Figure 1. The operation of the full Enigma machine.
Gary J. Shannon
(Also take a look at The Slide Rule Cipher and The Game Tile Cipher)
There are three variations on the Enigma machine that you can build; the Enigma, the Mini-Enigma and the Micro Enigma. These pages will demonstrate three different construction techniques on these three different machines, although any one of the machines could be constructed using any one of the techniques. This page will detail the construction of the full Enigma machine from scratch entirely from lightweight cardboard of the kind used for the backing board of a tablet of writing paper.
This is the most difficult of the three machines to build and operate, but when completed it will produce coded messages in a way that is functionally identical to the original Enigma machine. The original Enigma machine was electromechanical but the machine we will build is entirely manual. Where the original used wires inside rotors to connect different points of the alphabet we will use pairs of alphabets written on the outside of each rotor to accomplish the same end result.
The full Enigma consists of an input/out strip, three rotors and a reflector. ( The mini-Enigma uses two rotors and no reflector while the micro-Enigma uses only one rotor and no reflector, producing what is essentially a Vinegere machine.) The Enigma is operated by locating the cleartext letter on the input/output strip, following a circuitous course down through the rotors, bouncing off the reflector, and following another circuitous path back to the input/output strip where the ciphertext letter is read off. Here's what the process looks like:
Figure 1. The operation of the full Enigma machine.
The figure shows the four alphabet strips of the Enigma rotors as they would appear if unwrapped from the cylindrical rotors. The top row is the input/output alphabet. The middle three rows, each consisting of two mixed alphabets, are the rotors. The bottom row, also holding two mixed alphabets, is the reflector. In this example, the encoding of the cleartext letter 'E' is explained. It looks a good deal more complicated than it really is, and with a little practise it goes very quickly. You will just repeat the same steps over and over for each rotor from top to bottom and them back to the top. Follow the red lines down to the reflector, and the blues lines back up to the output.
Before we encode the next cleartext letter, however, we work the magic that made the Enigma famously difficult to crack. We turn the top rotor by one letter position to the right. The rotors look like figure 2 after this simple move. Notice how the cleartext letter 'E' now follows an entirely different path through the machine to be encoded as ciphertext 'O'.
Figure 2. The same cleartext letter encoded after one move of the top rotor.
After each letter is encoded the top rotor is moved one letter to the right. However, when this rotor returns to its starting position the second rotor down is moved one letter to the right. And, like the digits on an automobile odometer, when the second rotor finally returns to its starting position, the third rotor is turned by one letter position. In this way 26 X 26 X 26 = 17,576 different substitution alphabets are used over time.
Constructing Enigma
The top, input/output band remains fixed, and the so does the bottom reflector band. In the cardboard version of the machine the rotors are cylindrical bands of cardboard stacked on a cylindrical barrel that holds them in place while permitting them to rotate. Construction begins with the letter strips themselves. Rather than try to make precise measurements it works out better to start with the alphabet strips on paper and cut all the other parts to match those strips.
Here is a full-size image you can print to make all the necessary alphabet strips, or you can design and print one of your own, or you can write the letter strips by hand on a piece of graph paper.
Figure 3. Full-size alphabet strips.
Building in Cardboard
To begin with, working with cardboard, paper and glue takes a bit of practise. You may want to print two copies of the alphabet strips since it is very likely you will mess up the first one or two rotors you try to build. But be patient. Your cardboard construction technique will improve with practise and by the time you've completed the final rotor you'll wonder what all the fuss was about back when you messed up that first rotor. Like anything else, it's easy when you know how to do it.
When gluing pieces together it helps to put a bit of white glue on the first piece and then use a small piece of scrap cardboard like a trowel to spread the glue thin so it doesn't leave globs and blobs between the pieces.
Building the Rotors
Each alphabet strip is cut out and glued to a strip of cardboard. Figure 4 shows an alphabet strip and its cardboard strip ready to be glued together. Don't fuss over cutting the cardboard strip accurately at this stage. Later, after the glue has dried, we'll trim the cardboard to its proper size. Just be sure it's a bit larger than the paper alphabet strip on all four edges. The illustrations show an earlier black and white version of the alphabet strips. The second alphabet on each rotor was changed to red to make it easier to spot which alphabet you are working with at each step.
Figure 4. Ready to glue the alphabet to cardboard.
Once the alphabet is glued to the cardboard strip wrap the strip around a conveniently sized bottle, jar, or can and hold it in place with a rubber band. Set the rotor aside to dry thoroughly.
Figure 5. The strip left to dry.
The next step is to turn the strip into a cylindrical rotor. First trim the cardboard with scissors to match the paper alphabet strip, getting rid of the excess width and length. Next cut a slightly oversized strip of cardboard and glue to one end of the the strip as shown in figure 6.
