Enigma/Paper Enigma

Although the Enigma cipher as a whole is quite complex (it's complexity is comparable to modern cryptographic algorithms) the individual transformations making it up are relatively simple. In fact they are simple enough that enciphering an Enigma message can be done with just a paper model.

Our model is three-dimensional, so as to illustrate how a real Enigma machine is wired, needs only common household items to construct, and is completely compatible with all settings of a real Enigma machine (models I, M1, M2 and M3).

Materials Needed

You will need these PDF templates printed on to 2 A4 sheets of paper (make sure you turn off any "scaling" options in your printer software so that it is printed at the exact size required), a crisp tube (75mm in diameter and at least 235mm long), clear sticky tape and a pair of scissors.

Using low-tack "removable" sticky tape can make it easier to swap round and reuse the rotors if you want to do that, but it's not essential.

Assembling the Basic Enigma

You can start off with the basic Enigma machine (using three rotors with ring settings of 01 01 01) using just the 5 pieces shaded in this diagram:

You will fasten these round the crisp tube in this order, from left to right:

Reflector B, Rotor I, Rotor II, Rotor III, Input/Output

To fasten each piece, apply some sticky tape to the square end, with half the tape overlapping like this:

Now, starting with the rounded end, wrap the paper piece around the tube and stick it to itself, covering the rounded end.

Wrap the reflector and input/output pieces tightly as you don't want those to move during your enciphering; if you put the rotor pieces on a bit looser they will be easier to turn as required.

You should end up with something looking like this:

Using the Basic Enigma

Set up

• Make sure that the grey bars on the Reflector and the Input/Output cylinders are lined up; this shows the start position of your Enigma machine and lets you track the turnover positions of the rotors.
• Turn the rotors so that the three letters of your message key are in line with the grey bars; for practice use A B C.

For each letter in your message

• Turn just the right-hand rotor one step towards you (so the letter in line with the grey bar becomes the next one alphabetically); make sure that the other rotors and the Input/Output cylinder stay still. You must do this before you read off the letter.
• Find the letter from your message on the Input/Output cylinder, and trace the line from it through all three rotors, in to the reflector, out again back through all three rotors and into the Input/Output cylinder again. Write down the letter you ended up at.

For practice, try this message:

A E F A E  J X X B N  X Y J T Y

If you got it right, you should have written down one correct English word!

Rotor Turnover

When the right-hand rotor turns one step, at some positions other rotors turn over as well, which makes the scrambling harder to predict. In the example above we chose the message key A B C with a short message so that no turnovers occurred.

To accurately handle turnover, we need to add to our instructions above for turning the rotors, based on the letters showing in line with the grey bars:

• If the letter on the middle rotor is shaded grey, turn all three rotors one step towards you
• otherwise, if the letter on the right-hand rotor is shaded grey, turn the middle and right-hand rotors one step towards you
• otherwise, turn just the right-hand rotor one step towards you.

Notice that the shading of the letter on the left-hand rotor doesn't matter; it would only come in to play if that rotor was in a different place in the order.

For practice, try deciphering this message with the rotors in the same order as our basic example above (I, II, III) and with message key A B R:

M A B E K  G Z X S G

When you've finished, you should have written down two correct English words, and your rotors should finish at positions A C B.

Double Stepping

Because of the above turnover rules, if the middle rotor steps so that its shaded letter moves into the start position, it must step again (along with the other two rotors) when the next letter in the message is processed. This is called the "double stepping" behaviour and is often misunderstood. To try this for yourself, use rotors I, II and III with message key A D S to decipher this message:

R Z F O G  F Y H P L

You should end up with two correct English words, and your rotors at positions B F C.

Ring Settings

On a real Enigma machine, the position of the letters (and the turnover points) on each rotor could be changed by pressing out a pin and rotating the outer ring relative to the position of the wiring inside the rotor. This was part of the machine settings that were changed on a daily basis, making the messages harder to crack.

You can represent ring settings on our paper model by cutting out the ring templates, shaded in this diagram:

Note that the rings for rotors II, III, IV and V are printed in two parts due to lack of space on the page; you may find it easiest to tape the two halves together as a block (so the letter N on each ring joins on to letter M on its other half) before separating the individual rings.

Keeping the rotors I, II and III that you put on for the basic machine, put rings I, II and III over the top of the letters on the rotor, just taping the ring to itself so it can still move over the top of the rotor; make it fairly snug so it stays in the same place relative to the rotor when the rotor is turned.

You apply the ring settings by turning the ring around the rotor so that the setting letter is covering the letter A on the rotor underneath (you can move the ring sideways over the rotor temporarily to see what's underneath). The ring settings are often given as numbers, so the letter to cover A for each setting is as follows:

Ring setting	01	02	03	04	05	06	07	08	09	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26
Letter	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z

Using rotors I, II and III as before, place the ring settings at 10, 14 and 21. Then turn the rotors to set the message key to X Y Z (the letters showing on the rings, not the letters underneath them) and decipher the following message:

Q K T P E  B Z I U K

As before, the result should be two correct English words.

The Plug Board

The final component that we need to be fully compatible with a real German army Enigma machine is the plug board. This was added when the German military adapted the commercial version of the Enigma machine for their own use, and it improves the security a lot. There are 26 sockets on the front of the machine (one for each letter) which can be connected together in pairs with jumper cables. If a letter has no connection to it, it is passed through unchanged. Any two letters connected together are swapped round before being passed through the machine and then swapped back again for output. Different numbers of connections were used at different times, but later they standardised on 10.

To represent this in our model, we need to write in the jumpered letters on our input/output cylinder. If you use a pencil you can rub them out afterwards and reuse the cylinder (it helps if you used matte-finish sticky tape as that's easy to write on and rub out). For each letter that is jumpered, write the paired letter in next to it. For example, if D and Q are paired, write D next to Q, and Q next to D. Do this for all the jumpered pairs, and then for the rest of letters which have no plugs in, write the letter next to itself.

The enciphering and deciphering process is the same as before, except you start tracing the line from where you wrote the letter from your message, and you read off the letter you wrote at the place where you finish tracing the line.

To try this out, write in the plug board settings for these 10 pairs:

AP BR CM FZ GJ IL NT OV QS WX

Using rotors I, II and III with ring settings 10, 14 and 21 from our previous example and message key V Q Q decipher the following:

H A B H V  H L Y D F  N A D Z Y

Your result should be four English words and your rotors should finish at positions V R F.

Acknowledgements

Alan Turing, in his World War II Treatise on the Enigma described a model using what he called Comic Strips. Each rotor is represented by a separate slip of paper which is slid across a flat sheet of paper representing the fixed parts of the machine. Turing's model can be used to encipher any message with exactly the same results as a real Enigma machine.

In 2003, Mike Koss published a simplified Comic Strips model. In 2004, Gary Shannon independently developed a model using cardboard cylinders. Neither of those models included ring settings, and Gary Shannon's model didn't include rotor turnover points, so they are not completely compatible with the real thing.

UK company Mindsets sells an Enigma kit consisting of cut-out-and-glue paper cylinders wrapping around pieces of drainpipe. Although this form factor is very useful for teaching people about the operation of a real Enigma machine, their design is not at all compatible with one, as there is no reflector and the rotor connections are shorter than the real thing.