Enigma how many combinations

There were experienced codebreakers, secret service officers, mathematicians, scientists, crossword experts, international chess players, students, actresses and even astrologers and debutants. Fortunately for the British codebreakers, in the years running up to the war Poland had worked on various techniques for cracking Enigma.

Shortly before the German invasion of Poland, they shared their work with their British allies. Poland's government was the first to employ mathematicians as code-breakers, and the mathematicians' logical minds proved to be just what was needed to tackle Enigma. This vital headstart from the Polish, coupled with the unique problem-solving and intuitive thinking skills of Bletchley's recruits, meant that Enigma was cracked in early a reliable technique for cracking Enigma was established.

The British code breakers worked in shifts around the clock for the whole of the war, using paper and pencil as well as newly invented mechanical techniques to work out the particular Enigma machine settings for each and every single day. These lapses provided the codebreakers with clues, called cribs , about how the Enigma machines had been set up on that day. These cribs were essential for breaking the ciphers. For example, without a crib it would still take several months today to decipher an A4 page of ciphertext using a modern PC with trial and error methods.

However, the cribs alone were not enough. The codebreakers at Bletchley Park developed new procedures and algorithms for determining the set-up of the Enigma and also had to develop electronic computing devices to implement these methods. Today, historians believe that the work of the code breakers at Bletchley Park shortened the war by two years. Among the most famous of the leading code breakers at Bletchley Park was a mathematician from the University of Cambridge, Alan Turing.

Turing was regarded by many as a genius. He played a leading role in breaking the more complicated Naval Enigma cipher codenamed Shark and also established the principles behind the modern computer.

Despite their remarkable work, however, for a long time afterwards none of the second world war code breakers received the public recognition they deserved. In order to preserve British security, the breaking of Enigma remained a tightly guarded secret for the duration of the war, and for the following 30 years. The people who had worked at Bletchley Park were forbidden from talking about what they had done and as a result their contribution to the war effort was entirely forgotten.

However, over the past 30 years more and more information has been released about the incredible story of Bletchley Park. Tragically, for some, however, the acknowledgments have come too late. Alan Turing committed suicide before he was ever publicly recognised for his extraordinary part in the war and before his contributions to the science of codes and code breaking were fully understood. The British Government still operates a code breaking department, at "Government Communication Headquarters" in Cheltenham.

And to this day they rely on mathematicians for their problem solving abilities and logical thinking: GCHQ boasts the highest concentration of pure mathematicians in the country. Today's secret codes are much more sophisticated than the Enigma cipher and their strength relies on the inability to factorise large numbers, so with today's worries about global terrorism, the role of our code breakers is just as vital as during the second world war.

For the first slot, you can choose any one of 5 rotors. For the second, you can choose any one of 4 rotors. For the last, you can choose any one of 3 rotors. So there are ways of positioning 5 rotors in 3 slots. Back to question 1. As there are 26 letters of the alphabet, each of the 3 rotors could be set in any one of 26 different starting positions. This gives a total of distinct starting positions. Back to question 2.

The first ring can be set in any of 26 positions, as can the second, so there are ways of positioning the 2 rings on a 3-rotor army Enigma. Back to question 3. Claire Ellis has recently joined the Millennium Mathematics Project, the Cambridge-based mathematics enrichment and dissemination group that publishes Plus magazine.

She runs the Enigma Project. If you multiply the numbers: You end up with: How come it says here, that the calculations result is approx million million million? If the factor is already considered, exactly how do the ring settings alter the overall number? There are 17, possible starting positions.

You don't actually take into account the notch positions. They don't affect the number of permutations in the machine. Ignoring the factor of the notch settings ignores the fact that the notches changes the rotor setting at some point in the message.

So the 17, rotor settings can change after the first character of the message and must change by the 26th character. These changes are additions to the key length, when viewed over the entire message. That means that for a message length of 1 character, the key length is indeed 1. The fact that the movement of the rotors is regular like an odometer makes the cryptoanalysis easier but does not reduce the factor of Each of 5 rotors may be chosen for the 3 rotor slots.

Each rotor creates a permutation of the code. Now plug board: Apparently from pictures they didn't use jumpers blocks, so the plugs must indeed have internal switches so that a position without a plug shorts through from output to input.

