The Code Book - HOW TO MAKE IT, BREAK IT, HACK IT, CRACK IT by Simon Singh

Author:Simon Singh [Singh, Simon]
Language: eng
Format: epub, pdf
Publisher: ePub Bud (www.epubbud.com)
Published: 2011-12-27T16:00:00+00:00

T H E C O D E B O O K

chains. And, of course, the letters within the chains changed. The characteristics of the chains were clearly a result of the day key setting—a complex consequence of the plugboard settings, the scrambler arrangement and the scrambler orientations.

However, there remained the question of how Rejewski could determine the day key from these chains. Which of

10,000,000,000,000,000 possible day keys was related to a particular pattern of chains? The number of possibilities was simply too great. It was at this point that Rejewski had a profound insight. Although the plugboard and scrambler settings both affect the details of the chains, their contributions can to some extent be disentangled. In particular, there is one aspect of the chains that is wholly dependent on the scrambler settings and has nothing to do with the plugboard settings: the number of links in the chains, which is purely a consequence of the scrambler settings. For instance, let us take the example above and pretend that the day key required the letters S and G to be swapped as part of the plugboard settings. If we change this element of Figure 34 Hans-Thilo Schmidt.

Figure 35 Marian Rejewski.

130

The Mechanization of Secrecy

the day key, by removing the cable that swaps S and G, and use it to swap, say, T and K instead, then the chains would change to the following:

A r F r W r A

3 links

B r Q r Z r T r V r E r L r R r I r B

9 links

C r H r S r O r Y r D r P r C

7 links

J r M r X r G r K r N r U r J

7 links

Some of the letters in the chains have changed, but, crucially, the number of links in each chain remains constant. Rejewski had identified a facet of the chains that was solely a reflection of the scrambler settings.

The total number of scrambler settings is the number of

scrambler arrangements (6) multiplied by the number of

scrambler orientations (17,576), which comes to 105,456.

So, instead of having to worry about which of the

10,000,000,000,000,000 day keys was associated with a particular set of chains, Rejewski could busy himself with a drastically simpler problem: Which of the 105,456 scrambler settings was associated with the number of links within a set of chains? This number is still large, but it is roughly one hundred billion times smaller than the total number of possible day keys. In short, the task has become one hundred billion times easier, certainly within the realm of human endeavor.

Rejewski proceeded as follows. Thanks to Hans-Thilo

Schmidt’s espionage, he had access to replica Enigma machines. His team began the laborious chore of checking each of 105,456 scrambler settings and cataloging the chain lengths that were generated by each one. It took an entire year to complete the catalog, but once the Biuro had accumulated the data, Rejewski could finally begin to unravel the Enigma

cipher.

131

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