A cipher changes the letters of the message so that, without the key, the letters are meaningless.

To transpose something is to move it by a fixed amount.

In music, one may transpose music in the key of F to the key of G. Each note is moved by a fixed amount (i.e., one tone).

Example: Transpose the notes C E G A G down a minor third.

The result is A C# D# E D#.

The simplest transposition cipher, called a shift cipher, moves each letter by a fixed amount. What is the pattern in the following?

Each letter in the word SAVANNAH is moved forward one position, or backward one position. This can be seen in the following, written vertically instead of horizontally.

Obviously there are 26 ways to do this. The plain text SAVANNAH is one way. There are then 26-1=25 other ways to encrypt.

Historical note: In the classic movie, "2001: A Space Odyssey", the computer named "HAL" is, by transposing one letter, "IBM".

A Caesar cipher was done by wrapping a long strip of paper around a stick or pole, and then writing the message across the wrapped paper.

A substitute is something used in place of something else.

A substitute teacher teaches in place of the regular teacher.

In a sports game, one player may substitute for another player, subject to the rules of the game.

Math substitution:

let f(x) = 2*x+1

What is f(3)?

If f(x) = 2*x+1, then, to determine f(3), substitute 3 for x it 2*x+1 and simplify/reduce 2*3+1 to 7.

A substitution cipher is a cipher replaces every letter with some other letter.

• A = 1
• B = 2
• C = 3
• D = 4
• ... and so on ...

A simple substitution cipher using 26 letters and no spaces would have 26! possibilities.

Here is a Python program to compute 26! = 26*25*24*...*3*2*1.

Here is the output.

Formatted, this is 15,511,210,043,330,985,984,000,000, a very big number indeed.