Each cable enacts a swap, but all the 10 cables are identical. Likewise swapping ends of the cables produces an identical results. Still I think that the decoder wheels bore some vague relationship to the "bombs" construction and is useful for thought. Needs more for searching the plugboard settings than was shown in the movie. At least I'm making some progress in understanding this now. They do truly establish another multiplier of settins positions.

HOWEVER the decoding will on average go 13 characters before a "notch" kicks the 2nd wheel over, so one could see if there was an appearance of a recognizable word most likely.

Thus these don't have to be searched for as intently as a fractional word or phrase can lead to decoding the notch or ring positions later as the first breakpoint into unintelligibility. Thus leaving this out is just a convention. Also note that there are actually more possible plug board settings because the code sheets can indicate that a cable is not used, so one actually has 10 cables, 9 cables, 8 cables, etc.

They probably would not go too far down. We all know that the English invented everything but I read years ago that the Enigma code was first broken by a Polish person who passed it on to French intelligence who in turn passed it on to the English. As an interesting aside, Turing had a colleague and they experimented with robots. When this colleague retired he thought it would be interesting to look at the earlier models which were that simple anybody could build one.

Certainly a credit should be given to Polish mathematicians who for the first time worked out the secret of Enigma. In they already established inner rotors wiring which was probably one of the greatest break trough steps in decrypting messages. The also reconstructed prototype of Enigma itself and designed electromechanical machine called by them "Bomby" to find the keys to daily messages decryptions. Alan Turing did not design first computer. He worked on improved device the "Bomby" which later was further improved by American engineers.

Polish Cypher Bureau team gave all the secrets about Enigma machine, the "Bomby" design and other related information to the British crypto-analysts already in July of Part is just mechanics, many industrial robots work without any "artificial intelligence" AI like programming.

But others distinctly combine AI which can be independent of any robotic mechanism and the mechanisms, such as visual analylsis for feedback. These are all of course based upon the development of the general purpose computing devices--for which Turing did make significant early contributions.

In later years those developing ideas for computers and Turing differed on approaches and computer developers ignored turing's later ideas, but they certainly were part of the original foundations. Interestingly, relating to code breaking, some of my work and others on search methods for puzzle solving in AI could have been independently discovered back then and built into the hard-wired code breaking machines that essentially implemented a tree search for settings to match message fragments.

It is widely agreed that the design of the rotor and wiring system in the enigma resulted in the not so irrelevant error that a letter could not be coded into itself and hence gave a great help in using cribs. However I thought that the plugboard would eradicate most of this error or perhaps I do not understand it correctly. As an example assume A is connected on the plugboard to B.

Now we know that B will be coded to some letter other than B itself. I assume it could be coded to A and hence pressing key A would light up A. When you connect B to A, you also connect A to B! Which means that if you enter A, your letter turns to B, and the letter that comes back can be anything but B; but the only way to get an A as a result is if the letter going through the plugboard is a B! Which means that by extension, you cannot get A in return.

Trevor, According to this article, there are only 10 cords while there are 13 pairs of letters. Tony Sale's Codes and Ciphers. Secret indeed! This is an example of the setting sheets used:. Sending and receiving a message using the simple Enigma indicator system To send a message: 1. Set the Enigma machine into the base configuration for the day as given in the setting sheet for the month.

Wikipedia is your friend: "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 ,,,,,, nearly quintillion different settings. More in detail: if you consider an Enigma with 3 rotors out of 5 rotors of model known to the cryptanalyst, and a plugboard with 10 wires.

The answer depends on the Enigma model, on the number of rotors among which the active rotors are chosen, on the number of wires used for the reflector, and on what one accounts for as part of a setting. The discrepancy between the two numbers around is because the position of the rotors except the left one, which notch is inactive can be accounted for - or not. This number is often quoted, and makes sense, as that's also the size of the key space according to the basic setup procedure ; but this setup procedure has varied in secret ways, effectively increasing the key space.

For the left rotor, the position of the outer of the rotor is immaterial to encryption and decryption. Caution: none of the above numbers is related to the much lower number of operations involved by the attacks actually carried for cryptanalysis during WW2, which exploited weaknesses in both the transformation performed by the Enigma, and its setup procedures.

Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. How many possible Enigma machine settings? Ask Question. Asked 5 years, 8 months ago. Active 1 year, 8 months ago.