Rotor Machine - Background

Background

In classical cryptography, one of the earliest encryption methods was the simple substitution cipher, where letters in a message were systematically replaced using some secret scheme. Monoalphabetic substitution ciphers used only a single replacement scheme — sometimes termed an "alphabet"; this could be easily broken, for example, by using frequency analysis. Somewhat more secure were schemes involving multiple alphabets, polyalphabetic ciphers. Because such schemes were implemented by hand, only a handful of different alphabets could be used; anything more complex would be impractical. However, using only a few alphabets left the ciphers vulnerable to attack. The invention of rotor machines mechanised polyalphabetic encryption, providing a practical way to use a much larger number of alphabets.

The earliest cryptanalytic technique was frequency analysis, in which letter patterns unique to every language could be used to discover information about the substitution alphabet(s) in use in a mono-alphabetic substitution cipher. For instance, in English, the plaintext letters E, T, A, O, I, N and S, are usually easy to identify in ciphertext on the basis that since they are very frequent (see ETAOIN SHRDLU), their corresponding ciphertext letters will also be as frequent. In addition, bigram combinations like NG, ST and others are also very frequent, while others are rare indeed (Q followed by anything other than U for instance). The simplest frequency analysis relies on one ciphertext letter always being substituted for a plaintext letter in the cipher: if this is not the case, deciphering the message is more difficult. For many years, cryptographers attempted to hide the telltale frequencies by using several different substitutions for common letters, but this technique was unable to fully hide patterns in the substitutions for plaintext letters. Such schemes were being widely broken by the 16th century.

In the mid-15th century, a new technique was invented by Alberti, now known generally as polyalphabetic ciphers, which recognised the virtue of using more than a single substitution alphabet; he also invented a simple technique for "creating" a multitude of substitution patterns for use in a message. Two parties exchanged a small amount of information (referred to as the key) and used it to create many substitution alphabets, and so many different substitutions for each plaintext letter over the course of a single plaintext. The idea is simple and effective, but proved more difficult to use than might have been expected. Many ciphers were only partial implementations of Alberti's, and so were easier to break than they might have been (e.g. the Vigenère cipher).

Not until the 1840s (Babbage) was any technique known which could reliably break any of the polyalphabetic ciphers. His technique also looked for repeating patterns in the ciphertext, which provide clues about the length of the key. Once this is known, the message essentially becomes a series of messages, each as long as the length of the key, to which normal frequency analysis can be applied. Charles Babbage, Friedrich Kasiski, and William F. Friedman are among those who did most to develop these techniques.

Cipher designers tried to get users to use a different substitution for every letter, but this usually meant a very long key, which was a problem in several ways. A long key takes longer to convey (securely) to the parties who need it, and so mistakes are more likely in key distribution. Also, many users do not have the patience to carry out lengthy, letter perfect evolutions, and certainly not under time pressure or battlefield stress. The 'ultimate' cipher of this type would be one in which such a 'long' key could be generated from a simple pattern (ideally automatically), producing a cipher in which there are so many substitution alphabets that frequency counting and statistical attacks would be effectively impossible. Enigma, and the rotor machines generally, were just what was needed since they were seriously polyalphabetic, using a different substitution alphabet for each letter of plaintext, and automatic, requiring no extraordinary abilities from their users. Their messages were, generally, much harder to break than any previous ciphers.