Simple Ciphers

Abstract

Until the computer age, making and breaking ciphers was a task that required extreme concentration and care. Search trees based on guesses can be programmed on computers and run at high speed, where we can use the computer’s speed and the ease of keeping track of the data in data structures to allow us not to care too much about following low probability paths. The cost in time and effort to search using pencil and paper would have demanded much better guesses as to the correct path down the tree. Cryptanalysis in the first half of the twentieth century required knowledge of language patterns and frequency statistics, and both encryption and decryption had to be processes that could easily be remembered and followed. In this chapter we will describe some classical ciphers (that would be easily attacked with a program running on a desktop computer) as well as some statistical characteristics of language that could be used to attack these now-outdated ciphers. There are two basic forms of simple cipher. In a substitution cipher , one substitutes for each letter in the underlying alphabet another symbol (perhaps a different letter in the same alphabet, or sometimes another symbol entirely). In a transposition cipher , the letters of the underlying alphabet remain the same, but their order is transposed into a different order. In this, one can take the term “letter” to mean a single letter or perhaps a pair of letters. We distinguish at the outset a codebook from a cipher, although the two can be closely related. Traditional codebooks were a form of making communications secret by substituting a fixed length (often five) sequence of numbers for each of the individual words in the message. One can think of such a codebook as a substitution cipher in which the symbols are words (of variable length, of course) for which one substitutes numerical symbols. We will also mention only briefly (right here) the notion of steganography, where a message is hidden in some seemingly innocuous communication. One version of this would be a letter in which the hidden message was the sequence of first letters of words of the text. A more modern reverse version of steganography is digital watermarking, in which a digital pattern is inserted into a document, usually an image document, so that the provenance of the image can be authenticated if it is illegally taken without attribution or royalty. This is not unlike the apparent inclusion of intentional errors in maps, say, so that the owner of the map’s copyright could argue that the map had been illegally copied. The author wishes very much that he had kept the road map of Louisiana (where he grew up) that showed a road south from Venice, Louisiana, and a bridge across the Mississippi to reach Pilottown. No such road or bridge has ever existed; Pilottown is where the Mississippi River pilots meet the incoming vessels and take the conn on the way up the river to the Port of New Orleans, and where on the outward voyage they turn over the conn to the seagoing pilots. The “city” can only be reached by water; there is no road south from Venice and no bridge across the Mississippi.