[2978] in cryptography@c2.net mail archive
Re: Turing Bombe story
daemon@ATHENA.MIT.EDU (Carl Ellison)
Thu Jul 16 18:21:51 1998
Date: Thu, 16 Jul 1998 17:45:33 -0400
To: Steve Reid <sreid@alpha.sea-to-sky.net>
From: Carl Ellison <cme@acm.org>
Cc: Marcus Leech <Marcus.Leech.mleech@nt.com>, cryptography@c2.net
In-Reply-To: <Pine.LNX.3.95.iB1.0.980716114655.21066B-100000@alpha.sea-t
o-sky.net>
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At 12:03 PM 7/16/98 -0700, Steve Reid wrote:
>Are these figures accurate?
>
>I thought the Enigma had a much smaller number of combinations, around
>10^5, give or take a digit...?
Enigma's message key was 3 letters -- so 26^3 = 17576 --
but the key of the (part-)day included the plugboard wiring that had
C(26,6)*19*17*15*13*11*9*7*5*3 possibilities and the wheel order
that had P(5,3).
The brilliance of the Bombe was that it needed to test only for
the non-plugboard elements: (26^3)*P(5,3) = 1054560 possibilities,
or half that to the expected break. This comes out to about an hour
and a half, for a single Bombe, if it runs at 10 msec per rotor
position. [Don't quote me on that speed -- it's from a distant
memory of something I read.]
As for a modern Pentium beating the Bombe, maybe -- but the Bombe did an
incredible number of LIPS. It was testing for logical contradictions and if
you were to do the Bombe in Prolog, it could bog down a modern processor....
- Carl
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|Carl M. Ellison cme@acm.org http://www.pobox.com/~cme |
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+-Officer, officer, arrest that man. He's whistling a dirty song.--+
