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Optimal Stecker Combinations on an Enigma #ACE2012

I attended the ACE2012 conference over the weekend, and the issue of the stecker patching on the front of the Enigma came up.  The Germans used 10 stecker cables to cross connect 20 letters in the Enigma.  It was presented that the 10 cables that the Germans used was the most mathematically complex combination that can be used.  However, it is not!

The optimal number of stecker cables is, in fact, 11 which would increase the complexity of the Enigma by just over 36% (as the table below shows).

It is believed that the reason the Germans chose 10 instead of 11 was in part due to the physical difficult of squeezing an eleventh cable in the confined space at the front of the Enigma; and perhaps, the increased possibility of operator error.  Additionally, the Germans could have made life more interesting by increasing the combination from 150 billion to over 500 billion by having a variable number of stecker pairs instead of the fixed 10.

The formula and the mathematical results are here:
In Microsoft Excel terms, the formula looks like this:
=FACT(26)/(FACT()*FACT((26-2*))*2^) where is the number of cables in the second column

If you want more information on this, then the excellent cryptomusem site at http://www.cryptomuseum.com/crypto/enigma/working.htm has the same maths on show, along with a lot more information on the Enigma and other crypto devices.

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After the delights of lunch in King\’s (#ACE2012)

Neo-Gothic Hall designed in the 1820\’s the concrete and plain wood of the Keynes Hall is a bit of a climb down…
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The monkey in the cage looking out #ACE2012

A busy touristy day in Cambridge and the hordes are photographing away.
From my privileged position behind the wire at King\’s I thought I\’d bite back…
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But another gorgeous morning at King\’s #ACE2012

Starting today with Brian Randall \”From Ludgate to Los Alamos\”
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What is the nature of your distress #Peterhouse?

I hope this was a student prank and not ignorance…

On my way to day 2 of ACE2012.  Brain most definitely not in standby mode!

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ACE2012 Turing Uncategorized

#ACE2012 #Turing Birthday (nice one #Photosynth)

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ACE2012 Turing Uncategorized

The story of #Tunny

Tunny (Lorenz SZ40)
Bill Tutte
Capt Jerry Roberts

\”It should never have been broken.\”

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ACE2012 Turing Uncategorized

Capt Jerry Roberts speaking to #ACE2012 King\’s College

Lauding his colleague Alan Turing, and telling the Tunny tale