(translated
from French)
COULD THE CRYPTANYSIS OF ENIGMA
FAIL?
WHAT WOULD HAVE BEEN THE CONSEQUENCES?
ENIGMA: A ROTOR WITH VARIABLE CONNECTIONS
In
the french WEB site "cryptanalysis of enigma", we find the following
sentence the importance of which seems essential: "If the Germans had
changed their rotors more often, it is possible that the efforts of the experts
of Bletchley Park remained vain".
Indeed,
many military experts consider that if the enormous efforts granted for the décryptement
of ENIGMA had been fruitless, the war would perhaps have lasted one year more.
The photos which we can find in some works
dedicated to this device show obviously that the modification of the
connections between the letters of a rotor is a complex operation which could
be made only in a workshop by a specialist, but who is certainly not within the
reach of a cipher clerk.
We are then driven to wonder if it would not
have been possible to conceive a device of connection such as a cipher clerk
can modify these connections as easily as he modifies the position of the pins
of a machine Hagelin C. 36. In this hypothesis, it would have been possible to
put in operation daily a set of rotors completely new.
The rotor described and represented below
(figure N ° 1), realizable without excessive technical difficulties, would have
perhaps allowed to bring a solution of this problem.
I - The ROTOR (Figure nr1)
1) The internal circles represent the insulating material which
separates the rings of brass.
2) The tinted parts represent the insulating material.
Fromthe center, we find :
A
nucleus made of insulating material, drilled by a hole for the passage of the
axis of rotation (the device of training, foreign to this study, is not
represented).
Thirteen
concentric circles, made of brass, four millimeters thick, electrically
insulated some of the others.
A
circle of an insulating material where are inlaid 26 brass studs corresponding
to the 26 letters of the alphabet.
According
to the13 diameters connecting two opposite "letter-studs" , the
circles of brass and letter-studs are drilled by holes two millimeters in
diameter.
II -
ACCESSORIES OF THE ROTOR
Every
rotor is provided with thirteen pairs of two-pins-plugs, or connectors made of brass in the form of U. The central part is
insulated, both side branches are two millimeters in diameter.
(Figure nr 2)
1) Only one exemplar of each pair of connectors has
been represented
2)The insulating material which wraps the central part
of the connectors has not been represented
These
thirteen pairs of connectors differ by the length of the central part : the
smallest one is equal to the distance which separates the hole drilled in a
letter-stud of that drilled in the circle of brass nr 1 ( from the outside).
For the second pair of connectors, this length is equal to the distance between
the hole of a letter-stud and that drilled in the circle nr 2 and so on for the
following pairs of connectors.
To connect any pair of letter-studs,
it is enough to connect them to some brass circle by mean of two connectors of equal length. We
can so realize any model of connection between the various letter-studs.
III - EXAMPLE OF THE ROTOR WITH A DETERMINATE KEY
The black bars represent the
connectors.
The key is the following one: B C D
E F G O R S T V W Z
A
P Q U L Y I X M N K H J
Figure nr 3
N.B. Of course, the diameter of such a rotor would have been appreciably superior to that of the rotors which were used, what would have led to a different structure of the machine, but this seems to be a minor problem towards the advantages which would have resulted from it.
IV - QUESTIONS THAT YOU PERHAPS ARISE ?
Doubtless it is convenient to anticipate the questions that the readers could arise, if there is (I mean the readers, not the questions).
1) Are errors to be dreaded during
the implementation of connectors? They are placed by pairs (we can imagine a
small case with thirteen compartments). Moreover, an erroneous position of a
connector would show itself during the implementation of the following ones. In
these conditions, an error of connection would constitute an unforgivable
fault. The machine C.36 contained a much
superior risk during the daily implementation of the pins. Nevertheless, it was
employed during numerous years. It is
true that it was provided with a system of check which some survivors perhaps
still remember. A similar solution could doubtless be applied in the case which
occupies us. Besides three keys, the key-book would supply the cryptogram
corresponding to the encoding, from a key of message well defined (position of
departure of rotors) of a sentence containing the twenty six letters of the
alphabet: KAUFEN SIE JEDE WOCHE VIER GUTE BEQUEME PELZE BEI XY.
