All operations

Bifid

Every ciphertext letter carries half of one plaintext letter and half of another.

The square above

The grid loaded here reads B G W K Z along its top row and T H Y V R along its bottom, the mixed square Bifid is usually taught from. FLEE AT ONCE comes out as UAEOLWRINS.

Splitting a letter in two

Each letter is found in the square and becomes two digits, a row and a column. Bifid writes the row digits of a block along one line, the column digits along a second line beneath, reads both lines off as one stream, then cuts that stream into fresh pairs. Every pair is a coordinate again, and every coordinate is a letter.

The two halves of a letter end up far apart. F in the loaded message puts its row digit into the first ciphertext letter and its column digit into the sixth. Each output letter is therefore assembled from pieces of two different inputs, which is what fractionation means and why a frequency count has nothing to hold on to.

Twenty-five cells force one pair of letters to share. I and J here, with the control beside the key offering the other three conventions.

The period

The period is the block size, and it decides how far a letter’s halves travel. At 5 the message is cut into fives and no digit leaves its group: set the loaded example to 5 and FLEE AT ONCE becomes UAIEYYDINS. At 0 the message is one block, which spreads the digits furthest and fails worst: one letter lost in transmission moves the boundary between the rows and the columns, and the whole decryption comes back as noise.

At 1 the cipher stops enciphering. A block of one letter holds one row digit and one column digit, they pair straight back together, and the output is the input.

What breaks it

The period is a small whole number, so guessing it costs a dozen tries. Once it is known the block structure is fixed, and a hill-climbing search over the twenty-five cells recovers the square from a few hundred letters. The square is the whole secret, and one filled from a keyword rather than shuffled at random reduces that search to a dictionary run.

Delastelle’s first published account of it appeared in 1893, in a Paris brochure called Cryptographie nouvelle. He designed it for a pencil and squared paper, and by that standard it was strong.

Trifid carries the same trick into a cube. ADFGX scatters the digits with a columnar transposition instead of interleaving them, and the Polybius square is the bare lookup all three start from.