The Electromechanical Workings of the Enigma Machine
by
Ardill
The Enigma code, a cipher famed for its complexity, was used in World War II by the Germans to encrypt messages.[1] Though the complexity generated by this machine was huge (3 X 10114)[2], the mechanical system is relatively simple. It consists of a plugboard, three or four rotors, (depending on the version) and a reflector.[3]
Each rotor had an inner wiring, connecting every electrical contact on one side to a contact on the other.[4] Five (later eight) rotors of different wirings were available placed into the machine, but only three (later four) could be used at a time.[5] Rotors also had a notch on the left side, which controlled the rotational motion of the rotor on its left.[6] The ring setting on a rotor served two purposes: it allowed the positions of the contacts on one side to be changed relative to the position of those on the other side,[7] and it changed the position of the notch relative to the internal alphabet.[8] Because the outer alphabet moved with the notch, these two operations are the same,[9] and the second can be ignored, as the relativistic frame of the inner alphabet is not relevant to this paper. The first effect of the ring meant that encoding a letter with a ring setting of A at position A was equivalent to encoding that same letter with a ring setting of B at position B. The ring setting still caused an increase in complexity, as it does not change during a message, while the rotor position does.
The rotors were turned a moment before an electrical signal was transmitted through the rotors, reflector, and plugboard. The rightmost rotor would turn once for every key turn, but the others would only turn once for every revolution of the rotor to the right of it.[10] (Excepting, of course, the later-added fourth rotor, which was stationary.)[11]
[Image pending permission for use]
[12]
[Image pending permission for use]
[13]
[Image pending permission for use]
[14]
The reflector had a construction very similar to a rotor, with one major difference. Instead of allowing the signal to pass through, as the rotors did, it would redirect the signal to another contact on the receiving side, bouncing the signal back through the rotors.[15] (Thus the name “reflector”.) There were multiple reflectors used by the Germans, each with a different wiring.[16] A diagram of a sample reflector and three-rotor system is shown below. Note that it excludes the plugboard.
[Image pending permission for use]
[17]
The plugboard, or Steckerbrett, was a set of plugs that could be changed manually by the operator, connecting a pair of letters to each other.[18] If a letter was part of a pair, that letter would be changed to the other of its pair before it went through the rotors, and the letter resulting from the rotor path would also be transformed by the plugboard.[19] It was, in effect, “an easily modifiable stationary rotor to positioned the right of the three movable rotors.”[20]A major weakness in the plugboard was that one-way pairs were not possible. If A was connected to B, B was connected to A.[21] This is a major weakness, but without it, the Enigma would have been impossible for even the Germans to decode.
[Image pending permission for use]
[22]
An Enigma-encoded message could be decoded by re-encoding the ciphertext using the same settings through which it was initially encoded.[23] This is because the same electrical pathway that was traced by the encoding of a plaintext letter would be retraced (backwards) when the encoded letter was typed, lighting up the plaintext letter.[24] If a one-way plug had been used, the same output would be given by two different pathways with the same settings, meaning that the encoded letter was not uniquely defined for the settings, so it would be impossible to decode.
The Enigma had multiple factors for encryption, all of which contributed to electrically encode a message.[25] Because the rotors moved during a message, conventional techniques became useless.[26] The encoding also was decodable through re-encoding, a factor which significantly increased its allure, as a single machine could near-instantaneously encode and decode messages.[27]
Sources
Footnotes
[1] Wilcox, Jennifer, Solving the Enigma: History of the Cryptanalytic Bombe, (Fort Meade, MD, The Center for Cryptologic History of the National Security Agency, 2004), 1.
[2] Ibid.
[3] Ibid.
[4] Ibid.
[5] Ibid., 8.
[6] Ibid., 1.
[7] Miller, Dr. A Ray, The Cryptographic Mathematics of Enigma, (Fort Meade, MD, The Center for Cryptologic History of the National Security Agency, 20011), 17.
[8] Wilcox, 1.
[9] Miller, 17.
[10] Ibid., 11.
[11] Ibid., 18.
[12] Source: https://en.wikipedia.org/wiki/File:Enigma-rotor-flat-contacts.jpg
[13] Source: https://en.wikipedia.org/wiki/File:Enigma-rotor-pin-contacts.jpg
[14] Source: https://commons.wikimedia.org/wiki/File:Enigma_rotor_wiring.png
[15] Miller, 11.
[16] Ibid., 17.
[17] Source: https://web.stanford.edu/class/cs106j/handouts/36-TheEnigmaMachine.pdf
[18] Wilcox, 1.
[19] Ibid., 2.
[20] Miller, 8.
[21] Wilcox, 10.
[22] Source: https://commons.wikimedia.org/wiki/File:Enigma-plugboard.jpg
[23] Wilcox, 2.
[24] Ibid.
[25] Ibid., 1.
[26] Ibid., 2.
[27] Ibid., 2.