Figure 6. ready to connect the ends.
After the glue has dried, glue the other end of the strip to this joint piece, being careful to align the matching ends squarely. At this point our rotor won't be very round because of the tendency of the cardboard to buckle and bend rather than curve neatly. Notice how lopsided the loop looks in figure 7 as compared to a couple of finished rotors. Don't worry about that just yet. As we add a few more layers of cardboard to the inside of the rotor it will take on a nice rigid cylindrical shape.
Figure 7. The rotor strip is joined.
Next, cut another strip of cardboard to fit just inside the band. Cut it so that the ends are flush with the ends of the joining piece already inside the rotor. Don't let this new strip overlap the existing joining piece because that will make the layer too thick at that point and it won't fit properly onto the drum later on. It helps to wrap the fresh cardboard strip tightly around a small bottle or other cylindrical object to give a bit of a natural curve making it a little easier to get it to conform to the inside of the rotor. Cut it carefully, and double check the fit before putting glue on the strip. The time to find out that the piece doesn't fit is while it's still clean and dry, not when it smeared with sticky glue! By the way, it's perfectly okay for the inner strip to be a little short, leaving a slight gap where it comes back around, but don't let it be too long so that the ends overlap. Notice how this additional piece on the inside distributes the stress on the cardboard and brings it a bit closer to the round shape we are aiming for.
Figure 8. Adding the first inside layer to make it more round.
Once this second layer is glued in place and thoroughly dried we will trim the inner cardboard strip to match the outer strip. This is a tricky operation requiring a special tool that is indispensable in the cardboard machine shop; the large, square-ended toenail clipper. (A small diagonal wire clipper also works quite well, but I prefer the toenail clipper.) Scissors and knives work fine on flat pieces, but not very well on cylinders. Do not try to trim the strip with scissors because that will not trim it close enough and may damage the edges of the strip. Also do not try to trim the strip with a hobby knife. Because of its awkward shape you will end up squashing the strip or cutting your finger, or both. First trim away all but about 1/8 inch of the inner strip with scissors, then trim the remainder with the toenail clipper or diagonal wire cutters. Figure 9 shows the proper way to trim the strip.
Figure 9. Using the clipper to trim the strip.
Don't bother trying this with a small fingernail clipper. It doesn't
work because of the curve of the cutting blade and the smallness of the opening
between the cutter blades.
Figure 10. The completed rotors, input/output, and reflector.
For convenience I will identify each double-alphabet strip by the letter
that falls under 'A' on the strip. The first rotor will be called
the A/D rotor, the second is the A/B rotor, the third is the
A/S rotor and the reflector is the A/J strip. You can
place these rotors in any order you like, making your machine unique, but
I will place them is the specified order for consistency, and to enable you,
if you like, to use your completed Enigma machine to decode the message at
the bottom of this page. If you use different mixed alphabets on your
rotors, or if you assemble your rotors in a different order you will not
be able to decode the message on this page. You may change the alphabets
or the order of the rotors any way you like, but remember that in order to
exchange messages using the Enigma both the sender and receiver must have
identical Enigma machines and set all three rotors in identical starting
positions.
Building the Barrel
There are two different ways the rotors might be mounted together to allow
them to turn. The first is to place them over a slightly smaller cylinder
or barrel that they fit snugly over. The second method would be to
glue a cardboard cap on both ends of each rotor and put holes in the caps
to fit a wooden dowel that is then threaded through the rotors like stringing
beads. For this project I'll use the former method because it is more
durable than using a dowel. It also avoids the problem of dowel holes
that are not perfectly aligned and centered causing the rotors to wobble
out of alignment during use.
The build the barrel begin with a piece of cardboard long enough to make
a complete circle inside the rotors and about half an inch taller than the
height of all the rotors, reflector, and input/out stacked up together.
Roll this piece up lengthwise to form a crude cylinder and place it
inside two of the rotors, which are only being used to hold it in place at
this time. Mark where the ends come together and cut the piece to length
so that it makes on full circle, without overlap, inside the rotors.
Figure 11 shows the piece cut, but not yet glues together. Again,
it helps to roll the piece around something cylindrical, but smaller than
the desired diameter, to give the piece a bit of natural curve.
Figure 11. Starting the barrel.
Notice again that a small gap where the ends come together is preferable
to any overlap. Now cut a narrow strip that will be glued inside the
barrel to hold it in its cylindrical form. At this point don't worry
about the exact height of the barrel, it will be trimmed to fit later.
Figure 12. A joiner strip to glue the barrel into shape.
When gluing in the joiner strip be sure that glue doesn't squeeze through
the gap in the barrel and glue the rotors to the barrel. To be sure
you can move the rotors around a bit while the glue is still wet. Even
if a little glue leaks through if you keep the rotors moving the glue won't
set on them and they will stay free.
