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| Mok-Kong Shen... |
 Posted: Tue Oct 27, 2009 4:31 am |
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Guest
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Hi,
A recent thread of moscherubin called attention to a classical
cipher by John F. Byrne, known as Chaocipher, which remains yet
unsolved to this day. From what is sofar known, it is quite certain
that this is based on the idea of sliding alphabets, conveniently
implementable e.g. with two concentric circular disks of slightly
different radiuses, the smaller one being freely rotatable above
the larger one. The plaintext and ciphertext alphabets are on the
boarders of the discs. On the larger disc there is another alphabet
on the circumference of a smaller radius. The smaller disc has an
aperture at the same radius such that one character (the 'key'
character) beneath can be seen, thus determining the relative
positions of the two discs, i.e. providing the amount of sliding
between the alphabets on the boarders of the two discs.
It seems interesting to examine how much complexity (complication
for the analyst) could be achieved through employing such a very
primitive mechanical device. Firstly it is clear that the two
alphabets on the boaders of the discs, for plaintext and ciphertext
respectively, should be two different random permutations of the
alphabetic characters. Secondly, the alphabet on the inner
circumference of the larger disc that provides the sliding amount
can also be a random permutation of the alphabetic characters
instead of being in the normal order, though one has then a
little bit inconvenience in searching for the needed character
when doing the encryption. Thirdly, the character that determines
the sliding amount can not only be based on 'autokey', i.e. either
the plaintext or the ciphertext charater that has been processed
immediately before, but can also be an encryption of the immediately
preceeding ciphertext character. That is, after determining C_i
from P_i one determines K_i by finding the character on the
ciphertext alphabet that is opposite to the character 'C_i' on the
plaintext alphabet (without any movement of the disks inbetween),
i.e. K_i results from double encryption of P_i. Fourthly, one
can have, instead of one pair of discs, a number of small and
large discs (with different random permutations on them, of
course) and thus a different combination of the discs can be used
on a particular occasion according to a 'key'. Fifthly, one can have
a number of pairs of discs (i.e. different combinations) operating
on the given stream of plaintext/chiphertext characters in round
robin fashion.
Such a device is evidently mechanically very simple. Disregarding
durability, it can also be made out of pieces of hard paper. If
the volume of materials being processed is (by nature) rather
limited, it seems that application of sliding alphabets probably
isn't too bad after all, if one happens not to have convenient
access to the certainly much much more secure modern encryption
methods. (Encryption of, for example, SMS messages this way
is definitely a better security than none, I would think.)
Thanks,
M. K. Shen |
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| Mok-Kong Shen... |
| Posted: Tue Oct 27, 2009 8:08 am |
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Guest
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Mok-Kong Shen wrote:
[snip]
[quote]........ ....................... That is, after determining C_i
from P_i one determines K_i by finding the character on the
ciphertext alphabet that is opposite to the character 'C_i' on the
plaintext alphabet (without any movement of the disks inbetween),
i.e. K_i results from double encryption of P_i. ...........
[/quote]
Sorry, typo. For K_i please read K_(i+1).
M. K. Shen |
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| Mok-Kong Shen... |
| Posted: Wed Oct 28, 2009 10:16 am |
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Guest
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Mok-Kong Shen wrote:
[snip]
[quote]It seems interesting to examine how much complexity (complication
for the analyst) could be achieved through employing such a very
primitive mechanical device. Firstly .....
[snip][/quote]
I like to add that one could even add some more 'complexity': The
alphabet on the inside of the large disk (i.e. the key alphabet
providing the sliding amount) can, instead of being directly located
on the large disc, be situated on a separate smaller disc and attached
(fixed onto) the large disc at a relative position (determined by
a certain 'key' character) at device setup time. Thus, suppose
one has 26 pieces each of the three types of discs (for plaintext-,
ciphertext-, and key-alphabet), all with arbitrary random permutations
of the alphabetic characters on them, the device setup can be
determined by a total of 5 characters to be given by the user, namely
one character each for choosing the three discs, one character for
positioning the key alphabet disc (just described) relative to the
large disc and finally one character K_(-1) that determines the
intitial position of the plaintext alphabet disc relative to the
ciphertext alphabet disc as the encryption process begins.
Thanks,
M. K. Shen |
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| Mok-Kong Shen... |
| Posted: Thu Oct 29, 2009 6:55 am |
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Guest
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Mok-Kong Shen wrote:
[snip]
[quote]It seems interesting to examine how much complexity (complication
for the analyst) could be achieved through employing such a very
primitive mechanical device. Firstly .......
[snip][/quote]
It may be mentioned that the device can be conveneintly used also
for digram substitution (analogous to playfair, see a recent thread
of mine: "Diagram substitution using a polyalphabetic substitution
table"), since sliding alphabet is in fact a special case of
polyalphabetic substitution. The "key" character used to determine
the sliding amount can be either "autokey", i.e. using one member
of the current plaintext or ciphertext character pair, or an encryption
of such a member using the current constellation of the plaintext
and ciphertext alphabet. Since digram substitution is generally
considered to be superior to single character substitution, the
feasibility of this mode of operation should be kept in mind in my
humble view.
Thanks,
M. K. Shen |
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| Mok-Kong Shen... |
| Posted: Sat Nov 07, 2009 9:29 am |
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Guest
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Mok-Kong Shen wrote:
[snip]
[quote]It seems interesting to examine how much complexity (complication
for the analyst) could be achieved through employing such a very
primitive mechanical device. ...........
[/quote]
[Addendum]
It goes without saying that algorithms that can be simply implemented
with mechanics can be even more conveniently implemented in software.
In communication the partner not having access to computer can use the
mechanical version, while the other can work with his computer, if he
has one.
Certainly it woold be downright folly to consider classical algorithms
such as sliding alphabets should ever substitute modern encryption
algorithms in usage, if the later ones are available. On the other hand,
it is well conceivable that there may be certain rare situations where
one has no access to modern security software and implementing one such
from scratch happens to be infeasible (lack of specification documents,
time, etc.) A hypothetical example would be when one is on travel
without carrying with oneself modern encryption software and some
sensitive data gathered en route need to be protected from the eyes of
mafias of all genre, including the omnipotent ones that practically
have all communications paths of the world permanently under their
control. In such cases the use of some comparatively good classical
algorithms, implemented either mechanically or very simply and quickly
on a computer would be clearly indicated and hopefully with some luck
one's secret informations wouldn't be solved even after decades of
effort of analysts like in the case of the Chaocipher (see the recent
thread of moscherubin).
Thanks,
M. K. Shen |
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