Re: How to cryptanalysis of Japanese PURPLE cipher machine.

From: Jim Gillogly (
Date: 10/13/04

Date: Wed, 13 Oct 2004 14:22:07 GMT

On Wed, 13 Oct 2004 06:22:53 -0700, jun takagi wrote:
> I wrote from Japan. I have a question about PURPLE.
> I read CRYPTOLOGIA Volume XV, David Kahn, "Pearl Harbor and the
> Inadequacy of Cryptanalysis". In this paper says, U.S. Army S.I.S.
> cryptanalysts, Genevieve Grotjan discovered intervals of Japanese
> PURPLE ciphertext in September 1940 and intervals revealed the
> advancement of PURPLE's mechanism.
> Because more than a year was needed for the discovery of intervals, I
> think it is a turning-point of cryptanalysis.
> But I can't well understand meaning and value of "intervals" from this
> paper.
> Is intervals demonstrated that PURPLE used stepping-switch?
> ENIGMA and Hagelin machines never show such intervals?
> Interval was founded in the same ciphertext or two different
> ciphertext?
> How to distinguish between true and accidental intervals?
> Is this method needs cribs?
> If you know more details of "intervals", please help me.

In Frank B. Rowlett's "The Story of Magic" the solution process is
laid out in some detail. Before Grotjan's discovery the team had
already completely broken the "sixes" -- early-on frequency counts
had determined that letters were enciphered in two groups: each
message had a group of six letters whose frequency "stood out"
from the others, so they assumed that as with the Red machine
(ANGOOKI TAIPU A) these letters substituted among themselves,
as did the other group of 20 letters. From the broken Red
messages they were able to guess the beginnings of messages from
specific senders with high confidence, and from this they developed
a chart that allowed them to recover the method used for enciphering
the "sixes", with a pencil-and-paper chart of 25 rows (different
polyalphabetic substitutions) and six columns.

The "twenties" were much more difficult, and required looking at a
great deal of matched (assumed) plaintext and ciphertext. They
were able to rule out Enigma-style equipment, and felt that
Hebern-style circuitry was a long shot at best. As they kept
working with the plaintext and ciphertext they became convinced
they were dealing with a new type of circuitry.

To help identify potential plaintext they decided to build a
special machine called a "Six Buster" to decipher the sixes
in a message and replace them with the plaintext equivalent,
using the substitution process they'd recovered, which could
be used to help guide the linguists who were working on
guessing plaintext.

As they were designing this, one of the analysts (Leo Rosen) found
a brochure for a 25-position telephone stepping switch that could
handle six separate circuits, and Rosen realized that this was
just what was needed to handle the substitution process that they
had worked out for the sixes -- one model of the switch could be
used without any modifications for this process. The success of
this machine allowed them to use their cryppies on analysis of the
rest of the system, rather than breaking sixes by hand.

Since the stepping switches were such a good match for the sixes,
they speculated that the whole machine was built around them, and
they started brainstorming different kinds of machines that could
be designed with this kind of equipment, without ruling out the
possibility tha the twenties could have been encrypted using a
different method. This was a strong possibility, because by this
time they were sure the twenties were encrypted with a much more
complicated system than the sixes.

In order to find the relationships between the plaintext and
ciphertext they needed a great many equivalent pairs. They also
found that messages sent on the same day with the same indicator
were encrypted with the same key.

The part you specifically asked about is on page 152 of Rowlett's
book: Genevieve Grotjan had found relationships among the plaintext
and ciphertext in two areas, then the same relationships among
the plaintext and ciphertext in two other areas. (Rowlett doesn't
say precisely what the relationships were.) This was the start of
the break on the "twenties" -- they now knew what kind of
relationship they were looking for, and were able to focus their
search looking for this specific phenomenon.

I strongly recommend Rowlett's book -- it's well-written, and is a
first-hand look from the man who led the team.

Frank B. Rowlett, "The Story of Magic - Memoirs of an American
Cryptologic Pioneer", Aegean Park Press, 1998 (foreword by David

	Jim Gillogly

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