Shuttle Rescue Mission Shuttle Rescue Mission Banburismus Banburismus • Monday Feb 23 and Wednesday Feb 25 Monday Feb 23 and Wednesday Feb 25 and the and the • MEC 205 until 5:30pm MEC 205 until 5:30pm Story So Far Story So Far • http://shuttle.cs.virginia.edu:8080/ http://shuttle.cs.virginia.edu:8080/ – Build and program Lego Mindstorms robot to Build and program Lego Mindstorms robot to remotely sense and navigate a barren remotely sense and navigate a barren environment and retrieve a life pod from a crater. environment and retrieve a life pod from a crater. • Exam 1 Extra Credit: Exam 1 Extra Credit: either either show up and show up and watch one day or or write paragraph about it write paragraph about it watch one day #2 One-Slide Summary Outline • British codebreakers used cribs (guesses), brute force, and analysis to break the Lorenz cipher. Guessed wheel settings were likely to be correct if they resulted in a Pick Up Graded • WWII Codebreaking Problem Sets message with the right linguistic properties for German. Before Spring Break • Double Deltas Or Possibly • If you've guessed the right wheel settings, two adjacent Lose Points! letters are more likely to be the same than they are to • Machines be different letters. Double Deltas . • Banburismus • We can tell if two messages were encrypted using the • Tree Sorting same wheel settings (= same key) because the output letters will match when the input letters match. So we • Course Roadmap can try to “line them up” using Banburismus to look for matches. • Tree sorting is only efficient if the trees are balanced . If not, it's Θ ( n 2 ) . The best possible sorting is Θ ( n log n ). #3 #4 Breaking WWII Traffic Recognizing a Good Guess • Knew machine structure, but a different • Intercepted Message (divided into 5 initial configuration was used for each channels for each Baudot code bit) message Z c = z 0 z 1 z 2 z 3 z 4 z 5 z 6 z 7 … • Need to determine wheel setting: z c, i = m c,i ⊕ x c,i ⊕ s c,i – Initial position of each of the 12 wheels Message Key (parts from S-wheels and rest) – 1271 possible starting positions • Look for statistical properties – Needed to try them fast enough to decrypt message while it was still strategically valuable – How many of the z c,i ’s are 0? ½ (not useful) – How many of (z c,i+1 ⊕ z c,i ) are 0? ½ This is what you did for PS4 (except with fewer wheels) #5 #6
Double Delta Actual Advantage ∆ Z c , i = Z c , i ⊕ Z c , i +1 • Probability of repeating letters Combine two channels: Prob[ ∆ M 1, i ⊕ ∆ M 2, i = 0] ~ 0.614 ∆ Z 1, i ⊕ ∆ Z 2, i = ∆ M 1, i ⊕ ∆ M 2, i 3.3% of German digraphs are repeating > ½ Yippee! ⊕ ∆ X 1, i ⊕ ∆ X 2, i • Probability of repeating S-keys = ½ (key) Prob[ ∆ S 1, i ⊕ ∆ S 2, i = 0] ~ 0.73 ⊕ ∆ S 1, i ⊕ ∆ S 2, i > ½ Yippee! Prob[ ∆ Z 1, i ⊕ ∆ Z 2, i ⊕ ∆ X 1, i ⊕ ∆ X 2, i = 0] Why is ∆ M 1,i ⊕ ∆ M 2,i > ½ Message is in German, more likely following = 0.614 * 0.73 + (1-0.614) * (1-0.73) letter is a repetition than random ∆ M and S are 0 ∆ M and S are 1 Why is ∆ S 1,i ⊕ ∆ S 2,i > ½ = 0.55 if the wheel settings guess is correct (0.5 otherwise) S-wheels only turn when M-wheel is 1 #7 #8 Heath Robinson Machine Using the Advantage • If the guess of X is correct, should see higher • Dec 1942: Decide to build a than ½ of the double deltas are 0 machine to do these ⊕ s • Try guessing different configurations to find quickly, due June 1943 • Apr 1943: first “Heath highest number of 0 double deltas Robinson” machine is • Problem : delivered! – Predecessor to Colossus # of double delta operations to try one config • Intercepted ciphertext on = length of Z * length of X tape: = for 10,000 letter message = 12 M for each setting – 2000 characters per second * 7 ⊕ per double delta (12 miles per hour) – Needed to perform 7 ⊕ = 89 M ⊕ operations Need a fast operations each ½ ms Heath Robinson, British Cartoonist (1872-1944) way to compute XOR! (that's a lot!) #9 #10 Colossus Design Colossus Ciphertext Tape Electronic Keytext Logic Tape Reader • Heath Robinson machines were too slow Generator • Colossus designed and first built in Jan 1944 • Replaced keytext tape loop with electronic keytext Position Counter Counter generator • Speed up ciphertext tape: – 5,000 chars per second = 30 mph – Perform 5 double deltas simultaneously Printer – Speedup = 2.5X for faster tape * 5X for parallelism #11 #12
