A Survey of Mathematics Related Topics: Pg. 502, The Enigma

This activity allows the user to see how modular arithmetic has been used for years as a means of encoding messages. The letters of the alphabet are coded as:

A   B   C   D   ...   Z

0   1   2   3   ...   25

and then the numbers are changed via an affine (linear) transformation to new, coded numbers. The coding function has the form:

where X is the uncoded number, A and B are constants (known to allies, but unknown to enemies) and Y is the calculated, coded number. The arithmetic is done mod 26 to ensure that we get numbers back that can be translated into letters before sending the coded message.

This method of coding messages is ancient. In fact, Caesar is said to have used the cipher with A = 1 and B = 3. This method of coding is fun to play with, but easy to crack, as can be seen from this activity.

Modern coding techniques still make use of modular arithmetic, but in a highly sophisticated way.