1. “IT IS A RIDDLE, WRAPPED IN A MYSTERY, INSIDE AN ENIGMA” * By: Michaela Wontroba Mr Kuniega; PD 5,6,7

2. WHAT WAS THE ENIGMA? ≈The Enigma machines were a series of electro-mechanical rotor cipher machines developed and used in the early- to mid-twentieth century to protect commercial, diplomatic and military communication. ≈The Enigma was invented by a German engineer named Arthur Scherbius at the end of World War I. ≈Several different Enigma models were produced, but the German military models are the most commonly recognized.

3. WHAT WAS THE NEED FOR SUCH A MACHINE? ≈The Germans were sending encrypted codes back and to one another so we, America, Britain, Poland, France, etc…, needed a way to crack said codes. ≈We needed world peace, to end WWI & WWII.

4. HOW DID THE ENIGMA WORK? ≈the Enigma machine is a combination of mechanical and electrical subsystems. ≈The mechanical subsystem consists of a keyboard; a set of rotating disks called rotors arranged adjacently along a spindle; and one of various stepping components to turn at least one rotor with each key press. ≈There are 26 lamps and keys, rotor wirings inside the rotors (of which there are either three or four) and between six and ten plug leads.

5. HOW DOES THIS CORRELATE TO MATHEMATICS? ≈The Enigma transformation for each letter can be specified mathematically as a product of permutations. Assuming a three-rotor German Army/Air Force Enigma, let P denote the plugboard transformation, U denote that of the reflector, and L,M,R denote those of the left, middle and right rotors respectively. Then the encryption E can be expressed as… ≈E=PRMLUL^{-1}M^{-1}R^{-1}P^{-1} ≈After each key press, the rotors turn, changing the transformation. For example, if the right-hand rotor R is rotated i positions, the transformation becomes \rho ^{i}R\rho ^{-i}, where \rho is the cyclic permutation mapping A to B, B to C, and so forth. Similarly, the middle and left-hand rotors can be represented as j and k rotations of M and L. The encryption transformation can then be described as ≈E=P(\rho ^{i}R\rho ^{-i})(\rho ^{j}M\rho ^{-j})(\rho ^{k}L\rho ^{-k})U(\rho ^{k}L^{-1}\rho ^{- k})(\rho ^{j}M^{-1}\rho ^{-j})(\rho ^{i}R^{-1}\rho ^{-i})P^{-1}. ≈Combining three rotors from a set of five, the rotor settings with 26 positions, and the plugboard with ten pairs of letters connected, the military Enigma has 158,962,555,217,826,360,000 (nearly 159 quintillion) different settings.

6. THE ENIGMA IN POP CULTURE ≈Hugh Whitemore's play Breaking the Code (1986) focuses on the life and death of Alan Turing. ≈Robert Harris' novel Enigma (1995) is set against the backdrop of World War II Bletchley Park and cryptologists working to read Naval Enigma in Hut 8. ≈An earlier Polish film dealing with Polish aspects of the subject was the 1979 Sekret Enigmy, whose title translates as The Enigma Secret. ≈The game Wolfenstein (2014), centered around the World Wars, gives you the option to pick up pieces if the “enigma code” labeled as The Enigma Code 1:1, 1:2,1:3, etc. At the end if you collect all the pieces, you unlock a special prize.

7. WHO CRACKED THE ENIGMA CODE? ≈The Poles had broken Enigma in 1932, when the encoding machine was undergoing trials with the German Army ≈ By the Polish Cipher Bureau, beginning in December 1932. This success was a result of efforts by three Polish cryptologists, Marian Rejewski, Jerzy Różycki and Henryk Zygalski, working for Polish military intelligence. Rejewski reverse-engineered the device, using theoretical mathematics and material supplied by French military intelligence. ≈The cipher altered only once every few months. ≈It changed at least once a day, giving 159 million million million possible settings to choose from. The Poles decided to inform the British in July 1939 once they needed help to break Enigma. ≈The first operational break into Enigma came around the 23 rd of January 1940, when the team working under Dilly Knox, with the mathematicians John Jeffreys, Peter Twinn and Alan Turing, unraveled the German Army administrative key that became known at Bletchley Park as ‘The Green’. Jerzy Różycki Marian Rejewski Henryk Zygalski

8. PICTURES OF THE ENIGMA MACHINE; HOW IT WORKS AND IN USE Enigma wiring diagram with arrows and the numbers 1 to 9 showing how current flows from key depression to a lamp being lit. The A key is encoded to the D lamp. D yields A, but A never yields A; this property was due to a patented feature unique to the Enigmas, and could be exploited by cryptanalysts in some situations Enigma in use, 1943 The scrambling action of Enigma's rotors is shown for two consecutive letters with the right- hand rotor moving one position between them. Military Enigma machine Passport photo of Alan Turing at aged 16 John Jeffreys was a British mathematician and WW II code breaker.

9. CITATIONS ≈https://en.wikipedia.org/wiki/Enigma_machinehttps://en.wikipedia.org/wiki/Enigma_machine ≈https://en.wikipedia.org/wiki/Turing_machinehttps://en.wikipedia.org/wiki/Turing_machine ≈http://www.bletchleypark.org.uk/content/hist/worldwartwo/enigma.rhtmhttp://www.bletchleypark.org.uk/content/hist/worldwartwo/enigma.rhtm ≈*Winston Churchill's quotation, made in a radio broadcast in October 1939: "I cannot forecast to you the action of Russia. It is a riddle, wrapped in a mystery, inside an enigma; but perhaps there is a key. That key is Russian national interest.“