a 5x5 square, that's 25! keys (another formulation consider any string to be a key; then strings leading to the same square are equivalent keys).

The rules of Playfair are such that any rotation of the lines in the square, and any rotation of its columns, lead to an equivalent key (in other words, the square reduce to a torus). It can be proven conclusively that there are no other equivalent keys (note: a transposition of line/columns leads to a key such that 200 out of 600 digrams with distinct letters are mapped to the same diagram as for the original key, and the other 400 are mapped to the digram obtained by exchanging the two letters in the digram mapped by the original key; also, an horizontal or [resp. and] vertical mirroring of the square leaves 500 (resp. 400) digrams invariants; these are near-equivalent related keys, but not equivalent keys).

I conclude Playfair has 25!/52=620448401733239439360000≈279 distinct keys classes (a 79-bit-key cipher). At least another source agrees."
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