Leon Battista Alberti and the cipher disk: polyalphabetic encryption

Architect, theorist of painting, humanist and writer, Leon Battista Alberti is known above all for his treatises on art and for buildings such as the Tempio Malatestiano in Rimini and the façade of Santa Maria Novella in Florence. Less familiar to the general public is a short Latin work of his maturity, the De componendis cifris, which many historians regard as a decisive step in the history of Western cryptography.

A conversation in the Vatican gardens

The treatise, composed around 1466 or 1467, opens with an almost theatrical scene. Alberti tells of walking in the Vatican gardens with his friend Leonardo Dati, an apostolic secretary, and discussing with him the work of those at the papal court who had to read intercepted ciphered letters. Dati asks him what he thinks of that art, and Alberti undertakes to write an orderly account of it.

The first part of the work is devoted not to creating ciphers but to breaking them. Alberti observes that in Latin and in the vernacular some letters recur more often than others, that vowels have a characteristic frequency and that certain combinations are impossible. It is one of the earliest European descriptions of frequency analysis, the method that makes every simple substitution vulnerable.

How the disk works

To overcome this weakness Alberti proposes an instrument made of two concentric copper disks. The outer one, fixed, bears twenty capital letters of the Latin alphabet and the numbers one to four; the inner one, movable, bears twenty-four lower-case characters in an irregular order. Sender and recipient own two identical disks and agree on a reference letter on the inner disk.

The crucial point is that the position of the inner disk does not stay fixed. After a few words the writer turns the disk and signals the change by inserting a capital letter in the text, which tells the recipient the new alignment. Thus the same letter of the message can be represented by different signs at different points of the text, and counting frequencies loses much of its effectiveness.

Codes and numbers

Alberti adds a further device. The numbers one to four on the outer disk, combined in groups of two, three or four digits, form a small repertory of agreed phrases written in a booklet. The number is then enciphered with the disk like any other letter. This combination of code and cipher, which anticipates practices that became common only many centuries later, is among the most original aspects of the treatise.

A legacy long overlooked

The De componendis cifris circulated in manuscript and was printed only in the sixteenth century, in Italian translation, within a collection of Alberti's moral essays. The Italian chanceries of the time long continued to prefer nomenclators, that is lists of symbols for letters, names and frequent words, which were easier to use. The polyalphabetic principle would be taken up and developed by Trithemius, Bellaso and Della Porta.

Alberti's disk is a simple object that can be built from two circles of cardboard. Yet it contains an idea that dominated cryptography until the twentieth century: changing the alphabet during the message. Rotor machines such as Enigma, after all, do nothing more than turn alphabetic disks, automatically and far more quickly.