Alberti Disk

IPhenomenon

Two concentric rings. The outer ring carries the ordinary alphabet in order. The inner ring carries a mixed alphabet built from a keyword, so that the mapping is no longer a simple shift.

Plaintext is read on the outer ring; ciphertext is taken from the inner ring. Change the keyword and every letter changes at once — the disk has replaced the shift with an arbitrary permutation.

The genuinely new part is the index. Alberti proposed that after a fixed number of letters — he suggested four — the operator rotate the inner disk by one position and signal the change by writing the index letter into the ciphertext. The reader follows the same schedule and rotates at the same point.

The bench beside this entry implements exactly that: a keyword alphabet on the inner ring, and a one-step rotation of the index after every four letters. Encipher LOOMKEEPS and you will see the substitution change at the fifth letter.

IIKey space

Two independent factors: the keyword that builds the inner alphabet, and the index schedule.

The keyword contributes a permutation. A five-letter keyword gives a mixed alphabet with 26! possibilities in principle, but in practice a few thousand distinct arrangements once human-chosen words are accounted for.

The index schedule contributes the length of the message divided by the rotation interval, and each turn multiplies the number of effective alphabets. A 200-letter message with a rotation every four letters uses fifty different substitution alphabets.

That is the design leap. Before Alberti, more security meant a bigger alphabet. After Alberti, more security meant more alphabets in one message.

The weakness of the schedule is that it is regular. A rotation every four letters produces a strictly repeating pattern of alphabets, and regularity is what Kasiski analysis was invented to find — a century and a half after Alberti, but it finds him all the same.

IIIEnciphering

• Make the inner alphabet: write the keyword, drop repeated letters, then append the rest of the alphabet in order.
• Mount the two rings so that index letter A on the outer ring lines up with a chosen starting letter on the inner ring.
• Write the plaintext in capitals.
• For each letter, find it on the outer ring and read the letter directly beneath it on the inner ring.
• After every fourth letter, rotate the inner ring by one position and write the current index letter into the ciphertext.
• Continue until the message ends. The rotation schedule is fixed and not secret; the keyword is.
• Group the output for transmission, keeping the index letters visible and distinct.

IVDeciphering

• Build the identical inner alphabet from the keyword — this must match the sender's exactly.
• Align the rings to the agreed starting position.
• Read the ciphertext, but treat the index letters as instructions rather than as data: when one appears, rotate the inner ring one position and continue.
• For each data letter, find it on the inner ring and read the letter above it on the outer ring.
• If the plaintext degrades into nonsense partway through, you have almost certainly missed a rotation. Rewind to the last index letter and re-sync from there.
• Check the total: the number of index letters should equal the message length divided by four.

VWeakness

The schedule is periodic. Rotating every N letters divides the message into N streams that are individually monoalphabetic. That is exactly the structure Kasiski examination hunts for.

The index letters are a gift. Alberti's convention of writing the index letter into the ciphertext tells the attacker where the alphabet changes — which is genuinely useful for keeping the receiver in sync and genuinely useful for the analyst too.

Manual operation is error-prone. The operator must track position, rotate on schedule, and write the index at the right moment. Surviving period documents contain frequent corrections, and a single missed rotation desynchronises the rest of the message.

The mixed alphabet is still an alphabet. Without the rotation, the inner ring is just a monoalphabetic substitution and falls to ordinary frequency analysis.

VIPractice

·History note

Leon Battista Alberti, the Florentine architect and polymath, described the disk in De componendis cifris, written around 1466 and presented to Pope Paul II. The work is the first known European treatise on cryptanalysis as well as cryptography; it contains the earliest recorded statement of frequency analysis in the West, four centuries before Kasiski. Alberti's disk was widely copied, and variants made in brass survive in several European collections; the principle reappeared in the discs of the nineteenth-century Confederate cipher and, indirectly, in every rotor machine of the twentieth century.

·Further reading

Every rotor machine is an Alberti disk that rotates itself. Enigma's three rotors are three permutations, and its stepping mechanism is Alberti's index schedule with the human removed — which removes the errors and, crucially, makes the schedule irregular enough to defeat Kasiski analysis for a while.

Alberti also wrote the first known Western treatise on cryptanalysis, De componendis cifris (1466), which contains the earliest recorded description of frequency analysis in Europe. He built the defence and the attack in the same decade.

Next on the loom: porta-cipher — a tableau designed so that encryption and decryption use exactly the same procedure.

+Weave into