The History and Mathematics of Codes and Code Breaking

Math Behind the Shark

In a section of Cryptonomicon entitled "Cycles," there are a few pages that go into detail explaining how the three wheels in the enigma machine give it a certain security level and how the adding of the fourth wheel in the system Shark increased the security of the machine. It is explained by comparing the chain of letters created by the enigma machine to a bicycle with a weak link in the chain. The "weak link" in the enigma machine is the first chain that is created to encipher the first letter and when the same chain is used again which occurs 17,576 letters later. When the Germans added another wheel they increased the number of links in the chain to 456,976 and since their messages were hardly ever that long the weak link usually never came into play.

This section of the book added onto my understanding of the enigma machine and how the 4th wheel added so much more security. The increased security was explained through a number of pages with a lot of mathematics on them which helped me see more clearly what factors were actually playing a role in increasing the security of the enigma machine when adding the fourth wheel and creating Shark.







Image: "Chain," by Pratanti, Flickr (CC)


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1 Comment

  1. Derek

    I thought this was a clever section, too, especially the parallel between someone who steals the bike in question and someone trying to break the Enigma machine. But some of it was perhaps too clever. All that talk about what boils down to relatively prime numbers isn't needed to get the idea that the Engima machine repeats after 26x26x26 = 17,576 letters.

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