Bifid Cipher

IPhenomenon

Write the coordinates of the plaintext in the Polybius square, then split them into two streams — all the rows, then all the columns — and re-pair the digits to read off new letters.

Square with keyword BRASS:

Encipher LOOM (a single period of four, though the classical period is five):

LOOM became MTBA. Every letter changed value, and the change depended on the letters around it — the same diffusion property that makes Playfair more than a substitution, achieved with counting instead of a square rule.

IIKey space

Two parameters compose the key: the keyword that builds the square, and the period — the block length over which fractionation runs.

The keyword behaves as it does everywhere else: a few thousand plausible squares from memorable words. The period is the interesting part. A period of five is the classical choice, and it is the weakest useful setting; longer periods diffuse more and cost the analyst more.

The Bifid's period is a security parameter in the modern sense: a single dial that trades speed for strength, and one that the operator can turn without changing any other part of the system.

That is a surprisingly modern idea to find in an 1895 amateur's notebook. It is the same shape as the number of rounds in a modern block cipher.

Delastelle also invented the trifid cipher, which uses a 3 x 3 x 3 cube and coordinates in three digits rather than two, and the four-square cipher. All three are fractionating, and all three were ignored for most of a century because they were French, amateur, and published in journals nobody read.

IIIEnciphering

• Build the Polybius square from the keyword, merging I and J.
• Choose the period — five is the classical setting and the bench uses five.
• Split the plaintext into blocks of that length.
• For each block, write each letter's row number and column number.
• Write all the row numbers of the block in order, then all the column numbers, forming one continuous digit string.
• Re-pair the digits from the start: each new pair is a row and a column.
• Convert each new pair back to a letter using the same square.
• Join the blocks and group the output in fives.

IVDeciphering

• Rebuild the square and confirm the period. Getting the period wrong produces output that looks almost right and is entirely wrong, which is the most dangerous failure mode a hand cipher can have.
• Split the ciphertext into blocks of the period length.
• For each block, convert each letter to its two coordinates and write the digits in a single line.
• Split that line in half. The first half is the row stream; the second half is the column stream.
• Re-pair across the two halves: first row digit with first column digit, second with second, and so on.
• Convert each new pair back to a letter.
• If the result is close to readable but wrong, check the period first, then check whether the sender's square used K in place of J or vice versa.

VWeakness

The period is a crack. Bifid's fractionation resets at every period boundary, and those boundaries are where the statistics restart. An analyst who guesses the period correctly can attack each block independently.

Digraph statistics still leak across blocks. Within a block, letters are correlated in ways that are not natural language's ways, and comparing the observed digraph distribution to the expected one narrows the square quickly.

It is a hand cipher, and hand ciphers are used by tired people. A single arithmetic slip in the coordinate streams corrupts an entire block — five or more letters — and the receiver has no way to tell where the error is except by re-deriving the whole message.

The square is small. 25 cells and one keyword: the same weak key-generation problem every keyword square has.

It was published. Delastelle's work appeared in the Revue du Génie Militaire, and by the First World War French military cryptanalysts had detailed methods for it. A cipher your own side can break is a cipher you cannot use.

VIPractice

·History note

Felix Delastelle (1840-1902) was a French civil servant and amateur cryptographer who published the Bifid and Trifid ciphers in the Revue du Génie Militaire in the 1890s and collected his work in Traité élémentaire de cryptographie in 1902, the year of his death. He was not a professional cryptographer and his ciphers were not adopted by any government; they were rediscovered by twentieth-century cryptologists and are now standard material in every serious introductory text. The Bifid is regarded as one of the two or three strongest ciphers that can be worked by hand in the field, and Delastelle's use of a tunable period anticipates a design principle that did not become general until the 1970s.

·Further reading

The Bifid is the best available illustration of a claim made earlier in this collection: that the operation of splitting letters into pieces and recombining the pieces is more powerful than any clever substitution rule. Fractionation destroys the one-to-one relationship between plaintext and ciphertext letters without needing arithmetic, machinery or a large key.

Delastelle's own note is worth quoting in spirit: he was interested in ciphers a person could use at a desk, with a pencil, in a room that had no electricity. Every design decision in the Bifid follows from that constraint, and the cipher is better for it.

Next on the loom: ADFGVX Field Cipher — fractionation taken to its industrial extreme, with a six-by-six square and a second transposition.

+Weave into