Impact on WWII Colossus History Kept secret after the war, all machines destroyed • 10 Colossus machines operated at Bletchley park – Various improvements in speed • Decoded 63 million letters in Nazi command messages • Learned German troop locations to plan D-Day (knew the deception was working) Rebuild, Bletchley Park, During WWII Summer 2004 #13 #14 How could the folks at Bletchley Park solve a problem ~ 1 quintillion times harder than ps4? Poster in RAF Museum #15 #16 Motivation Helps… Liberal Arts Trivia: Maritime Law • A letter of marque is an official government Confronted with the prospect of defeat, document authorizing an agent to search, the Allied cryptanalysts had worked night seize, or destroy specified assets or personnel and day to penetrate German ciphers. It belonging to a foreign party beyond the would appear that fear was the main borders of the nation ("marque" or frontier). driving force, and that adversity is one of They are usually used to authorize private the foundations of successful parties to raid and capture merchant shipping codebreaking. of an enemy nation. In the past, a ship operating under a letter of marque and Simon Singh, The Code Book reprisal was privately owned and was called a "private man-of-war" or ... what? #17 #18
Liberal Arts Trivia: Geography Banburismus • This capital city of Uttar Pradesh, the most Given two Enigma- populous state of India, is popularly known as encrypted messages, how the The City of Nawabs. It is also known as can we determine if they the Golden City of the East, Shiraz-i-Hind and were encrypted starting The Constantinople of India. It is a center of with the same wheel Hindi and Urdu literature, and the birthplace settings? of Kathak, a classic Indian dance form. The city was besieged during the Indian Rebellion of 1857. Enigma in Use, 10 December 1943 #19 #20 Enigma Reverse • Invented commercially, 1923 Engineering • German Navy, Army, Air Force Enigma • About 50,000 in use (many were captured by Allies) • Modified throughout WWII, “This fictional movie about a fictional U.S. submarine Germans believed perfectly secure mission is followed by a mention in the end credits of • Kahn’s Codebreakers (1967) didn’t those actual British missions. Oh, the British deciphered the Enigma code, too. Come to think of it, they pretty know it was broken much did everything in real life that the Americans do in Enigma machine • Turing’s 1940 Treatise on Enigma this movie.” at Bletchley declassified in 1996 Roger Ebert’s review of U-571 Park (2000 Academy Award Winner) #21 #22 Rotor Wheels Simple Substitution Ciphers Simple substitution ABCDEFGHIJKLMNOPQRSTUVWXYZ Latch turns encrypt decrypt next rotor once per rotation JIDKQACRSHLGWNFEXUZVTPMYOB HELLO ⇒ RQGGF #23 #24
http://en.wikipedia.org/wiki/Image:Enigma-action.png Language is Non-Random • Random strings: the probability of two letters in the two messages matching is 1/26 (number of letters in alphabet) • Same-encrypted strings: the output letters will match when the input letters match Image from – This happens much more frequently because some letters (e.g., “e” is ~13% of all letters) are more common #25 #26 Alan Turing’s Solution Banbury Bletchley Park M1: GXCYBGDSLVWBDJLKWIPEHVYGQZWDTHRQXIKEESQS M2: YNSCFCCPVIPEMSGIZWFLHESCIYSPVRXMCFQAXVXDVU #27 #28 Banburismus Intercepted Message 2 Intercepted Message 1 A A B B C C D D E E F F G G H H I I J J K K L L M M N N O O P P Q Q R R S S T T U U V V W W M1: GXCYBGDSLVWBDJLKWIPEHVYGQZWDTHRQXIKEESQS X X Y Y Z Z M2: YNSCFCCPVIPEMSGIZWFLHESCIYSPVRXMCFQAXVXDVU CKGLPIFLR... PICJTTIOQN... #29 #30
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