The perfect cipher

Abstract

The history of cryptography is punctuated by the invention of clever systems to encipher messages and, sometime later, equally clever systems for cryptanalysing the enciphered messages to determine their meaning. Most enciphering schemes of any worth enjoy a relatively lengthy period of prominence before sufficiently determined cryptanalysts undermine their security by figuring out how to attack them. In response, cryptographers devise new and improved schemes and then the cycle repeats. Cryptographers have learned from history that it is dangerous to declare any enciphering scheme unbreakable; at best they are considered to be very secure. But there is one scheme, a scheme that has been around since 1917, that truly is unbreakable. It is the perfect cipher.

Cryptography based on algebraic perpendicularities

“…Not all maximal perpendicularities in arise by only choosing and , but there are maximal perpendicularities of another kind, too [4]. The existence of various types of maximal perpendicularities makes the scheme more secure because the finding of the correct perpendicularity becomes more difficult for the 'enemy'.…”

“…To learn more about them, the reader can consult the articles [2,3] listed at the end of this paper. The reference list also contains a couple of articles published in the Gazette which serve well as an introduction to the basics of cryptography [1,4].…”

I, Claudius and the cipher extraordinary

“…I therefore thought it would be worthwhile to write a short article to draw attention to what is perhaps not a particularly well-known cipher appearing in fiction. I will assume that the reader is familiar with the principle behind the famous Vigenere cipher (see [2] or [3]).…”

“…We note that the Vigenere square is more usually taken with mij = e;+}, but this is a matter of convention, and any Latin square would suffice (since it is the method of the Vigenere cipher that is important, rather than the order of the letters), although it makes sense to choose one that is defined by a simple rule. We note that the squares adopted in [2] and [3], for example, do in fact differ: Singh takes mij = e; +}, whilst Lewand takes mij = ei+ji-We adopt the above form for simplicity-it is very easy to see that this operates in exactly the same manner as the 'standard' Vigenere square-it is easy to get from one to the other. For us to use the 'standard' square would make the mathematics hereafter a little more complicated than it needs to be.…”