Each rotor had an inner wiring, connecting every electrical contact on one side to a contact on the other.[4] Five (later eight) rotors of different wirings were available placed into the machine, but only three (later four) could be used at a time.[5] Rotors also had a notch on the left side, which controlled the rotational motion of the rotor on its left.[6] The ring setting on a rotor served two purposes: it allowed the positions of the contacts on one side to be changed relative to the position of those on the other side,[7] and it changed the position of the notch relative to the internal alphabet.[8] Because the outer alphabet moved with the notch, these two operations are the same,[9] and the second can be ignored, as the relativistic frame of the inner alphabet is not relevant to this paper. The first effect of the ring meant that encoding a letter with a ring setting of A at position A was equivalent to encoding that same letter with a ring setting of B at position B. The ring setting still caused an increase in complexity, as it does not change during a message, while the rotor position does.
The rotors were turned a moment before an electrical signal was transmitted through the rotors, reflector, and plugboard. The rightmost rotor would turn once for every key turn, but the others would only turn once for every revolution of the rotor to the right of it.[10] (Excepting, of course, the later-added fourth rotor, which was stationary.)[11]
[Image pending permission for use]
[12]
[Image pending permission for use]
[13]
[Image pending permission for use]
[14]
The reflector had a construction very similar to a rotor, with one major difference. Instead of allowing the signal to pass through, as the rotors did, it would redirect the signal to another contact on the receiving side, bouncing the signal back through the rotors.[15] (Thus the name “reflector”.) There were multiple reflectors used by the Germans, each with a different wiring.[16] A diagram of a sample reflector and three-rotor system is shown below. Note that it excludes the plugboard.
[Image pending permission for use]
[17]
The plugboard, or Steckerbrett, was a set of plugs that could be changed manually by the operator, connecting a pair of letters to each other.[18] If a letter was part of a pair, that letter would be changed to the other of its pair before it went through the rotors, and the letter resulting from the rotor path would also be transformed by the plugboard.[19] It was, in effect, “an easily modifiable stationary rotor to positioned the right of the three movable rotors.”[20]A major weakness in the plugboard was that one-way pairs were not possible. If A was connected to B, B was connected to A.[21] This is a major weakness, but without it, the Enigma would have been impossible for even the Germans to decode.
[Image pending permission for use]
[22]
An Enigma-encoded message could be decoded by re-encoding the ciphertext using the same settings through which it was initially encoded.[23] This is because the same electrical pathway that was traced by the encoding of a plaintext letter would be retraced (backwards) when the encoded letter was typed, lighting up the plaintext letter.[24] If a one-way plug had been used, the same output would be given by two different pathways with the same settings, meaning that the encoded letter was not uniquely defined for the settings, so it would be impossible to decode.
The Enigma had multiple factors for encryption, all of which contributed to electrically encode a message.[25] Because the rotors moved during a message, conventional techniques became useless.[26] The encoding also was decodable through re-encoding, a factor which significantly increased its allure, as a single machine could near-instantaneously encode and decode messages.[27]
Sources
- Miller, A. Ray. The Cryptographic Mathematics of Enigma. Fort Meade, MD: The Center for Cryptologic History of the National Security Agency, 2011.
- Willcox, Jennifer. Solving the Enigma: History of the Cryptanalytic Bombe. Fort Meade, MD: The Center for Cryptologic History of the National Security Agency, 2004.
Footnotes
[1] Wilcox, Jennifer, Solving the Enigma: History of the Cryptanalytic Bombe, (Fort Meade, MD, The Center for Cryptologic History of the National Security Agency, 2004), 1.
[2] Ibid.
[3] Ibid.
[4] Ibid.
[5] Ibid., 8.
[6] Ibid., 1.
[7] Miller, Dr. A Ray, The Cryptographic Mathematics of Enigma, (Fort Meade, MD, The Center for Cryptologic History of the National Security Agency, 20011), 17.
[8] Wilcox, 1.
[9] Miller, 17.
[10] Ibid., 11.
[11] Ibid., 18.
[12] Source: https://en.wikipedia.org/wiki/File:Enigma-rotor-flat-contacts.jpg
[13] Source: https://en.wikipedia.org/wiki/File:Enigma-rotor-pin-contacts.jpg
[14] Source: https://commons.wikimedia.org/wiki/File:Enigma_rotor_wiring.png
[15] Miller, 11.
[16] Ibid., 17.
[17] Source: https://web.stanford.edu/class/cs106j/handouts/36-TheEnigmaMachine.pdf
[18] Wilcox, 1.
[19] Ibid., 2.
[20] Miller, 8.
[21] Wilcox, 10.
[22] Source: https://commons.wikimedia.org/wiki/File:Enigma-plugboard.jpg
[23] Wilcox, 2.
[24] Ibid.
[25] Ibid., 1.
[26] Ibid., 2.
[27] Ibid., 2.