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Latest Articles

Enigma - Mechanization of Secrecy

Arrow Image Description of Enigma, how it works, a bit about its history, and how it was eventually broken! Enjoy!



------------------------------------------------------------------------------------
---- German Enigma Cypher -- The Mechanization of Secrecy ----
------------------------------------------------------------------------------------

------
Intro
------

Well as there is such a small amount of articles on encryption I decided to write one about the Enigma machine. Before I start

off I want to mention that most of the information I will use in this article came from an excellent Cryptography book "The Code

Book" by Simon Singh. I will start off with the mechanics of the Enigma, or how it is built and implemented, I will add links to

picture to help with the illustrations, as it is hard to describe a 3-dimensional scrambler in text, and I will then give a very

brief overview of how the Enigma was used up to and within WWII. I will then follow with how its code was broken, and how to

break such codes. With that said, let's get cracking! (pun intended :P)

----------
Mechanics
----------

An Enigma encoder is a complex machine compromised of Scramblers, a Reflector, a Plugboard, and a set of 26 Buttons and

lightbulbs, representing each letter of the alphabet. Depending on the specific model of the Enigma machine, the amount of

scramblers used varies(between 3 and 5), however I will concentrate on the more common 3-rotered Enigmas used by Germans prior to

and in the beginning of WWII.
Heres a picture of a typical Enigma machine http://www.linkparis.com/images/slideshow/A15.jpg

The scramblers will be set up much like an old analog clock. Each Scrambler has 26 connections, again, each representing a letter

of the english alphabet. Each individual Scrambler will also have a distinct internal wiring, Scrambling the letter differently

then the other two Scramblers. When a key is entered the first scrambler will rotate 1/26th of a rotation, or one letter,

essentially changing the way the next letter is encoded. Once the first scrambler reaches a full rotation, it will "tumble" the

second scrambler 1/26th of a rotation. This pattern will continue for 26x26x26 keys entered, then begin all over again. The

Scrambler order may be changed; one day, it might follow 123 pattern, while the next the day, they may be oriented as 312.

The Reflector adds to the scramblers by passing the signal back through the Scramblers in a reverse order. To attempt to

simplify: A user enters a key, it will move into the first Scrambler, that Scrambler will rotate, then the signal will enter the

second Scrambler, and move to the third Scrambler. Once it reaches the end of the third scrambler, it will enter the Reflector,

which will redirect it back into a different slot of the third scrambler, and continue the process back through to the first

scrambler where it will then light up the corresponding cypher letter. An example of how this process works can be seen here

http://www.ellsbury.com/enigma/fig_1-1_enigma.gif .

Lastly, we come to the Plugboard. The plugboard is simply a series of plugs that will switch letters. Plugging B and G for

example will switch every B for a G, and vice versa. In the standard Enigma machine the user would be supplied with 6 cables to

create 6 sets of swaps.

-----------------
The Possibilties
-----------------

With all these possible settings, the amount of initial setups rose remarkably. With 3 Scramblers, 6 Different Scrambler

orientations(123,132,213,231,312,321), there came out to be 26x26x26x6 = 105456 Unique combinations. Adding a plugboard with the

ability to swap 6 sets of letters out of 26 increments this number to upwards 10,000,000,000,000,000. As you can see it would be

practically impossible to decode a message not knowing those initial settings.

--------------
The Challenge
--------------

Now that the machines were up and running, the German government had to find a way to implement their capabilities. If the

receiver of an encoded message didn't know the initial settings the sender used, they could never decrypt the message in time for

the meaning to be useful. To counter this, the German government created a monthly book of "Daily settings". Each day the sender

would arrange the Scramblers and plugboard the way the book said, and when sent, the receiver would set his Enigma with the same

settings before decrypting. What would happen if the Allies got a copy of the book you ask? Well the Germans also thought of that

and created another measure of security(with good reason, hundreds of code manueals were intercepted in the duration of the war).

What the Germans did was that at the beginning of the sent message they would use a unique "message code", such as APB. They

would then encrypt the "message code" twice(APBAPB) for security and acuracy's sake, using that day's code from the book of

"Daily settings", Then after those 6 characters, they would reset the Scramblers to the "Message code" setting, in our case APB

and encode the rest of the message. Thus, when an encoded message would be received, the decoders would decode the first 6

characters using that day's "Daily Settings", then change the Scramblers to the designated state, and decrypt the rest of the

message. If an Ally were to come into possession of the "Daily Setting" key, yet did not know about the message key swap, one

would attempt to decode it only using the "Daily Setting" key, and the resulting message would be gibberish.

