In geometric (or route) transposition systems, the 'smushed' together plaintext is placed in a geometrical pattern (usually a rectangular grid, but it could be a triangle, etc.) that will adequately fit the message. Then, one creates the ciphertext by following a route through the grid (up and down, left and right, diagonal). The ciphertext can be decoded by making a similar sized grid and placing the letters back into it by using the route that took them out. There are three general steps to remember:
1) The size and the shape of the geometrical pattern used
2) The starting place and route for placing text inside the pattern
3) The starting place and route for creating the ciphertext
An example will help illustrate how to encipher text using this type of transposition. Since a rectangular grid is easiest to learn from, we'll use it in our example. But, how do you know how big to make it? The first thing to do is count the number of characters in your message to determine how many units you will need in your grid. We will be enciphering the following message:
plaintext: line up alphabetically according to your height - Casey Stengel
This message contains 41 characters, so we need a grid with at least 41 spaces. We can therefore use several types, like a 4 by 11, or 6 by 8 grid, and add the necessary amount of nulls to the end so that the entire grid will be filled. The figure that we choose (a 6 by 8 grid) is shown to the right.
Next, we inscribe the plaintext of the message into the grid by simply adding it from left to right. More elaborate ways can be devised, but this serves the purpose.
Next, you must determine a route through the grid to create the ciphertext. One of the more interesting routes is the spiral, in which one starts at a specified corner and goes along the edge, working towards the center. To create the ciphertext, one just reads off each letter following the route. The grid below uses a clockwise spiral starting at the top left corner. Place your mouse over the grid to see the animation.
plaintext: line up alphabetically according to your height
ciphertext: lineupalcoyhgawpfoztoraphabeticogiehrudllyactgni
ciphertext (grouped): lin eup alc oyh gaw pfo zto rap hab eti cog ieh rud lly act gni
To decipher the text, the recipient simply creates a grid of the same size, and adds the ciphertext into the grid following the same route. Once the text is inside the grid, he can remove it using the opposite procedure used to place it in the grid. Now, if you're very observant, you probably noticed that the ciphertext at times contains bits of plaintext (notice: "lineup" and "phabetic"). This was caused by a bad inscribing/route combination. We included this error to illustrate the importance of choosing complementary methods that do not produce these types of errors. A better route than the spiral would have been one in which the text was taken out from the columns, avoiding any left to right movement that mirror the way the text was placed inside the message.
It is vital that the both the sender and receiver both understand each aspect of the encipherment so that the procedures can be reversed for decipherment. The size of the grid, method for inscribing the text into the grid and also the route for creating the ciphertext must all be predetermined before use.
In addition to the geometric/route transposition, column transposition is also very useful.
