Statistics in a very ingenious way to decrypt the code. However even in this case the code breakers had an answer if the number of different alphabets used is not too large. The use of many alphabets has a tendency to level out the frequencies for the letters in the encrypted text, thereby hiding their origin. Here more than one alphabet were being used, that way limiting the success of statistics being invoked. The first polyalphabetic system seems to be due to Leon Battista Alberti around 1467, according to Wikipedia, but the best known example is probably the so-called Vigenère cipher. To “repair” the weaknesses of a monoalphabetic cipher, the concept of a polyalphabetic substitution cipher was introduced. Will tend to approach the frequencies of an “average English text”. This procedure usually works if the encrypted text has a certain length, because the frequencies then In a similar way using statistics on the remaining letters it is usually possible to find the other substitutions as well. Because the letter e has the highest frequency of all letters in most English texts, there is a high probability that the letter occurring most frequently in a specific crypto-text (encrypted text) is in fact a substitution for an e. In English for example, an e is much more frequent However it was early on discovered to be a poor cipher, because statistics can be applied: Depending on the language, some letters will occur with much higher frequency than other letters. One of the simplest ciphers are the so-called monoalphabetic substitution ciphers, in which every letter in the plain-text (the original text) is substituted with another letter from the same alphabet, making it apparently unreadable. The situation before Enigma - history briefly I will get back to our visit in section 13.Ģ. First, however, let's start with the history of cryptography. In a later section we will look closer at our visit at Bletchley Park. Maybe it was the fear and the necessity to solve it, which drove the Allied and made them succeed in this major task, as indicated by Simon Singh in his book The Code Book. The Germans regarded their machine as unbreakable, and it is an extraordinary achievement that ingenious mathematicians and other people with Since then many books have been written explaining what took place during those critical years including the role of Enigma, and several movies have appeared too. Not until 1974 was it revealed for the public that the German crypto machine had been broken not only a few times, but intensively during World War II. The story about Enigma is a fascinating one. My colleague and part of the 22 students in front of the main building at Blechley Park Our goal was to experience how the famous code breakers at Bletchley Park back in 1939-45 made a big difference in the War by solving the GermanĬipher machine Enigma and to learn about the mathematics involved. One of the academic items was a visit at Bletchley Park, situated 90 kilometres north west of London - a 45 minutes trip by train from Euston Station in central London. The last week of September 2007 I was on a study tour to London together with one of my colleagues and my dear class 3F from Haderslev Katedralskole, a high school in Denmark. Enigma and the Turing Bombe in Excel VBA. The decryption procedure at Bletchley Park.The situation before Enigma - history briefly.Notice that in many occasions clicking an image yields an enlarged version! On my website and because of the kindness I received from the people from Bletchley Park, who arranged our visit and who have provided me with a few historic photos from Bletchley Park! I can be contacted on e-mail: Erik Vestergaard. Firstly I am grateful to Chris Christensen and MAA for giving me the permission to place an article about the Polish contributions to the solution of Enigma This time, however, I have decided to tell a story about the German ciphermachine Enigma in English too, because of several reasons. As a high school teacher and mathematician from Denmark, I normally only write in my native language, which is Danish. This webpage was created after an interesting study tour to London and Bletchley Park.
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