----------------
Cracking Enigma
----------------

Unfortunatly for the Germans, they believed their system to be completely uncrackable. As most of you know by now, every

encryption/encoding system will eventually be broken. The demise of the Enigma came at the hands of the Polish Mathematician

Marian Rejewski. Working out of the Biuro Szyfrow, the Polish Cypher bureau, Rejewski was handed hundreds of encoded messages a

day. Through espionage and captured documents, Rejewski knew about the "Daily Settings" and "Message Settings" and thefore

theorized that the repeated use of a "Daily Setting" would create a weakness in the encoding process. Rejewski then began to

catalog messages that he received each day. For example, on a certain day, he would receive 4 messages, each with the first 6

Letters as follows:

Message 1: L-O-K-R-G-M
Message 2: M-V-T-X-Z-E
Message 3: J-K-T-M-P-E
Message 4: D-V-Y-P-Z-X

In each message, we know they repeated the Message Setting twice. Therefor L and R are intimately related, using the "Daily

Setting". O & G, and K & M are also correlatively related. Given enough messages a day, Rejewski made a catalog of what letter

corresponded to which other letter. A completed example:

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
F-Q-H-P-L-W-O-G-B-M-V-R-X-U-Y-C-Z-I-T-N-J-E-A-S-D-K

He then made a crucial observation. That certain Chains would be created. That is, A > F > W > A. Given the example above, 4

chains of length 3, 9, 7, 7 would be created. The genius behind this observation is that these chains are INDEPENDENT of the

plugboard settings. Even if you switched letters around, the chains would be the same. This greatly reduces the task of finding

the "Daily Setting" from 10,000,000,000,000,000 to simply 105,456. This is much more realistic and therefore practically doable.

Rejewski then set off to catalog every possibility of those 105,456 settings and mark down the amount, and lenght of the Chains.

With this information, at the start of the day when Rejewski received messages, he would make a comparison chart as above, write

down the chains and their lenght, then check his catalog to find the exact Scrambler settings.

Although he had the Scrambler settings, there was still the Plugboard settings to deal with. However, compared with the Scrambler

settings this was relatively easy to break. One would simply set the Scramblers to the appropriate settings, and leave all of the

Plugs UNPLUGGED. Then, most of the message would probably be gibberish, however, occasionally we would come upon a string such as

"HEBBLOUND" in which we would assume B and L are swapped. We would set that Plug and continue the process until the message is

completely decoded!

------------------
Personal Cracking
------------------

To personally crack an Enigma cyphered message would be complicated to say the least. If your encoded message did not contain the

6 standard German Message Setting characters at the beginning of the message, then the only possible way would be to manually

check all 105,456 scrambler settings and check to see if there is at least some legible writting, all taking into consideration

we have not set any plugs on our Plugboard. The ideal situation is if we could acquire a copy of the "Catalog of Settings" that

Rejewski made (an aside, if anyone can find a copy somewhere, please let me know, and I'll add a link here), as well as having

multiple messages to write down a list of chains created by the settings.

-----------
Conclusion
-----------

Considering the initial success of the Enigma machine and the trouble that the Allies had in breaking tells us that this is a

somewhat good encoding system. The ultimate failure on the German side was the use of repeated settings and keys. Had they used

another way of distributing these keys, or simply found a way around that, the system would have been much more complex to crack,

and who knows, maybe the outcome of the war would not have turned out how it did? After all..."The pen is mightier then the

sword".

--A side note, this is mostly general information regarding Enigma, there were several variations of Enigma put to use, and which

each came a new set codes to be broken.

--A downloadable version of the Enigma machine is available at http://users.telenet.be/d.rijmenants/en/enigmasim.htm so by all

means download it and play around with how the Enigma works

--Thank you all for reading this article, hopefully I've cleared up a few areas about how the Enigma machine works, and how the

encoding works. Please feel free to let me know what you all think of this. Good night/morning/afternoon all!

Comments

lesserlightsofheavenon February 01 2008 - 04:34:57
good read, well written and explained. ;D
digitalchameleonon February 01 2008 - 05:35:49
Awesome article. Shame about the formatting. I disagree however when you say that it would be very difficult to crack an enigma encoded message in this day and age. One would simply need to make educated guesses about the plaintext. This article is an excellent example of how using a set protocol inside the message allows an attacker to determine plaintext, thus weakening any cryptosystem.
c4p_sl0ckon February 11 2008 - 21:25:55
Great article. Very interesting.
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