The cracking of Enigma in World War II

1. The cracking of Enigmain World War II CS 4235 Project 1: Security Events - Threats and Vulnerabilities John Bibb Harry Caplan Abhishek Chhikara Vladimir Grantcharov Aditi Kulkarni Nigel Lawrence Andrew Muldowney Hou Nguyen Sofia Tania

2. What is Enigma? • rotor machine used for the encryption and decryption of secret messages • Developed in early 1920s • Combination of mechanical and electrical subsystems • Keyboard • Rotating disks (“rotors”) • display lamps

3. What happened?

4. Cracking the Enigma • Enigma has so many possibilities, that an important aspect of breaking them, is deducing their logical structure. • Enigma generated a polyalphabetic substitution cipher with a long period. Given three single-notched rotors, the period was 16,900 (= 26 × 25 × 26).[7] • A letter could never be encrypted to itself. This property was of great help in using cribs and could be used to eliminate a crib in a particular position. It was this feature that the British mathematician and logician Alan Turing would exploit in designing the British bombe. • A second Enigma weakness was that the plugboard connections were reciprocal, so that if A was plugged to N, then N likewise became A. • A number of the officially-specified procedures for using Enigma also provided avenues for attack. Thus, for machines where there was a choice of more rotors than there were slots for them, a rule stipulated that no rotor should be in the same slot in the scrambler as it had been for the immediately preceding configuration. Also, no wheel order could be repeated on the monthly setting sheet. • It has been suggested by some who worked at breaking Enigma at Bletchley Park that the Enigma should have been unbreakable in practice, had its operating procedures been better thought out and had its operators been less ill-disciplined. • http://upload.wikimedia.org/wikipedia/commons/6/6c/Enigma-action.svg • http://enigmaco.de/enigma/enigma.swf Working Model

5. Bomba • Designed about October 1938 by Polish Cipher Bureau : Bomba • Each bomb essentially constituted an electrically-powered aggregate of six Enigmas and took the place of some one hundred workers • Using the knowledge that the first three letters of a message were the same as the second three, Polish mathematician–cryptologist Marian Rejewski was able to determine the internal wirings of the Enigma machine and thus to reconstruct the logical structure of the device. • In mid-November 1938 the bombs were ready, and the reconstructing of daily keys now took about two hours. • Up to July 25, 1939, the Poles had been breaking Enigma messages for over six and a half years without telling their French and British allies.

6. Bombe • On December 15, 1938, two new rotors were introduced. • Creator of Bomba: "we quickly found the [wirings] within the [new rotors], but [their] introduction...raised the number of possible sequences of drums from 6 to 60...and hence also raised tenfold the work of finding the keys. Thus the change was not qualitative but quantitative. • A bombe would consist of a number of these sets of rotors wired up according to a menu prepared by codebreakers. At each position of the rotors, an electrical test would be applied. For a large number of the settings, the test would lead to a logical contradiction, ruling out that setting. If the test did not lead to a logical contradiction, the machine would stop and ring a bell, and the candidate solution would be examined further, typically on a replica of the German Enigma machine, to see if that decryption produced German. Typically, there were many false matches before the correct match was found. • Designed by Alan Turing • Eventually over 200 Built by both • US and British Forces • Also built to contend with late model • 4 rotor Enigmas

7. What was the impact?

8. Impact • Germans thought ‘Enigma’ unbreakable • Used for all top secret communication • Dutch Idea -> German Spy -> French Spymasters -> British + French + Polish Efforts -> Breakthrough by Poland -> Later Britain • From 1933 – 1940 • Marginal Impact

9. The Breakthrough • Year 1941 & beyond • Allies detected German round-up near Greece • Allies’ Mediterranean fleet defeated the Italians at the Battle of Matapan • Allies gained important advantage in North Africa • German U-Boat program brought to standstill • 90% European Intelligence summaries provided to US based on Enigma • Larger context – “Information is Power”

10. Repercussions Undermined Axis offensive May have ended the war early Contributed to the eventual Allied victory

11. Why did this attack succeed?

12. Elements of Enigma Plaintext Algorithm Key It takes all three elements to perform the decryption.

13. Getting The Plaintext Infrastructure – ‘Y’ stations

14. Getting The Algorithm Marian Rejewski Photo from Wikipedia The role of mathematicians

15. Getting The Key The role of mathematicians

16. Getting The Key Clues based on patterns in messages • Opening • “Spruchnummer” (Message Number) • “An die Gruppe” (To the group) – Air Force messages • Content • Weather reports • “Keinebesondere Ereignisse” (Nothing to report) Duplicate messages

17. What happened inthe aftermath?

18. Perspective of Nazis • After the code was broken, the Nazis were unwilling to see the evidence of it as a breaking of the code rather, they assumed that the British simply had exceptional spies who were leaking information. Thus they concentrated their efforts on finding these spies, instead of adapting their code further. http://cultureandcommunication.org/deadmedia/index.php/Enigma_machine#Aftermath

19. Consequences • Hitler postponed invasion of Britain until spring 1941, after a failed invasion in Oct 1940.

20. Significance of Codebreak • It is estimated that the success of the efforts to code break the German Enigma machine helped The Allies defeat Nazi Germany two years earlier than they would without it. This saved countless lives, and making it one of the most successful intelligence operations in history.

21. Popularity of the Event • The Enigma intercepts came to be known by the codename ULTRA and while they were perhaps not directly responsible for winning the war as sometimes credited, the information provided by the Bletchley Park cryptanalysts certainly shortened the war and saved many lives.

22. What was done tomake systems less vulnerable to thiskind of threat?

23. Modification Before WWII • Added two rotors • Operators stopped sending individual message settings twice at the start of each message • Eliminated the original method of attack

24. Modifications During WWII • Occasionally added new rotors, but never on a widespread scale • Triton • New version of Enigma • Had 4 wheels instead of 3

25. What chapter in thebook will be helpfulin understandingthis event? Chapter 2 - Elementary Cryptography

26. Sources Marian Rejewski’s photohttp://en.wikipedia.org/wiki/File:MR_1932_small.jpg http://www.enigmahistory.org/main.html http://www.ams.org/featurecolumn/archive/enigma.html http://www.iwm.org.uk/upload/package/10/enigma/enigma9.htm http://math.usask.ca/encryption/lessons/lesson00/page8.html http://library.thinkquest.org/28005/flashed/timemachine/courseofhistory/bombe.shtml http://plus.maths.org/issue34/features/ellis/