In U.K., the usual sentence is
:THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG and, in France : PORTEZ CE VIEUX
WISKY AU JUGE BLOND QUI FUME (It is funny to notice that the facetious hazard
made that for the Germans the subject is the business, for the English people
the fox hunting and for the French people the tasting). It is necessary to
observe that the sentence of control, if it contains the 26 letters of the
alphabet, has a superior length, and that would entail the rotation of the last
two rotors, what would make illusory the check of their connections. To remedy
it, we could propose a touch "Control" (with an indicator light)
which would immobilize the three rotors,
with the key of message AAA (strictly forbidden for the real traffic); This
touch would be switched off immediately after the check. With such an
accumulation of precautions, an error of connections would become practically
impossible. The key-book would thus supply, for every day, (in the case of
machines with three rotors) three keys similar to the one that we can see
above, and the cryptogram of control.
2) Why the Germans did not find and did not adopt this
solution which brought a considerable increasing of security. I believe that to
this question we can furnish tree answers :
A) It is necessary to observe that the present
document concerns exclusively one organ of Enigma : the rotor. But the machine
contained other organs intended to improve the quality of the encoding :
a) First of all the
board of connections which acted as a simple substitution concerning some
letters of the alphabet
b) The ringstellung
incorporated into the rotor, which moved the connections between letters and
cabling, this last one remaining however unchanged.
c) The number of
rotors used simultaneously in the machine.
d) The number of
rotors susceptible to be employed.
During the war, the frequency of the
variations which these organs authorized
increased gradually, until they became daily for some of them. The German
cryptologists did not thus remain inactive. Nevertheless, with the risk to attract controversies, I must say that I
think that with rotors with variable connections, modified daily, most part of
the complications enumerated above would have become superfluous.
B)
The Germans had in the undecryptability of Enigma an unwavering confidence. We
can suppose that if some subordinate had come to propose a rotor whose
conception and dimensions would have
been completely different, he would have got the answer: " Enigma offers a
total reliability. You do not imagine that we are going to realize a new
machine only to exploit your little idea. Thus return to your occupations and
let your superiors watch over the safety of our communications ".
C) last argument : an idea is always simple when it has been found....
V - QUESTIONS THAT WE CAN CERTAINLY ARISE.
Let us imagine that Bletchley Park
had met with a check and that the war had gone on for one year as some military
experts envisage it , what would have
happened? On such a subject, the average Internet user can ask the questions,
but not answer them. But it is not sterile to ask questions, because they call
answers.
We can suppose that, probably, the
landing would not have taken place in 1944. In this hypothesis, would the Nazis
have been able to dispose of a supplement of military resources to contain the
Russian push one year furthermore?
All the German scientific research
was aimed at the means of massive destruction. It had outstripped the Allies in
the domains of jet propelled planes (Messerschmitt 262) and rockets (V1, V2).
War factories, (most of them buried) had even, under the remarkable impulse
of Albert Speer, increased their
production, in spite of the massive bombardments.
In spite of the splendid exploits of
the Norwegian resistance, where were they in the field of the atom bomb, which
benefited certainly from an absolute priority?
The American government was
compelled to use two atom bombs to defeat the Japanese people, who gave so many
proofs of his fanatical dedication to his country and to his emperor. It has
been said that the american government had no other bomb ready to use. If that
is true, how much time would have been
necessary to produce others and make them operational? What would have been the
effect on cities already destroyed, on
indestructible factories and on a chief of state whose only obsession was to
spare time, in the point to sacrifice an army rather than to retreat?
What would have happened? Beautiful
subject of site for the one who would possess the exceptional necessary skills!
Maybe he exists in this bushy jungle that is Internet.
Please, forgive the
failures of the translator !