Once the glue has dried on the joiner strip we are ready to mount the reflector.
Now locate the A/J rotor (the one that has 'A' above
'J'). This rotor is actually the reflector. Now we're
going to glue the reflector in place on the bottom of the barrel.
STOP! Before gluing the reflector rotor in place be sure you
have the correct rotor, and be sure you are gluing in place with the alphabets
upright as viewed with the reflector at the bottom of the barrel.
The reflector should be a fairly tight fit on the barrel. Once you've
tested the fit to be sure the reflector actually fits, spread a thin coat
of glue on the inside of the reflector rotor and slide it into place on the
bottom of the barrel. Don't worry about trying to get it even with
the bottom edge of the barrel as we will be trimming the barrel later.
Most of the glue will squeeze out but there should be enough left to
hold the rotor in place for now. If you are working on a web page while
assembling the barrel be careful not to get glue on the keyboard.
Once the reflector glue is dry use the toenail clipper to trim the bottom
of the barrel to match. At one point, where the joint is spliced, you'll
be cutting through two layers of cardboard so it might take a little more
muscle power to cut through. Once the bottom is flush with the reflector,
put the other three rotors and the input/output ring onto the barrel. Do
not glue anything in place yet. We are doing this only so that we can
trim the top of the barrell to match where the input/output strip will eventually
be when we do the final assembly. Make sure all the rotors are fairly
snug together as shown in figure 13, and trim the top of the barrel to match
the top of the input/output ring.
Figure 13. Ready to trim the top of the barrel.
Next we'll add the first reinforcing layer inside the barrel just like we
did with the rotors. As before, cut the piece so that it fits inside
the barrel without overlapping the splice, and glue it in place. You
may leave the rotors in place while you glue in the reinforcing layer, but
you should remove the input/output ring while gluing to avoid getting glue
on it. Trim this first reinforcing layer flush with the top and bottom
as before and then add a second reinforcing layer, for three layers in all.
Final Assembly
Before gluing anything more in place check each of the rotors to be sure
they turn freely and easily on the barrel. If a rotor is hard to turn
peal off a thin layer of cardboard from the inside of the rotor until it
turns easily. A stuck rotor will be impossible to repair once the whole
assembly is glued into place. Once you are satisfied that all the rotors
move freely, place the rotors onto the barrel as follows: The
A/D rotor goes first, just above the reflector. Next place the
A/B rotor, and finally the A/D rotor. Line up all three
rotors so the black 'A' of each is aligned with the black 'A'
on the reflector. This to help us align the input/output ring properly.
Next spread glue lightly on the inside of the input/output ring and slide
it into place on the barrel so that the 'A' on the input/output ring is aligned
directly above all the other A's. If this is not done carefully the
letters won't line up with each other when we begin to spin the rotors for
encoding and decoding. Be careful to prevent glue from getting under
the first rotor. Check to see that it still spins freely as you are
waiting for the top ring glue to dry.
Finally, we will add two end caps to the assembly to help give it strength
and give it a more finished look. Spread some glue around the bottom
edge of the assembly and push the glued assembly down onto a sheet of cardboard.
The set it aside to dry. Once it has dried trim around the edges
of the end cap. For added strength you can add a second layer to the
end caps. Finally, add an end cap to the top end. This completes
the assembly of the Enigma machine. Yours should look something like
this...
Figure 14. The completed Enigma machine.
And now, as promised, a message encoded with Enigma. First set all
the rotors so that the black A's all line up one above the other, and with
the A's on the reflector and the input/output ring. This is the initial
setup for this message. You can use any initial setup you wish, but
be sure to remember what your initial setup was because you will not be able
to decode the message without knowing the initial setup. This of it
as you Enigma password.
If you've built the Enigma according to directions you should be able to
decode the message below: There is one small difference, however, between
encoding and decoding a message. When you get to the reflector if you
are encoding you move down to the black letter on the reflector then find
the equivalent red letter and skip over the black row to the red row on rotor
one (review the diagrams above if this sounds confusing. Just remember,
the Germans meant it to be confusing!) If you are decoding,
however, when you get to the reflector you must jump over the black reflector
row to the red reflector row and then find the corresponding letter on the
black row and move upward from there. If you have built the Enigma
with the same mixed alphabets and assembled them in the same order you will
can set the rotors in the AAA position and decode the first 'J'
in the message as follows: (Follow along on your own Enigma to see how
it works.)
Don't forget to rotate the top rotor one letter to the right after decoding
each ciphertext letter.
Here's your secret message:
Thanks to Geoff Sullivan on sci.crypt for pointing me to
another paper Enigma Machine.
Thanks to David Hamer for pointing out one
technical inaccuracy
of my version of the Enigma Machine.
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